"""
Molecular integrals over Gaussian basis functions generated by sympleints.
See https://github.com/eljost/sympleints for more information.
sympleints version: 0.1.dev79+g63f1ef8.d20230515
symppy version: 1.10.1
sympleints was executed with the following arguments:
lmax = 3
lauxmax = 4
write = False
out_dir = devel_ints
keys = ['2c2e', '3c2e_sph']
sph = False
opt_basic = True
normalize = cgto
"""
import numpy
from pysisyphus.wavefunction.ints.boys import boys
[docs]
def int3c2e3d_sph_000(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ss|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 1, 1), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = cx + x0
# 1 item(s)
result[0, 0, 0] = numpy.sum(
34.98683665524972
* da
* db
* dc
* x1
* x2 ** (-0.5)
* boys(
0,
cx
* x0
* (
(-x1 * (ax * A[0] + bx * B[0]) + C[0]) ** 2
+ (-x1 * (ax * A[1] + bx * B[1]) + C[1]) ** 2
+ (-x1 * (ax * A[2] + bx * B[2]) + C[2]) ** 2
)
/ x2,
)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
/ cx
)
return result
[docs]
def int3c2e3d_sph_001(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ss|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 1, 3), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0]) + C[0]
x3 = cx + x0
x4 = -x1 * (ax * A[1] + bx * B[1]) + C[1]
x5 = -x1 * (ax * A[2] + bx * B[2]) + C[2]
x6 = (
34.98683665524972
* da
* db
* dc
* x3 ** (-1.5)
* boys(1, cx * x0 * (x2**2 + x4**2 + x5**2) / x3)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
/ cx
)
# 3 item(s)
result[0, 0, 0] = numpy.sum(-x2 * x6)
result[0, 0, 1] = numpy.sum(-x4 * x6)
result[0, 0, 2] = numpy.sum(-x5 * x6)
return result
[docs]
def int3c2e3d_sph_002(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ss|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 1, 6), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0]) + C[0]
x3 = x2**2
x4 = cx + x0
x5 = -x1 * (ax * A[1] + bx * B[1]) + C[1]
x6 = x5**2
x7 = -x1 * (ax * A[2] + bx * B[2]) + C[2]
x8 = x7**2
x9 = (
17.49341832762486
* da
* db
* dc
* x0
* x4 ** (-2.5)
* boys(2, cx * x0 * (x3 + x6 + x8) / x4)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
/ cx
)
x10 = 1.154700538379252 * x9
x11 = 2.0 * x2 * x9
# 6 item(s)
result[0, 0, 0] = numpy.sum(x10 * x3)
result[0, 0, 1] = numpy.sum(x11 * x5)
result[0, 0, 2] = numpy.sum(x11 * x7)
result[0, 0, 3] = numpy.sum(x10 * x6)
result[0, 0, 4] = numpy.sum(2.0 * x5 * x7 * x9)
result[0, 0, 5] = numpy.sum(x10 * x8)
return result
[docs]
def int3c2e3d_sph_003(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ss|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 1, 10), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = x1 * (ax * A[0] + bx * B[0]) - C[0]
x3 = cx + x0
x4 = x2**2
x5 = x1 * (ax * A[1] + bx * B[1]) - C[1]
x6 = x5**2
x7 = x1 * (ax * A[2] + bx * B[2]) - C[2]
x8 = x7**2
x9 = (
17.49341832762486
* da
* db
* dc
* x0**2
* x3 ** (-3.5)
* boys(3, cx * x0 * (x4 + x6 + x8) / x3)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
/ cx
)
x10 = 0.5163977794943223 * x9
x11 = x5 * x9
x12 = 1.154700538379252
x13 = x12 * x4
x14 = x7 * x9
x15 = x12 * x6
x16 = x2 * x9
x17 = x12 * x8
# 10 item(s)
result[0, 0, 0] = numpy.sum(x10 * x2**3)
result[0, 0, 1] = numpy.sum(x11 * x13)
result[0, 0, 2] = numpy.sum(x13 * x14)
result[0, 0, 3] = numpy.sum(x15 * x16)
result[0, 0, 4] = numpy.sum(2.0 * x11 * x2 * x7)
result[0, 0, 5] = numpy.sum(x16 * x17)
result[0, 0, 6] = numpy.sum(x10 * x5**3)
result[0, 0, 7] = numpy.sum(x14 * x15)
result[0, 0, 8] = numpy.sum(x11 * x17)
result[0, 0, 9] = numpy.sum(x10 * x7**3)
return result
[docs]
def int3c2e3d_sph_004(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ss|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 1, 15), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = x1 * (ax * A[0] + bx * B[0]) - C[0]
x3 = cx + x0
x4 = x2**2
x5 = x1 * (ax * A[1] + bx * B[1]) - C[1]
x6 = x5**2
x7 = x1 * (ax * A[2] + bx * B[2]) - C[2]
x8 = x7**2
x9 = (
17.49341832762486
* da
* db
* dc
* x0**3
* x3 ** (-4.5)
* boys(4, cx * x0 * (x4 + x6 + x8) / x3)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
/ cx
)
x10 = 0.1951800145897066 * x9
x11 = 0.5163977794943223 * x9
x12 = x11 * x2**3
x13 = 0.6666666666666667 * x9
x14 = x13 * x4
x15 = 1.732050807568877
x16 = x15 * x7
x17 = x5**3
x18 = x11 * x2
x19 = x13 * x6
x20 = x7**3
# 15 item(s)
result[0, 0, 0] = numpy.sum(x10 * x2**4)
result[0, 0, 1] = numpy.sum(x12 * x5)
result[0, 0, 2] = numpy.sum(x12 * x7)
result[0, 0, 3] = numpy.sum(x14 * x6)
result[0, 0, 4] = numpy.sum(x14 * x16 * x5)
result[0, 0, 5] = numpy.sum(x14 * x8)
result[0, 0, 6] = numpy.sum(x17 * x18)
result[0, 0, 7] = numpy.sum(x16 * x19 * x2)
result[0, 0, 8] = numpy.sum(x13 * x15 * x2 * x5 * x8)
result[0, 0, 9] = numpy.sum(x18 * x20)
result[0, 0, 10] = numpy.sum(x10 * x5**4)
result[0, 0, 11] = numpy.sum(x11 * x17 * x7)
result[0, 0, 12] = numpy.sum(x19 * x8)
result[0, 0, 13] = numpy.sum(x11 * x20 * x5)
result[0, 0, 14] = numpy.sum(x10 * x7**4)
return result
[docs]
def int3c2e3d_sph_010(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sp|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 3, 1), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = cx + x1
x3 = x2 ** (-1.0)
x4 = x1 ** (-1.0)
x5 = -x4 * (ax * A[0] + bx * B[0])
x6 = x5 + C[0]
x7 = -x4 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x4 * (ax * A[2] + bx * B[2])
x10 = x9 + C[2]
x11 = cx * x1 * x3 * (x10**2 + x6**2 + x8**2)
x12 = boys(0, x11) / cx
x13 = x3 * boys(1, x11)
x14 = A[1] - B[1]
x15 = A[2] - B[2]
x16 = (
34.98683665524972
* da
* db
* dc
* x2 ** (-0.5)
* x4
* numpy.exp(-ax * bx * x4 * (x0**2 + x14**2 + x15**2))
)
# 3 item(s)
result[0, 0, 0] = numpy.sum(x16 * (x0 * x12 - x12 * (x5 + A[0]) + x13 * x6))
result[0, 1, 0] = numpy.sum(x16 * (x12 * x14 - x12 * (x7 + A[1]) + x13 * x8))
result[0, 2, 0] = numpy.sum(x16 * (x10 * x13 + x12 * x15 - x12 * (x9 + A[2])))
return result
[docs]
def int3c2e3d_sph_011(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sp|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 3, 3), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = cx + x0
x5 = x4 ** (-1.0)
x6 = -x1 * (ax * A[1] + bx * B[1])
x7 = x6 + C[1]
x8 = -x1 * (ax * A[2] + bx * B[2])
x9 = x8 + C[2]
x10 = cx * x0 * x5 * (x3**2 + x7**2 + x9**2)
x11 = x5 * boys(2, x10)
x12 = cx ** (-1.0)
x13 = boys(1, x10)
x14 = x11 * x3 - x12 * x13 * (x2 + A[0])
x15 = 2.0 * x3
x16 = x12 * x13
x17 = x1 * x16
x18 = A[0] - B[0]
x19 = x16 * x18
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = (
17.49341832762486
* da
* db
* dc
* x4 ** (-1.5)
* numpy.exp(-ax * bx * x1 * (x18**2 + x20**2 + x21**2))
)
x23 = 2.0 * x7
x24 = -x22 * (x14 + x19)
x25 = 2.0 * x9
x26 = x16 * x20
x27 = x11 * x7 - x12 * x13 * (x6 + A[1])
x28 = -x22 * (x26 + x27)
x29 = x16 * x21
x30 = x11 * x9 - x12 * x13 * (x8 + A[2])
x31 = -x22 * (x29 + x30)
# 9 item(s)
result[0, 0, 0] = numpy.sum(x22 * (-x14 * x15 - x15 * x19 + x17))
result[0, 0, 1] = numpy.sum(x23 * x24)
result[0, 0, 2] = numpy.sum(x24 * x25)
result[0, 1, 0] = numpy.sum(x15 * x28)
result[0, 1, 1] = numpy.sum(x22 * (x17 - x23 * x26 - x23 * x27))
result[0, 1, 2] = numpy.sum(x25 * x28)
result[0, 2, 0] = numpy.sum(x15 * x31)
result[0, 2, 1] = numpy.sum(x23 * x31)
result[0, 2, 2] = numpy.sum(x22 * (x17 - x25 * x29 - x25 * x30))
return result
[docs]
def int3c2e3d_sph_012(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sp|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 3, 6), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = -x3
x5 = cx + x0
x6 = x5 ** (-1.0)
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x0 * x6
x14 = x13 * (x12**2 + x4**2 + x9**2)
x15 = boys(3, x14)
x16 = x15 * x6
x17 = cx ** (-1.0)
x18 = x17 * boys(2, x14)
x19 = -x18 * (x2 + A[0])
x20 = x3 * (x16 * x4 - x19)
x21 = x3**2
x22 = x8**2
x23 = x11**2
x24 = boys(2, x13 * (x21 + x22 + x23))
x25 = x17 * x24
x26 = x1 * x25
x27 = A[0] - B[0]
x28 = A[1] - B[1]
x29 = A[2] - B[2]
x30 = (
17.49341832762486
* da
* db
* dc
* x0
* x5 ** (-2.5)
* numpy.exp(-ax * bx * x1 * (x27**2 + x28**2 + x29**2))
)
x31 = x3 * x30
x32 = 1.154700538379252
x33 = x30 * (2.0 * x17 * x24 * x27 * x3 - 2.0 * x20 - x26)
x34 = x15 * x4 * x6 - x19 - x25 * x27
x35 = x30 * x32
x36 = x34 * x35
x37 = x11 * x30
x38 = 2.0 * x8
x39 = x25 * x28
x40 = -x18 * (x7 + A[1])
x41 = x15 * x6 * x9 - x39 - x40
x42 = x35 * x41
x43 = x8 * (x16 * x9 - x40)
x44 = x26 - 2.0 * x39 * x8 + 2.0 * x43
x45 = x30 * x8
x46 = x25 * x29
x47 = -x18 * (x10 + A[2])
x48 = x12 * x15 * x6 - x46 - x47
x49 = x35 * x48
x50 = x11 * (x12 * x16 - x47)
x51 = -2.0 * x11 * x46 + x26 + 2.0 * x50
# 18 item(s)
result[0, 0, 0] = numpy.sum(x31 * x32 * (x17 * x24 * x27 * x3 - x20 - x26))
result[0, 0, 1] = numpy.sum(x33 * x8)
result[0, 0, 2] = numpy.sum(x11 * x33)
result[0, 0, 3] = numpy.sum(-x22 * x36)
result[0, 0, 4] = numpy.sum(-x34 * x37 * x38)
result[0, 0, 5] = numpy.sum(-x23 * x36)
result[0, 1, 0] = numpy.sum(-x21 * x42)
result[0, 1, 1] = numpy.sum(-x31 * x44)
result[0, 1, 2] = numpy.sum(-2.0 * x11 * x31 * x41)
result[0, 1, 3] = numpy.sum(x32 * x45 * (x17 * x24 * x28 * x8 - x26 - x43))
result[0, 1, 4] = numpy.sum(-x37 * x44)
result[0, 1, 5] = numpy.sum(-x23 * x42)
result[0, 2, 0] = numpy.sum(-x21 * x49)
result[0, 2, 1] = numpy.sum(-x31 * x38 * x48)
result[0, 2, 2] = numpy.sum(-x31 * x51)
result[0, 2, 3] = numpy.sum(-x22 * x49)
result[0, 2, 4] = numpy.sum(-x45 * x51)
result[0, 2, 5] = numpy.sum(x32 * x37 * (x11 * x17 * x24 * x29 - x26 - x50))
return result
[docs]
def int3c2e3d_sph_013(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sp|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 3, 10), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = cx + x0
x5 = x4 ** (-1.5)
x6 = x3 * x5
x7 = x3**2
x8 = -x1 * (ax * A[1] + bx * B[1])
x9 = -x8 - C[1]
x10 = x9**2
x11 = -x1 * (ax * A[2] + bx * B[2])
x12 = -x11 - C[2]
x13 = x12**2
x14 = x0 / x4
x15 = cx * x14 * (x10 + x13 + x7)
x16 = 17.49341832762486
x17 = A[0] - B[0]
x18 = A[1] - B[1]
x19 = A[2] - B[2]
x20 = numpy.exp(-ax * bx * x1 * (x17**2 + x18**2 + x19**2))
x21 = 2.0 * x16 * x20
x22 = x1 * x21
x23 = x22 * boys(4, x15)
x24 = cx ** (-1.0)
x25 = x4 ** (-0.5)
x26 = boys(3, x15)
x27 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x2 + A[0]) - x23 * x6
x28 = x27 * x3
x29 = 0.5 / (ax + bx)
x30 = x24 * x26
x31 = x22 * x25 * x29 * x30
x32 = x14 * x3
x33 = x21 * x30
x34 = x29 * x33
x35 = x0 * x34 * x4 ** (-2.5)
x36 = x3**3
x37 = x0**2
x38 = x33 * x37 * x4 ** (-3.5)
x39 = x17 * x38
x40 = da * db * dc
x41 = 0.2581988897471611 * x40
x42 = x14 * x9
x43 = x34 * x5
x44 = x43 * x9
x45 = x3 * x9
x46 = x7 * x9
x47 = 0.5773502691896258 * x40
x48 = x12 * x14
x49 = x12 * x43
x50 = x12 * x35
x51 = x12 * x7
x52 = x37 / x4**2
x53 = x28 * x52
x54 = x10 * x35
x55 = x10 * x3
x56 = x52 * x9
x57 = x50 * x9
x58 = x12 * x45
x59 = x13 * x35
x60 = x13 * x3
x61 = x9**3
x62 = x0**3 / x4**3
x63 = x27 * x62
x64 = x10 * x12
x65 = x13 * x9
x66 = x12**3
x67 = x23 * x5
x68 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x8 + A[1]) - x67 * x9
x69 = x62 * x68
x70 = x18 * x38
x71 = x68 * x9
x72 = x31 + x71
x73 = x62 * x7
x74 = x42 * x72 + x44
x75 = x3 * x52
x76 = x48 * x71 + x49
x77 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x11 + A[2]) - x12 * x67
x78 = x62 * x77
x79 = x19 * x38
x80 = x12 * x77 + x31
x81 = x62 * x80
x82 = x48 * x80 + x49
# 30 item(s)
result[0, 0, 0] = numpy.sum(
x41 * (x14 * (x32 * (x32 * (x28 + x31) + x34 * x6) + x35 * x7) + x36 * x39)
)
result[0, 0, 1] = numpy.sum(
x47 * (x14 * (x32 * (x28 * x42 + x44) + x35 * x45) + x39 * x46)
)
result[0, 0, 2] = numpy.sum(
x47 * (x14 * (x3 * x50 + x32 * (x28 * x48 + x49)) + x39 * x51)
)
result[0, 0, 3] = numpy.sum(x47 * (x14 * (x10 * x53 + x54) + x39 * x55))
result[0, 0, 4] = numpy.sum(x40 * (x14 * (x12 * x28 * x56 + x57) + x39 * x58))
result[0, 0, 5] = numpy.sum(x47 * (x14 * (x13 * x53 + x59) + x39 * x60))
result[0, 0, 6] = numpy.sum(x41 * x61 * (x39 + x63))
result[0, 0, 7] = numpy.sum(x47 * x64 * (x39 + x63))
result[0, 0, 8] = numpy.sum(x47 * x65 * (x39 + x63))
result[0, 0, 9] = numpy.sum(x41 * x66 * (x39 + x63))
result[0, 1, 0] = numpy.sum(x36 * x41 * (x69 + x70))
result[0, 1, 1] = numpy.sum(x47 * (x46 * x70 + x72 * x73))
result[0, 1, 2] = numpy.sum(x47 * x51 * (x69 + x70))
result[0, 1, 3] = numpy.sum(x47 * (x55 * x70 + x74 * x75))
result[0, 1, 4] = numpy.sum(x40 * (x58 * x70 + x75 * x76))
result[0, 1, 5] = numpy.sum(x47 * x60 * (x69 + x70))
result[0, 1, 6] = numpy.sum(x41 * (x14 * (x42 * x74 + x54) + x61 * x70))
result[0, 1, 7] = numpy.sum(x47 * (x14 * (x42 * x76 + x57) + x64 * x70))
result[0, 1, 8] = numpy.sum(x47 * (x14 * (x13 * x52 * x71 + x59) + x65 * x70))
result[0, 1, 9] = numpy.sum(x41 * x66 * (x69 + x70))
result[0, 2, 0] = numpy.sum(x36 * x41 * (x78 + x79))
result[0, 2, 1] = numpy.sum(x47 * (x46 * x79 + x73 * x77 * x9))
result[0, 2, 2] = numpy.sum(x47 * (x51 * x79 + x73 * x80))
result[0, 2, 3] = numpy.sum(x47 * x55 * (x78 + x79))
result[0, 2, 4] = numpy.sum(x40 * (x45 * x81 + x58 * x79))
result[0, 2, 5] = numpy.sum(x47 * (x60 * x79 + x75 * x82))
result[0, 2, 6] = numpy.sum(x41 * x61 * (x78 + x79))
result[0, 2, 7] = numpy.sum(x47 * (x10 * x81 + x64 * x79))
result[0, 2, 8] = numpy.sum(x47 * (x56 * x82 + x65 * x79))
result[0, 2, 9] = numpy.sum(x41 * (x14 * (x48 * x82 + x59) + x66 * x79))
return result
[docs]
def int3c2e3d_sph_014(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sp|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 3, 15), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = cx + x0
x5 = x4 ** (-1.5)
x6 = x3 * x5
x7 = x3**2
x8 = -x1 * (ax * A[1] + bx * B[1])
x9 = -x8 - C[1]
x10 = x9**2
x11 = -x1 * (ax * A[2] + bx * B[2])
x12 = -x11 - C[2]
x13 = x12**2
x14 = x0 / x4
x15 = cx * x14 * (x10 + x13 + x7)
x16 = 17.49341832762486
x17 = A[0] - B[0]
x18 = A[1] - B[1]
x19 = A[2] - B[2]
x20 = numpy.exp(-ax * bx * x1 * (x17**2 + x18**2 + x19**2))
x21 = 2.0 * x16 * x20
x22 = x1 * x21
x23 = x22 * boys(5, x15)
x24 = cx ** (-1.0)
x25 = x4 ** (-0.5)
x26 = boys(4, x15)
x27 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x2 + A[0]) - x23 * x6
x28 = x27 * x3
x29 = 0.5 / (ax + bx)
x30 = x24 * x26
x31 = x22 * x25 * x29 * x30
x32 = x14 * x3
x33 = x21 * x30
x34 = x29 * x33
x35 = x34 * x7
x36 = x0 * x4 ** (-2.5)
x37 = x3**3
x38 = x0**2
x39 = x38 * x4 ** (-3.5)
x40 = x34 * x39
x41 = x3**4
x42 = x0**3
x43 = x33 * x4 ** (-4.5) * x42
x44 = x17 * x43
x45 = da * db * dc
x46 = 0.09759000729485332 * x45
x47 = x14 * x9
x48 = x34 * x5
x49 = x48 * x9
x50 = x3 * x9
x51 = x34 * x36
x52 = x7 * x9
x53 = x37 * x9
x54 = 0.2581988897471611 * x45
x55 = x12 * x14
x56 = x12 * x48
x57 = x12 * x51
x58 = x12 * x37
x59 = x38 / x4**2
x60 = x28 * x59
x61 = x10 * x51
x62 = x10 * x3
x63 = x10 * x7
x64 = 0.3333333333333333 * x45
x65 = x59 * x9
x66 = x57 * x9
x67 = x12 * x44
x68 = 1.732050807568877 * x64
x69 = x13 * x51
x70 = x13 * x7
x71 = x9**3
x72 = x42 / x4**3
x73 = x28 * x72
x74 = x40 * x71
x75 = x3 * x71
x76 = x10 * x12
x77 = x40 * x76
x78 = x13 * x9
x79 = x40 * x78
x80 = x13 * x50
x81 = x12**3
x82 = x40 * x81
x83 = x3 * x81
x84 = x9**4
x85 = x0**4 / x4**4
x86 = x27 * x85
x87 = x12 * x71
x88 = x10 * x13
x89 = x81 * x9
x90 = x12**4
x91 = x23 * x5
x92 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x8 + A[1]) - x9 * x91
x93 = x85 * x92
x94 = x18 * x43
x95 = x9 * x92
x96 = x31 + x95
x97 = x37 * x85
x98 = x47 * x96 + x49
x99 = x7 * x72
x100 = x55 * x95 + x56
x101 = x12 * x94
x102 = x47 * x98 + x61
x103 = x3 * x59
x104 = x100 * x47 + x66
x105 = x13 * x59 * x95 + x69
x106 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x11 + A[2]) - x12 * x91
x107 = x106 * x85
x108 = x19 * x43
x109 = x106 * x12 + x31
x110 = x109 * x85
x111 = x108 * x12
x112 = x109 * x55 + x56
x113 = x112 * x72
x114 = x112 * x55 + x69
# 45 item(s)
result[0, 0, 0] = numpy.sum(
x46
* (
x14 * (x32 * (x32 * (x32 * (x28 + x31) + x34 * x6) + x35 * x36) + x37 * x40)
+ x41 * x44
)
)
result[0, 0, 1] = numpy.sum(
x54
* (x14 * (x32 * (x32 * (x28 * x47 + x49) + x50 * x51) + x40 * x52) + x44 * x53)
)
result[0, 0, 2] = numpy.sum(
x54
* (
x14 * (x12 * x35 * x39 + x32 * (x3 * x57 + x32 * (x28 * x55 + x56)))
+ x44 * x58
)
)
result[0, 0, 3] = numpy.sum(
x64 * (x14 * (x32 * (x10 * x60 + x61) + x40 * x62) + x44 * x63)
)
result[0, 0, 4] = numpy.sum(
x68 * (x14 * (x12 * x40 * x50 + x32 * (x12 * x28 * x65 + x66)) + x52 * x67)
)
result[0, 0, 5] = numpy.sum(
x64 * (x14 * (x13 * x3 * x40 + x32 * (x13 * x60 + x69)) + x44 * x70)
)
result[0, 0, 6] = numpy.sum(x54 * (x14 * (x71 * x73 + x74) + x44 * x75))
result[0, 0, 7] = numpy.sum(x68 * (x14 * (x73 * x76 + x77) + x62 * x67))
result[0, 0, 8] = numpy.sum(x68 * (x14 * (x73 * x78 + x79) + x44 * x80))
result[0, 0, 9] = numpy.sum(x54 * (x14 * (x73 * x81 + x82) + x44 * x83))
result[0, 0, 10] = numpy.sum(x46 * x84 * (x44 + x86))
result[0, 0, 11] = numpy.sum(x54 * x87 * (x44 + x86))
result[0, 0, 12] = numpy.sum(x64 * x88 * (x44 + x86))
result[0, 0, 13] = numpy.sum(x54 * x89 * (x44 + x86))
result[0, 0, 14] = numpy.sum(x46 * x90 * (x44 + x86))
result[0, 1, 0] = numpy.sum(x41 * x46 * (x93 + x94))
result[0, 1, 1] = numpy.sum(x54 * (x53 * x94 + x96 * x97))
result[0, 1, 2] = numpy.sum(x54 * x58 * (x93 + x94))
result[0, 1, 3] = numpy.sum(x64 * (x63 * x94 + x98 * x99))
result[0, 1, 4] = numpy.sum(x68 * (x100 * x99 + x101 * x52))
result[0, 1, 5] = numpy.sum(x64 * x70 * (x93 + x94))
result[0, 1, 6] = numpy.sum(x54 * (x102 * x103 + x75 * x94))
result[0, 1, 7] = numpy.sum(x68 * (x101 * x62 + x103 * x104))
result[0, 1, 8] = numpy.sum(x68 * (x103 * x105 + x80 * x94))
result[0, 1, 9] = numpy.sum(x54 * x83 * (x93 + x94))
result[0, 1, 10] = numpy.sum(x46 * (x14 * (x102 * x47 + x74) + x84 * x94))
result[0, 1, 11] = numpy.sum(x54 * (x14 * (x104 * x47 + x77) + x87 * x94))
result[0, 1, 12] = numpy.sum(x64 * (x14 * (x105 * x47 + x79) + x88 * x94))
result[0, 1, 13] = numpy.sum(x54 * (x14 * (x72 * x81 * x95 + x82) + x89 * x94))
result[0, 1, 14] = numpy.sum(x46 * x90 * (x93 + x94))
result[0, 2, 0] = numpy.sum(x41 * x46 * (x107 + x108))
result[0, 2, 1] = numpy.sum(x54 * (x106 * x9 * x97 + x108 * x53))
result[0, 2, 2] = numpy.sum(x54 * (x108 * x58 + x109 * x97))
result[0, 2, 3] = numpy.sum(x63 * x64 * (x107 + x108))
result[0, 2, 4] = numpy.sum(x52 * x68 * (x110 + x111))
result[0, 2, 5] = numpy.sum(x64 * (x108 * x70 + x112 * x99))
result[0, 2, 6] = numpy.sum(x54 * x75 * (x107 + x108))
result[0, 2, 7] = numpy.sum(x62 * x68 * (x110 + x111))
result[0, 2, 8] = numpy.sum(x68 * (x108 * x80 + x113 * x50))
result[0, 2, 9] = numpy.sum(x54 * (x103 * x114 + x108 * x83))
result[0, 2, 10] = numpy.sum(x46 * x84 * (x107 + x108))
result[0, 2, 11] = numpy.sum(x54 * (x108 * x87 + x110 * x71))
result[0, 2, 12] = numpy.sum(x64 * (x10 * x113 + x108 * x88))
result[0, 2, 13] = numpy.sum(x54 * (x108 * x89 + x114 * x65))
result[0, 2, 14] = numpy.sum(x46 * (x108 * x90 + x14 * (x114 * x55 + x82)))
return result
[docs]
def int3c2e3d_sph_020(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sd|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 6, 1), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = cx + x0
x3 = x2 ** (-1.0)
x4 = -x1 * (ax * A[0] + bx * B[0])
x5 = x4 + C[0]
x6 = -x5
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x3
x14 = x0 * x13
x15 = x14 * (x12**2 + x6**2 + x9**2)
x16 = boys(1, x15)
x17 = x16 * x3
x18 = cx ** (-1.0)
x19 = x18 * boys(0, x15)
x20 = x1 * (x17 - x19)
x21 = A[0] - B[0]
x22 = x14 * (x11**2 + x5**2 + x8**2)
x23 = x18 * boys(0, x22)
x24 = x3 * boys(1, x22)
x25 = x4 + A[0]
x26 = 2.0 * x21
x27 = -x25
x28 = x17 * x6 - x19 * x27
x29 = x3 * boys(2, x15)
x30 = x16 * x18
x31 = x13 * x5
x32 = A[1] - B[1]
x33 = A[2] - B[2]
x34 = (
17.49341832762486
* da
* db
* dc
* x1
* x2 ** (-0.5)
* numpy.exp(-ax * bx * x1 * (x21**2 + x32**2 + x33**2))
)
x35 = 0.5773502691896258 * x34
x36 = x7 + A[1]
x37 = x23 * x32 - x23 * x36 + x24 * x8
x38 = -x36
x39 = x17 * x9 - x19 * x38
x40 = x29 * x9 - x30 * x38
x41 = 2.0 * x34
x42 = x10 + A[2]
x43 = x11 * x24 + x23 * x33 - x23 * x42
x44 = -x42
x45 = x12 * x17 - x19 * x44
x46 = x12 * x29 - x30 * x44
x47 = 2.0 * x32
x48 = x13 * x8
x49 = 2.0 * x33
# 6 item(s)
result[0, 0, 0] = numpy.sum(
x35
* (
-x20
+ 2.0 * x25 * x28
- x26 * x28
+ x26 * (x21 * x23 - x23 * x25 + x24 * x5)
+ 2.0 * x31 * (x27 * x30 - x29 * x6)
)
)
result[0, 1, 0] = numpy.sum(x41 * (x21 * x37 + x25 * x39 - x28 * x32 - x31 * x40))
result[0, 2, 0] = numpy.sum(x41 * (x21 * x43 + x25 * x45 - x28 * x33 - x31 * x46))
result[0, 3, 0] = numpy.sum(
x35 * (-x20 + 2.0 * x36 * x39 + x37 * x47 - x39 * x47 - 2.0 * x40 * x48)
)
result[0, 4, 0] = numpy.sum(x41 * (x32 * x43 - x33 * x39 + x36 * x45 - x46 * x48))
result[0, 5, 0] = numpy.sum(
x35 * (-2.0 * x11 * x13 * x46 - x20 + 2.0 * x42 * x45 + x43 * x49 - x45 * x49)
)
return result
[docs]
def int3c2e3d_sph_021(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sd|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 6, 3), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = x3 + C[0]
x5 = cx + x1
x6 = x5 ** (-1.0)
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x2 * (ax * A[2] + bx * B[2])
x10 = x9 + C[2]
x11 = cx * x6
x12 = x1 * x11
x13 = x12 * (x10**2 + x4**2 + x8**2)
x14 = x6 * boys(2, x13)
x15 = cx ** (-1.0)
x16 = x3 + A[0]
x17 = boys(1, x13)
x18 = x14 * x4 - x15 * x16 * x17
x19 = -x18
x20 = 2.0 * x19
x21 = x15 * x17
x22 = x2 * x21
x23 = x20 * x4 + x22
x24 = x0 * x21
x25 = 2.0 * x4
x26 = -x4
x27 = -x8
x28 = -x10
x29 = x12 * (x26**2 + x27**2 + x28**2)
x30 = boys(2, x29)
x31 = x30 * x6
x32 = x15 * boys(1, x29)
x33 = x2 * (x31 - x32)
x34 = -x16
x35 = 2.0 * x26 * x31 - 2.0 * x32 * x34
x36 = x6 * boys(3, x29)
x37 = x15 * x30
x38 = x11 * x4
x39 = -x16 * x35 + x33 + 2.0 * x38 * (x26 * x36 - x34 * x37)
x40 = A[1] - B[1]
x41 = A[2] - B[2]
x42 = (
17.49341832762486
* da
* db
* dc
* x5 ** (-1.5)
* numpy.exp(-ax * bx * x2 * (x0**2 + x40**2 + x41**2))
)
x43 = 0.5773502691896258 * x42
x44 = x43 * (x0 * x20 - 2.0 * x0 * (x18 + x24) + x39)
x45 = x7 + A[1]
x46 = x14 * x8 - x15 * x17 * x45
x47 = -x46
x48 = -x2 * x47
x49 = -x45
x50 = x27 * x31 - x32 * x49
x51 = x27 * x36 - x37 * x49
x52 = -x16 * x50 + x38 * x51
x53 = 2.0 * x52
x54 = x21 * x40
x55 = -x46 - x54
x56 = x0 * x55
x57 = 2.0 * x8
x58 = 2.0 * x47
x59 = x22 + x58 * x8
x60 = -x54 * x57 + x59
x61 = -x19 * x2
x62 = x19 * x40
x63 = 2.0 * x10
x64 = x9 + A[2]
x65 = x10 * x14 - x15 * x17 * x64
x66 = -x65
x67 = -x2 * x66
x68 = -x64
x69 = x28 * x31 - x32 * x68
x70 = x28 * x36 - x37 * x68
x71 = -x16 * x69 + x38 * x70
x72 = 2.0 * x71
x73 = x21 * x41
x74 = -x65 - x73
x75 = x0 * x74
x76 = x19 * x41
x77 = x22 + x63 * x66
x78 = -x63 * x73 + x77
x79 = 2.0 * x50
x80 = x11 * x51 * x57 + x33 - x45 * x79
x81 = x43 * (2.0 * x40 * x55 + x40 * x58 + x80)
x82 = x40 * x74
x83 = x41 * x47
x84 = x11 * x70
x85 = -x45 * x69 + x8 * x84
x86 = 2.0 * x41
x87 = 2.0 * x69
x88 = x33 + x63 * x84 - x64 * x87
x89 = x43 * (x66 * x86 + x74 * x86 + x88)
# 18 item(s)
result[0, 0, 0] = numpy.sum(
x43 * (x0 * x23 + x0 * (x23 - x24 * x25) - x2 * x35 + x39 * x4)
)
result[0, 0, 1] = numpy.sum(x44 * x8)
result[0, 0, 2] = numpy.sum(x10 * x44)
result[0, 1, 0] = numpy.sum(x42 * (x23 * x40 + x25 * x56 + x4 * x53 + x48))
result[0, 1, 1] = numpy.sum(x42 * (x0 * x60 + x53 * x8 + x57 * x62 + x61))
result[0, 1, 2] = numpy.sum(x42 * x63 * (x52 + x56 + x62))
result[0, 2, 0] = numpy.sum(x42 * (x23 * x41 + x25 * x75 + x4 * x72 + x67))
result[0, 2, 1] = numpy.sum(x42 * x57 * (x71 + x75 + x76))
result[0, 2, 2] = numpy.sum(x42 * (x0 * x78 + x10 * x72 + x61 + x63 * x76))
result[0, 3, 0] = numpy.sum(x4 * x81)
result[0, 3, 1] = numpy.sum(x43 * (-x2 * x79 + x40 * x59 + x40 * x60 + x8 * x80))
result[0, 3, 2] = numpy.sum(x10 * x81)
result[0, 4, 0] = numpy.sum(x25 * x42 * (x82 + x83 + x85))
result[0, 4, 1] = numpy.sum(x42 * (x41 * x59 + x57 * x82 + x57 * x85 + x67))
result[0, 4, 2] = numpy.sum(x42 * (x40 * x78 + x48 + x63 * x83 + x63 * x85))
result[0, 5, 0] = numpy.sum(x4 * x89)
result[0, 5, 1] = numpy.sum(x8 * x89)
result[0, 5, 2] = numpy.sum(x43 * (x10 * x88 - x2 * x87 + x41 * x77 + x41 * x78))
return result
[docs]
def int3c2e3d_sph_022(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sd|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 6, 6), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = -x3
x5 = cx + x0
x6 = x5 ** (-1.0)
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x6
x14 = x0 * x13
x15 = x14 * (x12**2 + x4**2 + x9**2)
x16 = boys(3, x15)
x17 = x16 * x6
x18 = x2 + A[0]
x19 = -x18
x20 = cx ** (-1.0)
x21 = x20 * boys(2, x15)
x22 = x19 * x21
x23 = x17 * x4 - x22
x24 = x23 * x3
x25 = x3**2
x26 = x8**2
x27 = x11**2
x28 = x14 * (x25 + x26 + x27)
x29 = boys(2, x28)
x30 = x20 * x29
x31 = x1 * x30
x32 = 2.0 * x24 + x31
x33 = x1 * (x17 - x21)
x34 = x6 * boys(4, x15)
x35 = -2.0 * x13 * x3 * (x16 * x19 * x20 - x34 * x4) - 2.0 * x18 * x23 + x33
x36 = x1 * x23
x37 = x24 + x31
x38 = A[0] - B[0]
x39 = 2.0 * x38
x40 = x3 * x39
x41 = A[1] - B[1]
x42 = A[2] - B[2]
x43 = (
17.49341832762486
* da
* db
* dc
* x0
* x5 ** (-2.5)
* numpy.exp(-ax * bx * x1 * (x38**2 + x41**2 + x42**2))
)
x44 = 0.3333333333333333 * x43
x45 = x6 * boys(3, x28)
x46 = x18 * x20 * x29 - x3 * x45
x47 = 1.732050807568877
x48 = x44 * x47
x49 = x48 * (
2.0 * x1 * x46 - x3 * x35 - x32 * x38 + x38 * (2.0 * x20 * x29 * x3 * x38 - x32)
)
x50 = 2.0 * x46
x51 = x44 * (x35 + x38 * x50 - x39 * (-x16 * x4 * x6 + x22 + x30 * x38))
x52 = x11 * x47
x53 = x17 * x9
x54 = x7 + A[1]
x55 = -x54
x56 = x21 * x55
x57 = x53 - x56
x58 = -x16 * x20 * x55 + x34 * x9
x59 = x13 * x4
x60 = x19 * x57 - x58 * x59
x61 = x3 * x60
x62 = x1 * x57
x63 = -x62
x64 = x30 * x41
x65 = -x53 + x56 + x64
x66 = -x65
x67 = x3 * x38
x68 = x3 * x43
x69 = 0.6666666666666667 * x47
x70 = x68 * x69
x71 = -x36
x72 = x60 * x8
x73 = 2.0 * x72
x74 = x57 * x8
x75 = x31 + 2.0 * x74
x76 = x1 * x75
x77 = -2.0 * x64 * x8 + x75
x78 = x32 * x41
x79 = x11 * x43
x80 = x31 + x74
x81 = x20 * x29 * x41 * x8 - x80
x82 = x41 * x8
x83 = x43 * x8
x84 = x69 * x83
x85 = -x77
x86 = x43 * x69
x87 = x12 * x17
x88 = x10 + A[2]
x89 = -x88
x90 = x21 * x89
x91 = x87 - x90
x92 = -x91
x93 = x12 * x34 - x16 * x20 * x89
x94 = -x93
x95 = -x19 * x92 + x59 * x94
x96 = x3 * x95
x97 = x1 * x91
x98 = -x97
x99 = x30 * x42
x100 = -x87 + x90 + x99
x101 = -x100
x102 = x32 * x42
x103 = x11 * x95
x104 = x11 * x91
x105 = 2.0 * x104 + x31
x106 = x1 * x105
x107 = -0.5 * x106
x108 = 2.0 * x11
x109 = x105 - x108 * x99
x110 = -x109
x111 = x104 + x31
x112 = x11 * x20 * x29 * x42 - x111
x113 = x11 * x42
x114 = x69 * x79
x115 = x20 * x29 * x54 - x45 * x8
x116 = 2.0 * x41
x117 = 2.0 * x8
x118 = x117 * x13 * x58 + x33 - 2.0 * x54 * x57
x119 = x44 * (x115 * x116 + x116 * x66 + x118)
x120 = x41 * x85
x121 = x41 * x75
x122 = -x118 * x8 + 2.0 * x62
x123 = x3 * x48
x124 = 2.0 * x82
x125 = x100 * x41
x126 = x13 * x9 * x94 - x55 * x92
x127 = x11 * x126
x128 = 2.0 * x42
x129 = x108 * x13 * x93 + x33 - 2.0 * x88 * x91
x130 = x44 * (x101 * x128 - x128 * (x11 * x45 - x20 * x29 * x88) + x129)
x131 = -x11 * x129 + 2.0 * x97
x132 = x105 * x42 - x110 * x42 - x131
x133 = 2.0 * x113
# 36 item(s)
result[0, 0, 0] = numpy.sum(
x44
* (
x1 * x32
- x3 * (x3 * x35 - 2.0 * x36)
- x37 * x40
+ x40 * (x20 * x29 * x3 * x38 - x37)
)
)
result[0, 0, 1] = numpy.sum(x49 * x8)
result[0, 0, 2] = numpy.sum(x11 * x49)
result[0, 0, 3] = numpy.sum(-x26 * x51)
result[0, 0, 4] = numpy.sum(-x51 * x52 * x8)
result[0, 0, 5] = numpy.sum(-x27 * x51)
result[0, 1, 0] = numpy.sum(-x70 * (x37 * x41 + x61 + x63 + x66 * x67))
result[0, 1, 1] = numpy.sum(
-0.5 * x43 * (2.0 * x3 * (x71 + x73) + 2.0 * x67 * x77 - x76 + 2.0 * x78 * x8)
)
result[0, 1, 2] = numpy.sum(-x79 * (x40 * x66 + 2.0 * x61 + x63 + x78))
result[0, 1, 3] = numpy.sum(x84 * (x36 + x38 * x81 - x46 * x82 - x72))
result[0, 1, 4] = numpy.sum(x79 * (x36 + x38 * x85 - x50 * x82 - x73))
result[0, 1, 5] = numpy.sum(x27 * x86 * (-x23 * x41 + x38 * x65 - x60))
result[0, 2, 0] = numpy.sum(-x70 * (x101 * x67 + x37 * x42 + x96 + x98))
result[0, 2, 1] = numpy.sum(-x83 * (x101 * x40 + x102 + 2.0 * x96 + x98))
result[0, 2, 2] = numpy.sum(
-x43 * (x102 * x11 + x107 + x109 * x67 + x3 * (2.0 * x103 + x71))
)
result[0, 2, 3] = numpy.sum(x26 * x86 * (x100 * x38 - x23 * x42 - x95))
result[0, 2, 4] = numpy.sum(
x83 * (-2.0 * x11 * x23 * x42 - 2.0 * x11 * x95 + x110 * x38 + x36)
)
result[0, 2, 5] = numpy.sum(x114 * (-x103 + x112 * x38 - x113 * x46 + x36))
result[0, 3, 0] = numpy.sum(-x119 * x25)
result[0, 3, 1] = numpy.sum(x123 * (x120 - x121 + x122))
result[0, 3, 2] = numpy.sum(-x119 * x3 * x52)
result[0, 3, 3] = numpy.sum(x44 * (x122 * x8 - x124 * x80 + x124 * x81 + x76))
result[0, 3, 4] = numpy.sum(x11 * x48 * (2.0 * x1 * x115 - x118 * x8 + x120 - x121))
result[0, 3, 5] = numpy.sum(-x119 * x27)
result[0, 4, 0] = numpy.sum(x25 * x86 * (x125 - x126 - x42 * x57))
result[0, 4, 1] = numpy.sum(x68 * (x117 * x125 - 2.0 * x126 * x8 - x42 * x75 + x97))
result[0, 4, 2] = numpy.sum(
x68 * (-2.0 * x11 * x126 - 2.0 * x11 * x42 * x57 + x110 * x41 + x62)
)
result[0, 4, 3] = numpy.sum(-x84 * (x101 * x82 + x126 * x8 + x42 * x80 + x98))
result[0, 4, 4] = numpy.sum(
-x43 * (x107 + x109 * x82 + x11 * x42 * x75 + x8 * (2.0 * x127 + x63))
)
result[0, 4, 5] = numpy.sum(x114 * (x112 * x41 - x113 * x115 - x127 + x62))
result[0, 5, 0] = numpy.sum(-x130 * x25)
result[0, 5, 1] = numpy.sum(-x130 * x3 * x47 * x8)
result[0, 5, 2] = numpy.sum(-x123 * x132)
result[0, 5, 3] = numpy.sum(-x130 * x26)
result[0, 5, 4] = numpy.sum(-x132 * x48 * x8)
result[0, 5, 5] = numpy.sum(x44 * (x106 + x11 * x131 - x111 * x133 + x112 * x133))
return result
[docs]
def int3c2e3d_sph_023(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sd|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 6, 10), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = x4**2
x6 = -x2 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = x7**2
x9 = -x2 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = x10**2
x12 = cx + x1
x13 = x12 ** (-1.0)
x14 = x1 * x13
x15 = cx * x14 * (x11 + x5 + x8)
x16 = boys(4, x15)
x17 = x12 ** (-1.5)
x18 = 17.49341832762486
x19 = A[1] - B[1]
x20 = A[2] - B[2]
x21 = numpy.exp(-ax * bx * x2 * (x0**2 + x19**2 + x20**2))
x22 = 2.0 * x18 * x21
x23 = x2 * x22
x24 = x17 * x23
x25 = x16 * x24
x26 = cx ** (-1.0)
x27 = x12 ** (-0.5)
x28 = -x3 - A[0]
x29 = boys(3, x15)
x30 = 2.0 * x18 * x2 * x21 * x26 * x27 * x28 * x29 - x25 * x4
x31 = x30 * x4
x32 = 0.5 / (ax + bx)
x33 = x26 * x29
x34 = x23 * x27 * x32 * x33
x35 = x31 + x34
x36 = x14 * x4
x37 = x22 * x33
x38 = x32 * x37
x39 = x17 * x38
x40 = x35 * x36 + x39 * x4
x41 = x1 * x12 ** (-2.5) * x38
x42 = x14 * (x36 * x40 + x41 * x5)
x43 = x4**3
x44 = x1**2
x45 = x12 ** (-3.5) * x37 * x44
x46 = x0 * x45
x47 = x32 * (2.0 * x18 * x2 * x21 * x26 * x27 * x29 - x25)
x48 = x24 * boys(5, x15)
x49 = cx * x13
x50 = x4 * x49
x51 = (
x28 * x30 + x47 - x50 * (2.0 * x16 * x18 * x2 * x21 * x26 * x27 * x28 - x4 * x48)
)
x52 = x4 * x51
x53 = x30 * x32
x54 = 2.0 * x53
x55 = x14 * x32
x56 = 2.0 * x55
x57 = da * db * dc
x58 = 0.06666666666666667 * x57
x59 = 2.23606797749979 * x58
x60 = x14 * x7
x61 = x39 * x7
x62 = x31 * x60 + x61
x63 = x4 * x7
x64 = x14 * (x36 * x62 + x41 * x63)
x65 = x46 * x5
x66 = 0.3333333333333333 * x57
x67 = x10 * x14
x68 = x10 * x39
x69 = x31 * x67 + x68
x70 = x10 * x41
x71 = x14 * (x36 * x69 + x4 * x70)
x72 = x44 / x12**2
x73 = x72 * x8
x74 = x41 * x8
x75 = x14 * (x31 * x73 + x74)
x76 = x4 * x46
x77 = x7 * x72
x78 = x10 * x77
x79 = x7 * x70
x80 = x14 * (x31 * x78 + x79)
x81 = x10 * x63
x82 = 1.732050807568877 * x66
x83 = x11 * x72
x84 = x11 * x41
x85 = x14 * (x31 * x83 + x84)
x86 = x7**3
x87 = x1**3 / x12**3
x88 = x86 * x87
x89 = x30 * x88
x90 = x8 * x87
x91 = x10 * x90
x92 = x30 * x91
x93 = x10 * x8
x94 = x11 * x87
x95 = x7 * x94
x96 = x30 * x95
x97 = x11 * x7
x98 = x10**3
x99 = x87 * x98
x100 = x30 * x99
x101 = -x6 - A[1]
x102 = 2.0 * x101 * x18 * x2 * x21 * x26 * x27 * x29 - x25 * x7
x103 = x43 * x87
x104 = x102 * x103
x105 = x19 * x45
x106 = x104 + x105 * x43
x107 = x102 * x32
x108 = 2.0 * x101 * x16 * x18 * x2 * x21 * x26 * x27 - x48 * x7
x109 = x102 * x28 - x108 * x50
x110 = x109 * x4
x111 = x5 * x72
x112 = 3.872983346207417 * x58
x113 = x102 * x7
x114 = x113 + x34
x115 = x5 * x87
x116 = x114 * x115
x117 = x105 * x5
x118 = x116 + x117 * x7
x119 = x114 * x14
x120 = x119 * x32
x121 = x109 * x7
x122 = x121 + x53
x123 = x4 * x72
x124 = x123 * x32
x125 = x10 * x115
x126 = x102 * x125
x127 = x10 * x117 + x126
x128 = x107 * x67
x129 = x119 * x7 + x61
x130 = x123 * x129
x131 = x105 * x4
x132 = x130 + x131 * x8
x133 = x129 * x55
x134 = x60 * (x122 + x53)
x135 = x113 * x67 + x68
x136 = x123 * x135
x137 = x105 * x81 + x136
x138 = x135 * x55
x139 = x53 * x67
x140 = x121 * x67 + x139
x141 = x4 * x94
x142 = x102 * x141
x143 = x11 * x131 + x142
x144 = x107 * x83
x145 = x14 * (x129 * x60 + x74)
x146 = x105 * x86 + x145
x147 = x14 * (x135 * x60 + x79)
x148 = x105 * x93 + x147
x149 = x14 * (x113 * x83 + x84)
x150 = x105 * x97 + x149
x151 = x53 * x83
x152 = x102 * x99
x153 = x105 * x98 + x152
x154 = -x9 - A[2]
x155 = -x10 * x25 + 2.0 * x154 * x18 * x2 * x21 * x26 * x27 * x29
x156 = x103 * x155
x157 = x20 * x45
x158 = x156 + x157 * x43
x159 = x155 * x32
x160 = -x10 * x48 + 2.0 * x154 * x16 * x18 * x2 * x21 * x26 * x27
x161 = x155 * x28 - x160 * x50
x162 = x161 * x4
x163 = x115 * x7
x164 = x155 * x163
x165 = x157 * x5
x166 = x164 + x165 * x7
x167 = x159 * x60
x168 = x123 * x7
x169 = x10 * x155 + x34
x170 = x115 * x169
x171 = x10 * x165 + x170
x172 = x169 * x55
x173 = x10 * x161 + x53
x174 = x4 * x90
x175 = x155 * x174
x176 = x157 * x4
x177 = x175 + x176 * x8
x178 = x159 * x73
x179 = x63 * x87
x180 = x169 * x179
x181 = x157 * x81 + x180
x182 = x169 * x32 * x77
x183 = x169 * x67 + x68
x184 = x123 * x183
x185 = x11 * x176 + x184
x186 = x183 * x55
x187 = x139 + x173 * x67
x188 = x155 * x88
x189 = x157 * x86 + x188
x190 = x169 * x90
x191 = x157 * x93 + x190
x192 = x183 * x77
x193 = x157 * x97 + x192
x194 = x14 * (x183 * x67 + x84)
x195 = x157 * x98 + x194
x196 = x49 * x7
x197 = x101 * x102 - x108 * x196 + x47
x198 = x197 * x7
x199 = 2.0 * x107
x200 = x198 + x199
x201 = 2.0 * x120 + x200 * x60
x202 = x67 * (x198 + x199)
x203 = x101 * x155 - x160 * x196
x204 = x159 + x203 * x7
x205 = x10 * x203 + x107
x206 = x167 + x204 * x60
x207 = x172 + x205 * x60
x208 = x128 + x205 * x67
x209 = -x10 * x160 * x49 + x154 * x155 + x47
x210 = x10 * x209 + 2.0 * x159
x211 = 2.0 * x172 + x210 * x67
# 60 item(s)
result[0, 0, 0] = numpy.sum(
x59
* (
x0 * x42
+ x0 * (x42 + x43 * x46)
+ x14 * (x36 * (x35 * x56 + x36 * (x52 + x54)) + x40 * x56)
)
)
result[0, 0, 1] = numpy.sum(
x66
* (x0 * x64 + x0 * (x64 + x65 * x7) + x14 * (x36 * x60 * (x52 + x54) + x56 * x62))
)
result[0, 0, 2] = numpy.sum(
x66
* (
x0 * x71
+ x0 * (x10 * x65 + x71)
+ x14 * (x36 * x67 * (x52 + x54) + x56 * x69)
)
)
result[0, 0, 3] = numpy.sum(
x66 * (x0 * x75 + x0 * (x75 + x76 * x8) + x14 * x73 * (x52 + x54))
)
result[0, 0, 4] = numpy.sum(
x82 * (x0 * x80 + x0 * (x46 * x81 + x80) + x14 * x78 * (x52 + x54))
)
result[0, 0, 5] = numpy.sum(
x66 * (x0 * x85 + x0 * (x11 * x76 + x85) + x14 * x83 * (x52 + x54))
)
result[0, 0, 6] = numpy.sum(x59 * (x0 * x89 + x0 * (x46 * x86 + x89) + x51 * x88))
result[0, 0, 7] = numpy.sum(x66 * (x0 * x92 + x0 * (x46 * x93 + x92) + x51 * x91))
result[0, 0, 8] = numpy.sum(x66 * (x0 * x96 + x0 * (x46 * x97 + x96) + x51 * x95))
result[0, 0, 9] = numpy.sum(x59 * (x0 * x100 + x0 * (x100 + x46 * x98) + x51 * x99))
result[0, 1, 0] = numpy.sum(
x112
* (x0 * x106 + x14 * (x107 * x111 + x36**2 * (2.0 * x107 + x110)) + x19 * x42)
)
result[0, 1, 1] = numpy.sum(
x82 * (x0 * x118 + x14 * (x114 * x124 + x36 * (x120 + x122 * x36)) + x19 * x64)
)
result[0, 1, 2] = numpy.sum(
x82
* (x0 * x127 + x14 * (x10 * x107 * x123 + x36 * (x110 * x67 + x128)) + x19 * x71)
)
result[0, 1, 3] = numpy.sum(x82 * (x0 * x132 + x14 * (x133 + x134 * x36) + x19 * x75))
result[0, 1, 4] = numpy.sum(x57 * (x0 * x137 + x14 * (x138 + x140 * x36) + x19 * x80))
result[0, 1, 5] = numpy.sum(x82 * (x0 * x143 + x14 * (x110 * x83 + x144) + x19 * x85))
result[0, 1, 6] = numpy.sum(
x112 * (x0 * x146 + x14 * (x134 * x60 + x53 * x73) + x19 * x89)
)
result[0, 1, 7] = numpy.sum(
x82 * (x0 * x148 + x14 * (x140 * x60 + x53 * x78) + x19 * x92)
)
result[0, 1, 8] = numpy.sum(x82 * (x0 * x150 + x14 * (x121 * x83 + x151) + x19 * x96))
result[0, 1, 9] = numpy.sum(x112 * (x0 * x153 + x100 * x19 + x109 * x99))
result[0, 2, 0] = numpy.sum(
x112
* (x0 * x158 + x14 * (x111 * x159 + x36**2 * (2.0 * x159 + x162)) + x20 * x42)
)
result[0, 2, 1] = numpy.sum(
x82 * (x0 * x166 + x14 * (x159 * x168 + x36 * (x162 * x60 + x167)) + x20 * x64)
)
result[0, 2, 2] = numpy.sum(
x82 * (x0 * x171 + x14 * (x124 * x169 + x36 * (x172 + x173 * x36)) + x20 * x71)
)
result[0, 2, 3] = numpy.sum(x82 * (x0 * x177 + x14 * (x162 * x73 + x178) + x20 * x75))
result[0, 2, 4] = numpy.sum(
x57 * (x0 * x181 + x14 * (x168 * x173 + x182) + x20 * x80)
)
result[0, 2, 5] = numpy.sum(x82 * (x0 * x185 + x14 * (x186 + x187 * x36) + x20 * x85))
result[0, 2, 6] = numpy.sum(x112 * (x0 * x189 + x161 * x88 + x20 * x89))
result[0, 2, 7] = numpy.sum(x82 * (x0 * x191 + x173 * x90 + x20 * x92))
result[0, 2, 8] = numpy.sum(x82 * (x0 * x193 + x187 * x77 + x20 * x96))
result[0, 2, 9] = numpy.sum(
x112 * (x0 * x195 + x100 * x20 + x14 * (x151 + x187 * x67))
)
result[0, 3, 0] = numpy.sum(x59 * (x103 * x197 + x104 * x19 + x106 * x19))
result[0, 3, 1] = numpy.sum(x66 * (x115 * x200 + x116 * x19 + x118 * x19))
result[0, 3, 2] = numpy.sum(x66 * (x125 * x197 + x126 * x19 + x127 * x19))
result[0, 3, 3] = numpy.sum(x66 * (x123 * x201 + x130 * x19 + x132 * x19))
result[0, 3, 4] = numpy.sum(x82 * (x123 * x202 + x136 * x19 + x137 * x19))
result[0, 3, 5] = numpy.sum(x66 * (x141 * x197 + x142 * x19 + x143 * x19))
result[0, 3, 6] = numpy.sum(
x59 * (x14 * (2.0 * x133 + x201 * x60) + x145 * x19 + x146 * x19)
)
result[0, 3, 7] = numpy.sum(
x66 * (x14 * (2.0 * x138 + x202 * x60) + x147 * x19 + x148 * x19)
)
result[0, 3, 8] = numpy.sum(
x66 * (x14 * x83 * (x198 + x199) + x149 * x19 + x150 * x19)
)
result[0, 3, 9] = numpy.sum(x59 * (x152 * x19 + x153 * x19 + x197 * x99))
result[0, 4, 0] = numpy.sum(x112 * (x103 * x203 + x104 * x20 + x158 * x19))
result[0, 4, 1] = numpy.sum(x82 * (x115 * x204 + x116 * x20 + x166 * x19))
result[0, 4, 2] = numpy.sum(x82 * (x115 * x205 + x126 * x20 + x171 * x19))
result[0, 4, 3] = numpy.sum(x82 * (x123 * x206 + x130 * x20 + x177 * x19))
result[0, 4, 4] = numpy.sum(x57 * (x123 * x207 + x136 * x20 + x181 * x19))
result[0, 4, 5] = numpy.sum(x82 * (x123 * x208 + x142 * x20 + x185 * x19))
result[0, 4, 6] = numpy.sum(
x112 * (x14 * (x178 + x206 * x60) + x145 * x20 + x189 * x19)
)
result[0, 4, 7] = numpy.sum(
x82 * (x14 * (x182 + x207 * x60) + x147 * x20 + x19 * x191)
)
result[0, 4, 8] = numpy.sum(
x82 * (x14 * (x186 + x208 * x60) + x149 * x20 + x19 * x193)
)
result[0, 4, 9] = numpy.sum(
x112 * (x14 * (x144 + x208 * x67) + x152 * x20 + x19 * x195)
)
result[0, 5, 0] = numpy.sum(x59 * (x103 * x209 + x156 * x20 + x158 * x20))
result[0, 5, 1] = numpy.sum(x66 * (x163 * x209 + x164 * x20 + x166 * x20))
result[0, 5, 2] = numpy.sum(x66 * (x115 * x210 + x170 * x20 + x171 * x20))
result[0, 5, 3] = numpy.sum(x66 * (x174 * x209 + x175 * x20 + x177 * x20))
result[0, 5, 4] = numpy.sum(x82 * (x179 * x210 + x180 * x20 + x181 * x20))
result[0, 5, 5] = numpy.sum(x66 * (x123 * x211 + x184 * x20 + x185 * x20))
result[0, 5, 6] = numpy.sum(x59 * (x188 * x20 + x189 * x20 + x209 * x88))
result[0, 5, 7] = numpy.sum(x66 * (x190 * x20 + x191 * x20 + x210 * x90))
result[0, 5, 8] = numpy.sum(x66 * (x192 * x20 + x193 * x20 + x211 * x77))
result[0, 5, 9] = numpy.sum(
x59 * (x14 * (2.0 * x186 + x211 * x67) + x194 * x20 + x195 * x20)
)
return result
[docs]
def int3c2e3d_sph_024(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sd|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 6, 15), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = x4**2
x6 = -x2 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = x7**2
x9 = -x2 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = x10**2
x12 = cx + x1
x13 = x12 ** (-1.0)
x14 = x1 * x13
x15 = cx * x14 * (x11 + x5 + x8)
x16 = boys(5, x15)
x17 = x12 ** (-1.5)
x18 = 17.49341832762486
x19 = A[1] - B[1]
x20 = A[2] - B[2]
x21 = numpy.exp(-ax * bx * x2 * (x0**2 + x19**2 + x20**2))
x22 = 2.0 * x18 * x21
x23 = x2 * x22
x24 = x17 * x23
x25 = x16 * x24
x26 = cx ** (-1.0)
x27 = x12 ** (-0.5)
x28 = -x3 - A[0]
x29 = boys(4, x15)
x30 = 2.0 * x18 * x2 * x21 * x26 * x27 * x28 * x29 - x25 * x4
x31 = x30 * x4
x32 = 0.5 / (ax + bx)
x33 = x26 * x29
x34 = x23 * x27 * x32 * x33
x35 = x31 + x34
x36 = x14 * x4
x37 = x22 * x33
x38 = x32 * x37
x39 = x17 * x38
x40 = x35 * x36 + x39 * x4
x41 = x38 * x5
x42 = x1 * x12 ** (-2.5)
x43 = x36 * x40 + x41 * x42
x44 = x4**3
x45 = x1**2
x46 = x12 ** (-3.5) * x45
x47 = x38 * x46
x48 = x14 * (x36 * x43 + x44 * x47)
x49 = x4**4
x50 = x1**3
x51 = x12 ** (-4.5) * x37 * x50
x52 = x0 * x51
x53 = x32 * (2.0 * x18 * x2 * x21 * x26 * x27 * x29 - x25)
x54 = x24 * boys(6, x15)
x55 = cx * x13
x56 = x4 * x55
x57 = (
x28 * x30 + x53 - x56 * (2.0 * x16 * x18 * x2 * x21 * x26 * x27 * x28 - x4 * x54)
)
x58 = x4 * x57
x59 = x30 * x32
x60 = 2.0 * x59
x61 = x14 * x32
x62 = 2.0 * x61
x63 = da * db * dc
x64 = 0.009523809523809524 * x63
x65 = 5.916079783099616 * x64
x66 = x14 * x7
x67 = x39 * x7
x68 = x31 * x66 + x67
x69 = x38 * x42
x70 = x4 * x69
x71 = x36 * x68 + x7 * x70
x72 = x41 * x46
x73 = x14 * (x36 * x71 + x7 * x72)
x74 = x44 * x52
x75 = 0.06666666666666667 * x63
x76 = 2.23606797749979 * x75
x77 = x10 * x14
x78 = x10 * x39
x79 = x31 * x77 + x78
x80 = x10 * x70 + x36 * x79
x81 = x14 * (x10 * x72 + x36 * x80)
x82 = x45 / x12**2
x83 = x8 * x82
x84 = x69 * x8
x85 = x31 * x83 + x84
x86 = x4 * x8
x87 = x14 * (x36 * x85 + x47 * x86)
x88 = x5 * x8
x89 = 1.732050807568877
x90 = 0.1111111111111111 * x63 * x89
x91 = x7 * x82
x92 = x10 * x91
x93 = x10 * x7
x94 = x69 * x93
x95 = x31 * x92 + x94
x96 = x14 * (x36 * x95 + x4 * x47 * x93)
x97 = x5 * x93
x98 = 0.3333333333333333 * x63
x99 = x11 * x82
x100 = x11 * x69
x101 = x100 + x31 * x99
x102 = x11 * x4
x103 = x14 * (x101 * x36 + x102 * x47)
x104 = x11 * x5
x105 = x7**3
x106 = x50 / x12**3
x107 = x105 * x106
x108 = x105 * x47
x109 = x14 * (x107 * x31 + x108)
x110 = x105 * x52
x111 = x106 * x8
x112 = x10 * x111
x113 = x10 * x47 * x8
x114 = x14 * (x112 * x31 + x113)
x115 = x10 * x86
x116 = x106 * x7
x117 = x11 * x116
x118 = x11 * x47 * x7
x119 = x14 * (x117 * x31 + x118)
x120 = x102 * x7
x121 = x10**3
x122 = x106 * x121
x123 = x121 * x47
x124 = x14 * (x122 * x31 + x123)
x125 = x121 * x4
x126 = x7**4
x127 = x1**4 / x12**4
x128 = x126 * x127
x129 = x128 * x30
x130 = x105 * x127
x131 = x10 * x130
x132 = x131 * x30
x133 = x127 * x30
x134 = x11 * x8
x135 = x133 * x134
x136 = x127 * x57
x137 = x121 * x7
x138 = x133 * x137
x139 = x10**4
x140 = x127 * x139
x141 = x140 * x30
x142 = -x6 - A[1]
x143 = 2.0 * x142 * x18 * x2 * x21 * x26 * x27 * x29 - x25 * x7
x144 = x127 * x49
x145 = x143 * x144
x146 = x19 * x51
x147 = x145 + x146 * x49
x148 = x143 * x32
x149 = 2.0 * x142 * x16 * x18 * x2 * x21 * x26 * x27 - x54 * x7
x150 = x143 * x28 - x149 * x56
x151 = x150 * x4
x152 = x5 * x82
x153 = x106 * x44
x154 = 10.2469507659596 * x64
x155 = x143 * x7
x156 = x155 + x34
x157 = x127 * x44
x158 = x156 * x157
x159 = x146 * x44
x160 = x158 + x159 * x7
x161 = x14 * x156
x162 = x161 * x32
x163 = x150 * x7
x164 = x163 + x59
x165 = x4 * x82
x166 = x156 * x32
x167 = x106 * x5
x168 = 3.872983346207417 * x75
x169 = x10 * x157
x170 = x143 * x169
x171 = x10 * x159 + x170
x172 = x148 * x77
x173 = x10 * x148
x174 = x161 * x7 + x67
x175 = x167 * x174
x176 = x146 * x88 + x175
x177 = x174 * x61
x178 = x66 * (x164 + x59)
x179 = x165 * x32
x180 = x155 * x77 + x78
x181 = x167 * x180
x182 = x146 * x97 + x181
x183 = x180 * x61
x184 = x59 * x77
x185 = x163 * x77 + x184
x186 = x89 * x98
x187 = x127 * x143
x188 = x104 * x187
x189 = x104 * x146 + x188
x190 = x148 * x99
x191 = x174 * x66 + x84
x192 = x165 * x191
x193 = x105 * x146
x194 = x192 + x193 * x4
x195 = x191 * x61
x196 = x178 * x66 + x59 * x83
x197 = x180 * x66 + x94
x198 = x165 * x197
x199 = x115 * x146 + x198
x200 = x197 * x61
x201 = x185 * x66 + x59 * x92
x202 = x100 + x155 * x99
x203 = x165 * x202
x204 = x120 * x146 + x203
x205 = x202 * x61
x206 = x59 * x99
x207 = x163 * x99 + x206
x208 = x125 * x187
x209 = x125 * x146 + x208
x210 = x122 * x148
x211 = x14 * (x108 + x191 * x66)
x212 = x126 * x146 + x211
x213 = x14 * (x113 + x197 * x66)
x214 = x10 * x193 + x213
x215 = x14 * (x118 + x202 * x66)
x216 = x134 * x146 + x215
x217 = x14 * (x122 * x155 + x123)
x218 = x137 * x146 + x217
x219 = x122 * x59
x220 = x140 * x143
x221 = x139 * x146 + x220
x222 = -x9 - A[2]
x223 = -x10 * x25 + 2.0 * x18 * x2 * x21 * x222 * x26 * x27 * x29
x224 = x144 * x223
x225 = x20 * x51
x226 = x224 + x225 * x49
x227 = x223 * x32
x228 = -x10 * x54 + 2.0 * x16 * x18 * x2 * x21 * x222 * x26 * x27
x229 = x223 * x28 - x228 * x56
x230 = x229 * x4
x231 = x157 * x7
x232 = x223 * x231
x233 = x225 * x44
x234 = x232 + x233 * x7
x235 = x227 * x66
x236 = x165 * x7
x237 = x10 * x223 + x34
x238 = x157 * x237
x239 = x10 * x233 + x238
x240 = x237 * x61
x241 = x10 * x229 + x59
x242 = x237 * x32
x243 = x127 * x5
x244 = x243 * x8
x245 = x223 * x244
x246 = x225 * x88 + x245
x247 = x227 * x83
x248 = x111 * x4
x249 = x243 * x7
x250 = x237 * x249
x251 = x225 * x97 + x250
x252 = x242 * x91
x253 = x116 * x4
x254 = x237 * x77 + x78
x255 = x167 * x254
x256 = x104 * x225 + x255
x257 = x254 * x61
x258 = x184 + x241 * x77
x259 = x130 * x4
x260 = x223 * x259
x261 = x105 * x225
x262 = x260 + x261 * x4
x263 = x107 * x227
x264 = x127 * x86
x265 = x237 * x264
x266 = x115 * x225 + x265
x267 = x111 * x242
x268 = x253 * x254
x269 = x120 * x225 + x268
x270 = x254 * x32 * x91
x271 = x100 + x254 * x77
x272 = x165 * x271
x273 = x125 * x225 + x272
x274 = x271 * x61
x275 = x206 + x258 * x77
x276 = x128 * x223
x277 = x126 * x225 + x276
x278 = x130 * x237
x279 = x10 * x261 + x278
x280 = x111 * x254
x281 = x134 * x225 + x280
x282 = x271 * x91
x283 = x137 * x225 + x282
x284 = x14 * (x123 + x271 * x77)
x285 = x139 * x225 + x284
x286 = x55 * x7
x287 = x142 * x143 - x149 * x286 + x53
x288 = x287 * x7
x289 = 2.0 * x148
x290 = x288 + x289
x291 = 2.0 * x162 + x290 * x66
x292 = x77 * (x288 + x289)
x293 = x127 * x287
x294 = 2.0 * x177 + x291 * x66
x295 = 2.0 * x183 + x292 * x66
x296 = x99 * (x288 + x289)
x297 = x142 * x223 - x228 * x286
x298 = x227 + x297 * x7
x299 = x10 * x297 + x148
x300 = x235 + x298 * x66
x301 = x240 + x299 * x66
x302 = x172 + x299 * x77
x303 = x247 + x300 * x66
x304 = x252 + x301 * x66
x305 = x257 + x302 * x66
x306 = x190 + x302 * x77
x307 = -x10 * x228 * x55 + x222 * x223 + x53
x308 = x10 * x307 + 2.0 * x227
x309 = 2.0 * x240 + x308 * x77
x310 = 2.0 * x257 + x309 * x77
# 90 item(s)
result[0, 0, 0] = numpy.sum(
x65
* (
x0 * x48
+ x0 * (x48 + x49 * x52)
+ x14
* (x36 * (x36 * (x35 * x62 + x36 * (x58 + x60)) + x40 * x62) + x43 * x62)
)
)
result[0, 0, 1] = numpy.sum(
x76
* (
x0 * x73
+ x0 * (x7 * x74 + x73)
+ x14 * (x36 * (x36 * x66 * (x58 + x60) + x62 * x68) + x62 * x71)
)
)
result[0, 0, 2] = numpy.sum(
x76
* (
x0 * x81
+ x0 * (x10 * x74 + x81)
+ x14 * (x36 * (x36 * x77 * (x58 + x60) + x62 * x79) + x62 * x80)
)
)
result[0, 0, 3] = numpy.sum(
x90
* (
x0 * x87
+ x0 * (x52 * x88 + x87)
+ x14 * (x36 * x83 * (x58 + x60) + x62 * x85)
)
)
result[0, 0, 4] = numpy.sum(
x98
* (
x0 * x96
+ x0 * (x52 * x97 + x96)
+ x14 * (x36 * x92 * (x58 + x60) + x62 * x95)
)
)
result[0, 0, 5] = numpy.sum(
x90
* (
x0 * x103
+ x0 * (x103 + x104 * x52)
+ x14 * (x101 * x62 + x36 * x99 * (x58 + x60))
)
)
result[0, 0, 6] = numpy.sum(
x76 * (x0 * x109 + x0 * (x109 + x110 * x4) + x107 * x14 * (x58 + x60))
)
result[0, 0, 7] = numpy.sum(
x98 * (x0 * x114 + x0 * (x114 + x115 * x52) + x112 * x14 * (x58 + x60))
)
result[0, 0, 8] = numpy.sum(
x98 * (x0 * x119 + x0 * (x119 + x120 * x52) + x117 * x14 * (x58 + x60))
)
result[0, 0, 9] = numpy.sum(
x76 * (x0 * x124 + x0 * (x124 + x125 * x52) + x122 * x14 * (x58 + x60))
)
result[0, 0, 10] = numpy.sum(
x65 * (x0 * x129 + x0 * (x126 * x52 + x129) + x128 * x57)
)
result[0, 0, 11] = numpy.sum(
x76 * (x0 * x132 + x0 * (x10 * x110 + x132) + x131 * x57)
)
result[0, 0, 12] = numpy.sum(
x90 * (x0 * x135 + x0 * (x134 * x52 + x135) + x134 * x136)
)
result[0, 0, 13] = numpy.sum(
x76 * (x0 * x138 + x0 * (x137 * x52 + x138) + x136 * x137)
)
result[0, 0, 14] = numpy.sum(
x65 * (x0 * x141 + x0 * (x139 * x52 + x141) + x140 * x57)
)
result[0, 1, 0] = numpy.sum(
x154
* (
x0 * x147
+ x14 * (x148 * x153 + x36 * (x148 * x152 + x36**2 * (2.0 * x148 + x151)))
+ x19 * x48
)
)
result[0, 1, 1] = numpy.sum(
x168
* (
x0 * x160
+ x14 * (x166 * x167 + x36 * (x165 * x166 + x36 * (x162 + x164 * x36)))
+ x19 * x73
)
)
result[0, 1, 2] = numpy.sum(
x168
* (
x0 * x171
+ x14 * (x167 * x173 + x36 * (x165 * x173 + x36 * (x151 * x77 + x172)))
+ x19 * x81
)
)
result[0, 1, 3] = numpy.sum(
x98 * (x0 * x176 + x14 * (x174 * x179 + x36 * (x177 + x178 * x36)) + x19 * x87)
)
result[0, 1, 4] = numpy.sum(
x186 * (x0 * x182 + x14 * (x179 * x180 + x36 * (x183 + x185 * x36)) + x19 * x96)
)
result[0, 1, 5] = numpy.sum(
x98
* (
x0 * x189
+ x103 * x19
+ x14 * (x102 * x106 * x148 + x36 * (x151 * x99 + x190))
)
)
result[0, 1, 6] = numpy.sum(
x168 * (x0 * x194 + x109 * x19 + x14 * (x195 + x196 * x36))
)
result[0, 1, 7] = numpy.sum(
x186 * (x0 * x199 + x114 * x19 + x14 * (x200 + x201 * x36))
)
result[0, 1, 8] = numpy.sum(
x186 * (x0 * x204 + x119 * x19 + x14 * (x205 + x207 * x36))
)
result[0, 1, 9] = numpy.sum(
x168 * (x0 * x209 + x124 * x19 + x14 * (x122 * x151 + x210))
)
result[0, 1, 10] = numpy.sum(
x154 * (x0 * x212 + x129 * x19 + x14 * (x107 * x59 + x196 * x66))
)
result[0, 1, 11] = numpy.sum(
x168 * (x0 * x214 + x132 * x19 + x14 * (x112 * x59 + x201 * x66))
)
result[0, 1, 12] = numpy.sum(
x98 * (x0 * x216 + x135 * x19 + x14 * (x117 * x59 + x207 * x66))
)
result[0, 1, 13] = numpy.sum(
x168 * (x0 * x218 + x138 * x19 + x14 * (x122 * x163 + x219))
)
result[0, 1, 14] = numpy.sum(x154 * (x0 * x221 + x140 * x150 + x141 * x19))
result[0, 2, 0] = numpy.sum(
x154
* (
x0 * x226
+ x14 * (x153 * x227 + x36 * (x152 * x227 + x36**2 * (2.0 * x227 + x230)))
+ x20 * x48
)
)
result[0, 2, 1] = numpy.sum(
x168
* (
x0 * x234
+ x14 * (x167 * x227 * x7 + x36 * (x227 * x236 + x36 * (x230 * x66 + x235)))
+ x20 * x73
)
)
result[0, 2, 2] = numpy.sum(
x168
* (
x0 * x239
+ x14 * (x167 * x242 + x36 * (x179 * x237 + x36 * (x240 + x241 * x36)))
+ x20 * x81
)
)
result[0, 2, 3] = numpy.sum(
x98 * (x0 * x246 + x14 * (x227 * x248 + x36 * (x230 * x83 + x247)) + x20 * x87)
)
result[0, 2, 4] = numpy.sum(
x186 * (x0 * x251 + x14 * (x242 * x253 + x36 * (x236 * x241 + x252)) + x20 * x96)
)
result[0, 2, 5] = numpy.sum(
x98 * (x0 * x256 + x103 * x20 + x14 * (x179 * x254 + x36 * (x257 + x258 * x36)))
)
result[0, 2, 6] = numpy.sum(
x168 * (x0 * x262 + x109 * x20 + x14 * (x107 * x230 + x263))
)
result[0, 2, 7] = numpy.sum(
x186 * (x0 * x266 + x114 * x20 + x14 * (x241 * x248 + x267))
)
result[0, 2, 8] = numpy.sum(
x186 * (x0 * x269 + x119 * x20 + x14 * (x236 * x258 + x270))
)
result[0, 2, 9] = numpy.sum(
x168 * (x0 * x273 + x124 * x20 + x14 * (x274 + x275 * x36))
)
result[0, 2, 10] = numpy.sum(x154 * (x0 * x277 + x128 * x229 + x129 * x20))
result[0, 2, 11] = numpy.sum(x168 * (x0 * x279 + x130 * x241 + x132 * x20))
result[0, 2, 12] = numpy.sum(x98 * (x0 * x281 + x111 * x258 + x135 * x20))
result[0, 2, 13] = numpy.sum(x168 * (x0 * x283 + x138 * x20 + x275 * x91))
result[0, 2, 14] = numpy.sum(
x154 * (x0 * x285 + x14 * (x219 + x275 * x77) + x141 * x20)
)
result[0, 3, 0] = numpy.sum(x65 * (x144 * x287 + x145 * x19 + x147 * x19))
result[0, 3, 1] = numpy.sum(x76 * (x157 * x290 + x158 * x19 + x160 * x19))
result[0, 3, 2] = numpy.sum(x76 * (x169 * x287 + x170 * x19 + x171 * x19))
result[0, 3, 3] = numpy.sum(x90 * (x167 * x291 + x175 * x19 + x176 * x19))
result[0, 3, 4] = numpy.sum(x98 * (x167 * x292 + x181 * x19 + x182 * x19))
result[0, 3, 5] = numpy.sum(x90 * (x104 * x293 + x188 * x19 + x189 * x19))
result[0, 3, 6] = numpy.sum(x76 * (x165 * x294 + x19 * x192 + x19 * x194))
result[0, 3, 7] = numpy.sum(x98 * (x165 * x295 + x19 * x198 + x19 * x199))
result[0, 3, 8] = numpy.sum(x98 * (x165 * x296 + x19 * x203 + x19 * x204))
result[0, 3, 9] = numpy.sum(x76 * (x125 * x293 + x19 * x208 + x19 * x209))
result[0, 3, 10] = numpy.sum(
x65 * (x14 * (2.0 * x195 + x294 * x66) + x19 * x211 + x19 * x212)
)
result[0, 3, 11] = numpy.sum(
x76 * (x14 * (2.0 * x200 + x295 * x66) + x19 * x213 + x19 * x214)
)
result[0, 3, 12] = numpy.sum(
x90 * (x14 * (2.0 * x205 + x296 * x66) + x19 * x215 + x19 * x216)
)
result[0, 3, 13] = numpy.sum(
x76 * (x122 * x14 * (x288 + x289) + x19 * x217 + x19 * x218)
)
result[0, 3, 14] = numpy.sum(x65 * (x140 * x287 + x19 * x220 + x19 * x221))
result[0, 4, 0] = numpy.sum(x154 * (x144 * x297 + x145 * x20 + x19 * x226))
result[0, 4, 1] = numpy.sum(x168 * (x157 * x298 + x158 * x20 + x19 * x234))
result[0, 4, 2] = numpy.sum(x168 * (x157 * x299 + x170 * x20 + x19 * x239))
result[0, 4, 3] = numpy.sum(x98 * (x167 * x300 + x175 * x20 + x19 * x246))
result[0, 4, 4] = numpy.sum(x186 * (x167 * x301 + x181 * x20 + x19 * x251))
result[0, 4, 5] = numpy.sum(x98 * (x167 * x302 + x188 * x20 + x19 * x256))
result[0, 4, 6] = numpy.sum(x168 * (x165 * x303 + x19 * x262 + x192 * x20))
result[0, 4, 7] = numpy.sum(x186 * (x165 * x304 + x19 * x266 + x198 * x20))
result[0, 4, 8] = numpy.sum(x186 * (x165 * x305 + x19 * x269 + x20 * x203))
result[0, 4, 9] = numpy.sum(x168 * (x165 * x306 + x19 * x273 + x20 * x208))
result[0, 4, 10] = numpy.sum(
x154 * (x14 * (x263 + x303 * x66) + x19 * x277 + x20 * x211)
)
result[0, 4, 11] = numpy.sum(
x168 * (x14 * (x267 + x304 * x66) + x19 * x279 + x20 * x213)
)
result[0, 4, 12] = numpy.sum(
x98 * (x14 * (x270 + x305 * x66) + x19 * x281 + x20 * x215)
)
result[0, 4, 13] = numpy.sum(
x168 * (x14 * (x274 + x306 * x66) + x19 * x283 + x20 * x217)
)
result[0, 4, 14] = numpy.sum(
x154 * (x14 * (x210 + x306 * x77) + x19 * x285 + x20 * x220)
)
result[0, 5, 0] = numpy.sum(x65 * (x144 * x307 + x20 * x224 + x20 * x226))
result[0, 5, 1] = numpy.sum(x76 * (x20 * x232 + x20 * x234 + x231 * x307))
result[0, 5, 2] = numpy.sum(x76 * (x157 * x308 + x20 * x238 + x20 * x239))
result[0, 5, 3] = numpy.sum(x90 * (x20 * x245 + x20 * x246 + x244 * x307))
result[0, 5, 4] = numpy.sum(x98 * (x20 * x250 + x20 * x251 + x249 * x308))
result[0, 5, 5] = numpy.sum(x90 * (x167 * x309 + x20 * x255 + x20 * x256))
result[0, 5, 6] = numpy.sum(x76 * (x20 * x260 + x20 * x262 + x259 * x307))
result[0, 5, 7] = numpy.sum(x98 * (x20 * x265 + x20 * x266 + x264 * x308))
result[0, 5, 8] = numpy.sum(x98 * (x20 * x268 + x20 * x269 + x253 * x309))
result[0, 5, 9] = numpy.sum(x76 * (x165 * x310 + x20 * x272 + x20 * x273))
result[0, 5, 10] = numpy.sum(x65 * (x128 * x307 + x20 * x276 + x20 * x277))
result[0, 5, 11] = numpy.sum(x76 * (x130 * x308 + x20 * x278 + x20 * x279))
result[0, 5, 12] = numpy.sum(x90 * (x111 * x309 + x20 * x280 + x20 * x281))
result[0, 5, 13] = numpy.sum(x76 * (x20 * x282 + x20 * x283 + x310 * x91))
result[0, 5, 14] = numpy.sum(
x65 * (x14 * (2.0 * x274 + x310 * x77) + x20 * x284 + x20 * x285)
)
return result
[docs]
def int3c2e3d_sph_030(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sf|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 10, 1), dtype=float)
x0 = A[0] - B[0]
x1 = 0.5 / (ax + bx)
x2 = ax + bx
x3 = x2 ** (-1.0)
x4 = -x3 * (ax * A[0] + bx * B[0])
x5 = -x4 - C[0]
x6 = -x3 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = -x3 * (ax * A[2] + bx * B[2])
x9 = -x8 - C[2]
x10 = cx + x2
x11 = cx / x10
x12 = x11 * x2 * (x5**2 + x7**2 + x9**2)
x13 = boys(1, x12)
x14 = 17.49341832762486
x15 = A[1] - B[1]
x16 = A[2] - B[2]
x17 = numpy.exp(-ax * bx * x3 * (x0**2 + x15**2 + x16**2))
x18 = 2.0 * x14 * x17 * x3
x19 = x10 ** (-1.5) * x18
x20 = x13 * x19
x21 = cx ** (-1.0)
x22 = x10 ** (-0.5)
x23 = boys(0, x12)
x24 = x1 * (2.0 * x14 * x17 * x21 * x22 * x23 * x3 - x20)
x25 = -x4 - A[0]
x26 = x20 * x5
x27 = -2.0 * x14 * x17 * x21 * x22 * x23 * x25 * x3 + x26
x28 = -x27
x29 = boys(2, x12)
x30 = x19 * x29
x31 = 2.0 * x13 * x14 * x17 * x21 * x22 * x25 * x3 - x30 * x5
x32 = x11 * x31
x33 = x24 + x25 * x28 - x32 * x5
x34 = x0 * x28 + x33
x35 = x18 * x21 * x22 * x23
x36 = x1 * (2.0 * x13 * x14 * x17 * x21 * x22 * x3 - x30)
x37 = x19 * boys(3, x12)
x38 = x11 * x5
x39 = da * db * dc
x40 = 0.2581988897471611 * x39
x41 = -x6 - A[1]
x42 = 2.0 * x13 * x14 * x17 * x21 * x22 * x3 * x41 - x30 * x7
x43 = x11 * x42
x44 = x20 * x7
x45 = -2.0 * x14 * x17 * x21 * x22 * x23 * x3 * x41 + x44
x46 = -x1 * (x43 + x45)
x47 = -x45
x48 = x43 * x5
x49 = x15 * x28 + x25 * x47 - x48
x50 = x15 * x35 + x35 * x41 - x44
x51 = x25 * x47 - x48
x52 = 2.0 * x14 * x17 * x21 * x22 * x29 * x3 * x41 - x37 * x7
x53 = 0.5773502691896258 * x39
x54 = -x8 - A[2]
x55 = 2.0 * x13 * x14 * x17 * x21 * x22 * x3 * x54 - x30 * x9
x56 = x11 * x55
x57 = x20 * x9
x58 = -2.0 * x14 * x17 * x21 * x22 * x23 * x3 * x54 + x57
x59 = -x1 * (x56 + x58)
x60 = -x58
x61 = x5 * x56
x62 = x16 * x28 + x25 * x60 - x61
x63 = x16 * x35 + x35 * x54 - x57
x64 = x25 * x60 - x61
x65 = 2.0 * x14 * x17 * x21 * x22 * x29 * x3 * x54 - x37 * x9
x66 = x24 + x41 * x47 - x43 * x7
x67 = x15 * x47 + x66
x68 = x15 * x50 + x67
x69 = x11 * x7
x70 = x36 + x41 * x42 - x52 * x69
x71 = x56 * x7
x72 = x16 * x47 + x41 * x60 - x71
x73 = x15 * x63 + x72
x74 = x41 * x60 - x71
x75 = x41 * x55 - x65 * x69
x76 = x24 + x54 * x60 - x56 * x9
x77 = x16 * x60 + x76
x78 = x16 * x63 + x77
x79 = x11 * x9
x80 = x36 + x54 * x55 - x65 * x79
# 10 item(s)
result[0, 0, 0] = numpy.sum(
x40
* (
x0 * x33
+ x0 * x34
+ x0 * (x0 * (x0 * x35 + x25 * x35 - x26) + x34)
- 2.0 * x1 * (x27 + x32)
+ x25 * x33
- x38
* (
x25 * x31
+ x36
- x38 * (2.0 * x14 * x17 * x21 * x22 * x25 * x29 * x3 - x37 * x5)
)
)
)
result[0, 1, 0] = numpy.sum(
x53
* (
x0 * x49
+ x0 * (x0 * x50 + x49)
+ x15 * x33
+ x25 * x51
- x38 * (x25 * x42 - x38 * x52)
+ x46
)
)
result[0, 2, 0] = numpy.sum(
x53
* (
x0 * x62
+ x0 * (x0 * x63 + x62)
+ x16 * x33
+ x25 * x64
- x38 * (x25 * x55 - x38 * x65)
+ x59
)
)
result[0, 3, 0] = numpy.sum(
x53 * (x0 * x68 + x15 * x49 + x15 * x51 + x25 * x66 - x38 * x70)
)
result[0, 4, 0] = numpy.sum(
x39 * (x0 * x73 + x15 * x62 + x16 * x51 + x25 * x74 - x38 * x75)
)
result[0, 5, 0] = numpy.sum(
x53 * (x0 * x78 + x16 * x62 + x16 * x64 + x25 * x76 - x38 * x80)
)
result[0, 6, 0] = numpy.sum(
x40 * (x15 * x66 + x15 * x67 + x15 * x68 + x41 * x66 + 2.0 * x46 - x69 * x70)
)
result[0, 7, 0] = numpy.sum(
x53 * (x15 * x72 + x15 * x73 + x16 * x66 + x41 * x74 + x59 - x69 * x75)
)
result[0, 8, 0] = numpy.sum(
x53 * (x15 * x78 + x16 * x72 + x16 * x74 + x41 * x76 - x69 * x80)
)
result[0, 9, 0] = numpy.sum(
x40 * (x16 * x76 + x16 * x77 + x16 * x78 + x54 * x76 + 2.0 * x59 - x79 * x80)
)
return result
[docs]
def int3c2e3d_sph_031(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sf|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 10, 3), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = 0.5 / (ax + bx)
x6 = -x2 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = -x2 * (ax * A[2] + bx * B[2])
x9 = -x8 - C[2]
x10 = cx + x1
x11 = x10 ** (-1.0)
x12 = x1 * x11
x13 = cx * x12 * (x4**2 + x7**2 + x9**2)
x14 = boys(2, x13)
x15 = x10 ** (-1.5)
x16 = 17.49341832762486
x17 = A[1] - B[1]
x18 = A[2] - B[2]
x19 = numpy.exp(-ax * bx * x2 * (x0**2 + x17**2 + x18**2))
x20 = x16 * x19 * x2
x21 = 2.0 * x15 * x20
x22 = x14 * x21
x23 = cx ** (-1.0)
x24 = x10 ** (-0.5)
x25 = boys(1, x13)
x26 = x5 * (2.0 * x16 * x19 * x2 * x23 * x24 * x25 - x22)
x27 = -x3 - A[0]
x28 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x27 + x22 * x4
x29 = -x28
x30 = boys(3, x13)
x31 = x21 * x30
x32 = 2.0 * x14 * x16 * x19 * x2 * x23 * x24 * x27 - x31 * x4
x33 = cx * x11
x34 = x32 * x33
x35 = x26 + x27 * x29 - x34 * x4
x36 = x29 * x5
x37 = x12 * (x35 * x4 + 2.0 * x36)
x38 = 2.0 * x5
x39 = x23 * x25
x40 = x20 * x24 * x38 * x39
x41 = x12 * (x29 * x4 + x40)
x42 = x0 * x41 + x37
x43 = 2.0 * x15 * x16 * x19 * x39
x44 = x0 * x43
x45 = x5 * (2.0 * x14 * x16 * x19 * x2 * x23 * x24 - x31)
x46 = x21 * boys(4, x13)
x47 = x33 * x4
x48 = (
x27 * x35
- x38 * (x28 + x34)
- x47
* (
x27 * x32
+ x45
- x47 * (2.0 * x16 * x19 * x2 * x23 * x24 * x27 * x30 - x4 * x46)
)
)
x49 = x35 * x5
x50 = da * db * dc
x51 = 0.2581988897471611 * x50
x52 = x12 * x7
x53 = x35 * x52
x54 = x29 * x52
x55 = x0 * x54 + x53
x56 = x12 * x9
x57 = x35 * x56
x58 = x29 * x56
x59 = x0 * x58 + x57
x60 = -x6 - A[1]
x61 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x60 + x22 * x7
x62 = -x61
x63 = x5 * x62
x64 = 2.0 * x14 * x16 * x19 * x2 * x23 * x24 * x60 - x31 * x7
x65 = x33 * x64
x66 = x27 * x62 - x4 * x65
x67 = x12 * (x4 * x66 + x63)
x68 = x17 * x41 + x67
x69 = x12 * x4
x70 = x62 * x69
x71 = x17 * x43
x72 = x4 * x71 + x70
x73 = -x5 * (x61 + x65)
x74 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x60 - x46 * x7
x75 = x27 * x66 - x47 * (x27 * x64 - x47 * x74) + x73
x76 = x5 * x66
x77 = 2.0 * x76
x78 = 0.5773502691896258 * x50
x79 = x12 * (x36 + x66 * x7)
x80 = x17 * x54 + x79
x81 = x12 * (x40 + x62 * x7)
x82 = x7 * x71 + x81
x83 = x56 * x66
x84 = x17 * x58 + x83
x85 = x56 * x62
x86 = x71 * x9 + x85
x87 = -x8 - A[2]
x88 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x87 + x22 * x9
x89 = -x88
x90 = x5 * x89
x91 = 2.0 * x14 * x16 * x19 * x2 * x23 * x24 * x87 - x31 * x9
x92 = x33 * x91
x93 = x27 * x89 - x4 * x92
x94 = x12 * (x4 * x93 + x90)
x95 = x18 * x41 + x94
x96 = x69 * x89
x97 = x18 * x43
x98 = x4 * x97 + x96
x99 = -x5 * (x88 + x92)
x100 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x87 - x46 * x9
x101 = x27 * x93 + x47 * (x100 * x47 - x27 * x91) + x99
x102 = x5 * x93
x103 = 2.0 * x102
x104 = x52 * x93
x105 = x104 + x18 * x54
x106 = x52 * x89
x107 = x106 + x7 * x97
x108 = x12 * (x36 + x9 * x93)
x109 = x108 + x18 * x58
x110 = x12 * (x40 + x89 * x9)
x111 = x110 + x9 * x97
x112 = x26 + x60 * x62 - x65 * x7
x113 = x112 * x69
x114 = x113 + x17 * x70
x115 = x114 + x17 * x72
x116 = x112 * x5
x117 = x33 * x7
x118 = -x117 * x74 + x45 + x60 * x64
x119 = x112 * x27 - x118 * x47
x120 = x12 * (x112 * x7 + 2.0 * x63)
x121 = x120 + x17 * x81
x122 = x121 + x17 * x82
x123 = x112 * x56
x124 = x123 + x17 * x85
x125 = x124 + x17 * x86
x126 = x60 * x89 - x7 * x92
x127 = x126 * x69
x128 = x127 + x18 * x70
x129 = x128 + x17 * x98
x130 = x126 * x5
x131 = -x100 * x117 + x60 * x91
x132 = x126 * x27 - x131 * x47
x133 = x12 * (x126 * x7 + x90)
x134 = x133 + x18 * x81
x135 = x107 * x17 + x134
x136 = x12 * (x126 * x9 + x63)
x137 = x136 + x18 * x85
x138 = x111 * x17 + x137
x139 = x26 + x87 * x89 - x9 * x92
x140 = x139 * x69
x141 = x140 + x18 * x96
x142 = x141 + x18 * x98
x143 = x139 * x5
x144 = x33 * x9
x145 = -x100 * x144 + x45 + x87 * x91
x146 = x139 * x27 - x145 * x47
x147 = x139 * x52
x148 = x106 * x18 + x147
x149 = x107 * x18 + x148
x150 = x12 * (x139 * x9 + 2.0 * x90)
x151 = x110 * x18 + x150
x152 = x111 * x18 + x151
x153 = x112 * x60 - x117 * x118 + 2.0 * x73
x154 = -x117 * x131 + x126 * x60 + x99
x155 = 2.0 * x130
x156 = -x117 * x145 + x139 * x60
x157 = x139 * x87 - x144 * x145 + 2.0 * x99
# 30 item(s)
result[0, 0, 0] = numpy.sum(
x51
* (
x0 * x37
+ x0 * x42
+ x0 * (x0 * (x4 * x44 + x41) + x42)
+ x12 * (x4 * x48 + 3.0 * x49)
)
)
result[0, 0, 1] = numpy.sum(
x51 * (x0 * x53 + x0 * x55 + x0 * (x0 * (x44 * x7 + x54) + x55) + x48 * x52)
)
result[0, 0, 2] = numpy.sum(
x51 * (x0 * x57 + x0 * x59 + x0 * (x0 * (x44 * x9 + x58) + x59) + x48 * x56)
)
result[0, 1, 0] = numpy.sum(
x78 * (x0 * x68 + x0 * (x0 * x72 + x68) + x12 * (x4 * x75 + x77) + x17 * x37)
)
result[0, 1, 1] = numpy.sum(
x78 * (x0 * x80 + x0 * (x0 * x82 + x80) + x12 * (x49 + x7 * x75) + x17 * x53)
)
result[0, 1, 2] = numpy.sum(
x78 * (x0 * x84 + x0 * (x0 * x86 + x84) + x17 * x57 + x56 * x75)
)
result[0, 2, 0] = numpy.sum(
x78 * (x0 * x95 + x0 * (x0 * x98 + x95) + x12 * (x101 * x4 + x103) + x18 * x37)
)
result[0, 2, 1] = numpy.sum(
x78 * (x0 * x105 + x0 * (x0 * x107 + x105) + x101 * x52 + x18 * x53)
)
result[0, 2, 2] = numpy.sum(
x78 * (x0 * x109 + x0 * (x0 * x111 + x109) + x12 * (x101 * x9 + x49) + x18 * x57)
)
result[0, 3, 0] = numpy.sum(
x78 * (x0 * x115 + x12 * (x116 + x119 * x4) + x17 * x67 + x17 * x68)
)
result[0, 3, 1] = numpy.sum(
x78 * (x0 * x122 + x12 * (x119 * x7 + x77) + x17 * x79 + x17 * x80)
)
result[0, 3, 2] = numpy.sum(x78 * (x0 * x125 + x119 * x56 + x17 * x83 + x17 * x84))
result[0, 4, 0] = numpy.sum(
x50 * (x0 * x129 + x12 * (x130 + x132 * x4) + x17 * x95 + x18 * x67)
)
result[0, 4, 1] = numpy.sum(
x50 * (x0 * x135 + x105 * x17 + x12 * (x102 + x132 * x7) + x18 * x79)
)
result[0, 4, 2] = numpy.sum(
x50 * (x0 * x138 + x109 * x17 + x12 * (x132 * x9 + x76) + x18 * x83)
)
result[0, 5, 0] = numpy.sum(
x78 * (x0 * x142 + x12 * (x143 + x146 * x4) + x18 * x94 + x18 * x95)
)
result[0, 5, 1] = numpy.sum(x78 * (x0 * x149 + x104 * x18 + x105 * x18 + x146 * x52))
result[0, 5, 2] = numpy.sum(
x78 * (x0 * x152 + x108 * x18 + x109 * x18 + x12 * (x103 + x146 * x9))
)
result[0, 6, 0] = numpy.sum(x51 * (x113 * x17 + x114 * x17 + x115 * x17 + x153 * x69))
result[0, 6, 1] = numpy.sum(
x51 * (x12 * (3.0 * x116 + x153 * x7) + x120 * x17 + x121 * x17 + x122 * x17)
)
result[0, 6, 2] = numpy.sum(x51 * (x123 * x17 + x124 * x17 + x125 * x17 + x153 * x56))
result[0, 7, 0] = numpy.sum(x78 * (x113 * x18 + x128 * x17 + x129 * x17 + x154 * x69))
result[0, 7, 1] = numpy.sum(
x78 * (x12 * (x154 * x7 + x155) + x120 * x18 + x134 * x17 + x135 * x17)
)
result[0, 7, 2] = numpy.sum(
x78 * (x12 * (x116 + x154 * x9) + x123 * x18 + x137 * x17 + x138 * x17)
)
result[0, 8, 0] = numpy.sum(x78 * (x127 * x18 + x128 * x18 + x142 * x17 + x156 * x69))
result[0, 8, 1] = numpy.sum(
x78 * (x12 * (x143 + x156 * x7) + x133 * x18 + x134 * x18 + x149 * x17)
)
result[0, 8, 2] = numpy.sum(
x78 * (x12 * (x155 + x156 * x9) + x136 * x18 + x137 * x18 + x152 * x17)
)
result[0, 9, 0] = numpy.sum(x51 * (x140 * x18 + x141 * x18 + x142 * x18 + x157 * x69))
result[0, 9, 1] = numpy.sum(x51 * (x147 * x18 + x148 * x18 + x149 * x18 + x157 * x52))
result[0, 9, 2] = numpy.sum(
x51 * (x12 * (3.0 * x143 + x157 * x9) + x150 * x18 + x151 * x18 + x152 * x18)
)
return result
[docs]
def int3c2e3d_sph_032(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sf|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 10, 6), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = 0.5 / (ax + bx)
x6 = x4**2
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = x8**2
x10 = -x2 * (ax * A[2] + bx * B[2])
x11 = -x10 - C[2]
x12 = x11**2
x13 = cx + x1
x14 = x13 ** (-1.0)
x15 = x1 * x14
x16 = cx * x15 * (x12 + x6 + x9)
x17 = boys(3, x16)
x18 = x13 ** (-1.5)
x19 = 17.49341832762486
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2))
x23 = x19 * x2 * x22
x24 = 2.0 * x18 * x23
x25 = x17 * x24
x26 = cx ** (-1.0)
x27 = x13 ** (-0.5)
x28 = boys(2, x16)
x29 = x5 * (2.0 * x19 * x2 * x22 * x26 * x27 * x28 - x25)
x30 = -x3 - A[0]
x31 = -2.0 * x19 * x2 * x22 * x26 * x27 * x28 * x30 + x25 * x4
x32 = -x31
x33 = boys(4, x16)
x34 = x24 * x33
x35 = 2.0 * x17 * x19 * x2 * x22 * x26 * x27 * x30 - x34 * x4
x36 = cx * x14
x37 = x35 * x36
x38 = x29 + x30 * x32 - x37 * x4
x39 = x38 * x4
x40 = x32 * x5
x41 = 2.0 * x40
x42 = x39 + x41
x43 = x15 * x4
x44 = x32 * x4
x45 = 2.0 * x5
x46 = x26 * x28
x47 = x45 * x46
x48 = x23 * x27 * x47
x49 = x44 + x48
x50 = x15 * x45
x51 = x15 * (x42 * x43 + x49 * x50)
x52 = x19 * x22
x53 = x4 * x52
x54 = x18 * x47
x55 = x15 * (x43 * x49 + x53 * x54)
x56 = x0 * x55 + x51
x57 = 2.0 * x1 * x13 ** (-2.5) * x46
x58 = x52 * x57
x59 = x0 * x58
x60 = x5 * (2.0 * x17 * x19 * x2 * x22 * x26 * x27 - x34)
x61 = x24 * boys(5, x16)
x62 = x36 * x4
x63 = (
x30 * x38
- x45 * (x31 + x37)
- x62
* (
x30 * x35
+ x60
- x62 * (2.0 * x19 * x2 * x22 * x26 * x27 * x30 * x33 - x4 * x61)
)
)
x64 = x4 * x63
x65 = x38 * x5
x66 = 3.0 * x65
x67 = x15 * x5
x68 = da * db * dc
x69 = 0.06666666666666667 * x68
x70 = 2.23606797749979 * x69
x71 = x15 * x8
x72 = x15 * x71 * (x39 + x41)
x73 = x52 * x54
x74 = x73 * x8
x75 = x15 * (x44 * x71 + x74)
x76 = x0 * x75 + x72
x77 = x53 * x57
x78 = x0 * x77
x79 = 3.872983346207417 * x69
x80 = x11 * x15
x81 = x15 * x80 * (x39 + x41)
x82 = x11 * x73
x83 = x15 * (x44 * x80 + x82)
x84 = x0 * x83 + x81
x85 = x1**2 / x13**2
x86 = x85 * x9
x87 = x38 * x86
x88 = x32 * x86
x89 = x0 * x88 + x87
x90 = x8 * x85
x91 = x11 * x90
x92 = x38 * x91
x93 = x32 * x91
x94 = x0 * x93 + x92
x95 = x11 * x8
x96 = x12 * x85
x97 = x38 * x96
x98 = x32 * x96
x99 = x0 * x98 + x97
x100 = -x7 - A[1]
x101 = -2.0 * x100 * x19 * x2 * x22 * x26 * x27 * x28 + x25 * x8
x102 = -x101
x103 = x102 * x5
x104 = 2.0 * x100 * x17 * x19 * x2 * x22 * x26 * x27 - x34 * x8
x105 = x104 * x36
x106 = x102 * x30 - x105 * x4
x107 = x106 * x4
x108 = x103 + x107
x109 = x15 * x43 * (x103 + x108)
x110 = x109 + x20 * x55
x111 = x6 * x85
x112 = x102 * x111
x113 = x20 * x58
x114 = x112 + x113 * x6
x115 = -x5 * (x101 + x105)
x116 = 2.0 * x100 * x19 * x2 * x22 * x26 * x27 * x33 - x61 * x8
x117 = x106 * x30 + x115 - x62 * (x104 * x30 - x116 * x62)
x118 = x117 * x4
x119 = x106 * x5
x120 = 2.0 * x119
x121 = 0.3333333333333333 * x68
x122 = x102 * x8
x123 = x122 + x48
x124 = x123 * x15
x125 = x106 * x8
x126 = x125 + x40
x127 = x15 * (x124 * x5 + x126 * x43)
x128 = x127 + x20 * x75
x129 = x4 * x85
x130 = x123 * x129
x131 = x20 * x77
x132 = x130 + x131 * x8
x133 = x117 * x8
x134 = x133 + x65
x135 = x126 * x50
x136 = 1.732050807568877 * x121
x137 = x103 * x80
x138 = x15 * (x107 * x80 + x137)
x139 = x138 + x20 * x83
x140 = x11 * x129
x141 = x102 * x140
x142 = x11 * x131 + x141
x143 = x120 * x80
x144 = x15 * x71 * (x126 + x40)
x145 = x144 + x20 * x88
x146 = x15 * (x124 * x8 + x74)
x147 = x113 * x9 + x146
x148 = x40 * x80
x149 = x15 * (x125 * x80 + x148)
x150 = x149 + x20 * x93
x151 = x15 * (x122 * x80 + x82)
x152 = x113 * x95 + x151
x153 = x65 * x80
x154 = x106 * x96
x155 = x154 + x20 * x98
x156 = x102 * x96
x157 = x113 * x12 + x156
x158 = -x10 - A[2]
x159 = x11 * x25 - 2.0 * x158 * x19 * x2 * x22 * x26 * x27 * x28
x160 = -x159
x161 = x160 * x5
x162 = -x11 * x34 + 2.0 * x158 * x17 * x19 * x2 * x22 * x26 * x27
x163 = x162 * x36
x164 = x160 * x30 - x163 * x4
x165 = x164 * x4
x166 = x161 + x165
x167 = x15 * x43 * (x161 + x166)
x168 = x167 + x21 * x55
x169 = x111 * x160
x170 = x21 * x58
x171 = x169 + x170 * x6
x172 = -x5 * (x159 + x163)
x173 = -x11 * x61 + 2.0 * x158 * x19 * x2 * x22 * x26 * x27 * x33
x174 = x164 * x30 + x172 - x62 * (x162 * x30 - x173 * x62)
x175 = x174 * x4
x176 = x164 * x5
x177 = 2.0 * x176
x178 = x161 * x71
x179 = x15 * (x165 * x71 + x178)
x180 = x179 + x21 * x75
x181 = x129 * x8
x182 = x160 * x181
x183 = x21 * x77
x184 = x182 + x183 * x8
x185 = x11 * x160 + x48
x186 = x15 * x185
x187 = x186 * x5
x188 = x11 * x164 + x40
x189 = x15 * (x187 + x188 * x43)
x190 = x189 + x21 * x83
x191 = x129 * x185
x192 = x11 * x183 + x191
x193 = x11 * x174 + x65
x194 = x188 * x50
x195 = x164 * x86
x196 = x195 + x21 * x88
x197 = x160 * x86
x198 = x170 * x9 + x197
x199 = x188 * x90
x200 = x199 + x21 * x93
x201 = x185 * x90
x202 = x170 * x95 + x201
x203 = x15 * (x148 + x188 * x80)
x204 = x203 + x21 * x98
x205 = x15 * (x11 * x186 + x82)
x206 = x12 * x170 + x205
x207 = x100 * x102 - x105 * x8 + x29
x208 = x111 * x207
x209 = x112 * x20 + x208
x210 = x114 * x20 + x209
x211 = x207 * x5
x212 = x36 * x8
x213 = x100 * x104 - x116 * x212 + x60
x214 = x207 * x30 - x213 * x62
x215 = x214 * x4
x216 = x207 * x8
x217 = 2.0 * x103
x218 = x216 + x217
x219 = x129 * x218
x220 = x130 * x20 + x219
x221 = x132 * x20 + x220
x222 = x218 * x67
x223 = x214 * x8
x224 = x120 + x223
x225 = x140 * x207
x226 = x141 * x20 + x225
x227 = x142 * x20 + x226
x228 = x211 * x80
x229 = x15 * (x124 * x45 + x218 * x71)
x230 = x146 * x20 + x229
x231 = x147 * x20 + x230
x232 = x15 * x80 * (x216 + x217)
x233 = x151 * x20 + x232
x234 = x152 * x20 + x233
x235 = x207 * x96
x236 = x156 * x20 + x235
x237 = x157 * x20 + x236
x238 = x100 * x160 - x163 * x8
x239 = x111 * x238
x240 = x112 * x21 + x239
x241 = x171 * x20 + x240
x242 = x238 * x5
x243 = x100 * x162 - x173 * x212
x244 = x238 * x30 - x243 * x62
x245 = x161 + x238 * x8
x246 = x129 * x245
x247 = x130 * x21 + x246
x248 = x184 * x20 + x247
x249 = x176 + x244 * x8
x250 = x103 + x11 * x238
x251 = x129 * x250
x252 = x141 * x21 + x251
x253 = x192 * x20 + x252
x254 = x11 * x244 + x119
x255 = x15 * (x178 + x245 * x71)
x256 = x146 * x21 + x255
x257 = x198 * x20 + x256
x258 = x15 * (x187 + x250 * x71)
x259 = x151 * x21 + x258
x260 = x20 * x202 + x259
x261 = x15 * (x137 + x250 * x80)
x262 = x156 * x21 + x261
x263 = x20 * x206 + x262
x264 = -x11 * x163 + x158 * x160 + x29
x265 = x111 * x264
x266 = x169 * x21 + x265
x267 = x171 * x21 + x266
x268 = x264 * x5
x269 = x11 * x36
x270 = x158 * x162 - x173 * x269 + x60
x271 = x264 * x30 - x270 * x62
x272 = x271 * x4
x273 = x181 * x264
x274 = x182 * x21 + x273
x275 = x184 * x21 + x274
x276 = x268 * x71
x277 = x11 * x264 + 2.0 * x161
x278 = x129 * x277
x279 = x191 * x21 + x278
x280 = x192 * x21 + x279
x281 = x277 * x67
x282 = x11 * x271 + x177
x283 = x264 * x86
x284 = x197 * x21 + x283
x285 = x198 * x21 + x284
x286 = x277 * x90
x287 = x201 * x21 + x286
x288 = x202 * x21 + x287
x289 = x15 * (x186 * x45 + x277 * x80)
x290 = x205 * x21 + x289
x291 = x206 * x21 + x290
x292 = x100 * x207 + 2.0 * x115 - x212 * x213
x293 = x292 * x8
x294 = 3.0 * x211
x295 = x293 + x294
x296 = x100 * x238 + x172 - x212 * x243
x297 = 2.0 * x242
x298 = x296 * x8 + x297
x299 = x11 * x296 + x211
x300 = x250 * x50
x301 = x100 * x264 - x212 * x270
x302 = x268 + x301 * x8
x303 = x11 * x301 + x297
x304 = x158 * x264 + 2.0 * x172 - x269 * x270
x305 = x11 * x304 + 3.0 * x268
# 60 item(s)
result[0, 0, 0] = numpy.sum(
x70
* (
x0 * x51
+ x0 * x56
+ x0 * (x0 * (x55 + x59 * x6) + x56)
+ x15 * (3.0 * x42 * x67 + x43 * (x64 + x66))
)
)
result[0, 0, 1] = numpy.sum(
x79
* (
x0 * x72
+ x0 * x76
+ x0 * (x0 * (x75 + x78 * x8) + x76)
+ x15 * x71 * (x64 + x66)
)
)
result[0, 0, 2] = numpy.sum(
x79
* (
x0 * x81
+ x0 * x84
+ x0 * (x0 * (x11 * x78 + x83) + x84)
+ x15 * x80 * (x64 + x66)
)
)
result[0, 0, 3] = numpy.sum(
x70 * (x0 * x87 + x0 * x89 + x0 * (x0 * (x59 * x9 + x88) + x89) + x63 * x86)
)
result[0, 0, 4] = numpy.sum(
x79 * (x0 * x92 + x0 * x94 + x0 * (x0 * (x59 * x95 + x93) + x94) + x63 * x91)
)
result[0, 0, 5] = numpy.sum(
x70 * (x0 * x97 + x0 * x99 + x0 * (x0 * (x12 * x59 + x98) + x99) + x63 * x96)
)
result[0, 1, 0] = numpy.sum(
x121
* (
x0 * x110
+ x0 * (x0 * x114 + x110)
+ x15 * (x108 * x50 + x43 * (x118 + x120))
+ x20 * x51
)
)
result[0, 1, 1] = numpy.sum(
x136
* (x0 * x128 + x0 * (x0 * x132 + x128) + x15 * (x134 * x43 + x135) + x20 * x72)
)
result[0, 1, 2] = numpy.sum(
x136
* (x0 * x139 + x0 * (x0 * x142 + x139) + x15 * (x118 * x80 + x143) + x20 * x81)
)
result[0, 1, 3] = numpy.sum(
x121
* (x0 * x145 + x0 * (x0 * x147 + x145) + x15 * x71 * (x134 + x65) + x20 * x87)
)
result[0, 1, 4] = numpy.sum(
x136
* (x0 * x150 + x0 * (x0 * x152 + x150) + x15 * (x133 * x80 + x153) + x20 * x92)
)
result[0, 1, 5] = numpy.sum(
x121 * (x0 * x155 + x0 * (x0 * x157 + x155) + x117 * x96 + x20 * x97)
)
result[0, 2, 0] = numpy.sum(
x121
* (
x0 * x168
+ x0 * (x0 * x171 + x168)
+ x15 * (x166 * x50 + x43 * (x175 + x177))
+ x21 * x51
)
)
result[0, 2, 1] = numpy.sum(
x136
* (x0 * x180 + x0 * (x0 * x184 + x180) + x15 * x71 * (x175 + x177) + x21 * x72)
)
result[0, 2, 2] = numpy.sum(
x136
* (x0 * x190 + x0 * (x0 * x192 + x190) + x15 * (x193 * x43 + x194) + x21 * x81)
)
result[0, 2, 3] = numpy.sum(
x121 * (x0 * x196 + x0 * (x0 * x198 + x196) + x174 * x86 + x21 * x87)
)
result[0, 2, 4] = numpy.sum(
x136 * (x0 * x200 + x0 * (x0 * x202 + x200) + x193 * x90 + x21 * x92)
)
result[0, 2, 5] = numpy.sum(
x121
* (x0 * x204 + x0 * (x0 * x206 + x204) + x15 * (x153 + x193 * x80) + x21 * x97)
)
result[0, 3, 0] = numpy.sum(
x121 * (x0 * x210 + x109 * x20 + x110 * x20 + x15 * x43 * (2.0 * x211 + x215))
)
result[0, 3, 1] = numpy.sum(
x136 * (x0 * x221 + x127 * x20 + x128 * x20 + x15 * (x222 + x224 * x43))
)
result[0, 3, 2] = numpy.sum(
x136 * (x0 * x227 + x138 * x20 + x139 * x20 + x15 * (x215 * x80 + x228))
)
result[0, 3, 3] = numpy.sum(
x121 * (x0 * x231 + x144 * x20 + x145 * x20 + x15 * (x135 + x224 * x71))
)
result[0, 3, 4] = numpy.sum(
x136 * (x0 * x234 + x149 * x20 + x15 * (x143 + x223 * x80) + x150 * x20)
)
result[0, 3, 5] = numpy.sum(x121 * (x0 * x237 + x154 * x20 + x155 * x20 + x214 * x96))
result[0, 4, 0] = numpy.sum(
x136
* (x0 * x241 + x109 * x21 + x15 * x43 * (2.0 * x242 + x244 * x4) + x168 * x20)
)
result[0, 4, 1] = numpy.sum(
x68 * (x0 * x248 + x127 * x21 + x15 * (x245 * x67 + x249 * x43) + x180 * x20)
)
result[0, 4, 2] = numpy.sum(
x68 * (x0 * x253 + x138 * x21 + x15 * (x250 * x67 + x254 * x43) + x190 * x20)
)
result[0, 4, 3] = numpy.sum(
x136 * (x0 * x257 + x144 * x21 + x15 * x71 * (x176 + x249) + x196 * x20)
)
result[0, 4, 4] = numpy.sum(
x68 * (x0 * x260 + x149 * x21 + x15 * (x188 * x67 + x254 * x71) + x20 * x200)
)
result[0, 4, 5] = numpy.sum(
x136 * (x0 * x263 + x15 * x80 * (x119 + x254) + x154 * x21 + x20 * x204)
)
result[0, 5, 0] = numpy.sum(
x121 * (x0 * x267 + x15 * x43 * (2.0 * x268 + x272) + x167 * x21 + x168 * x21)
)
result[0, 5, 1] = numpy.sum(
x136 * (x0 * x275 + x15 * (x272 * x71 + x276) + x179 * x21 + x180 * x21)
)
result[0, 5, 2] = numpy.sum(
x136 * (x0 * x280 + x15 * (x281 + x282 * x43) + x189 * x21 + x190 * x21)
)
result[0, 5, 3] = numpy.sum(x121 * (x0 * x285 + x195 * x21 + x196 * x21 + x271 * x86))
result[0, 5, 4] = numpy.sum(x136 * (x0 * x288 + x199 * x21 + x200 * x21 + x282 * x90))
result[0, 5, 5] = numpy.sum(
x121 * (x0 * x291 + x15 * (x194 + x282 * x80) + x203 * x21 + x204 * x21)
)
result[0, 6, 0] = numpy.sum(
x70 * (x111 * x292 + x20 * x208 + x20 * x209 + x20 * x210)
)
result[0, 6, 1] = numpy.sum(
x79 * (x129 * x295 + x20 * x219 + x20 * x220 + x20 * x221)
)
result[0, 6, 2] = numpy.sum(
x79 * (x140 * x292 + x20 * x225 + x20 * x226 + x20 * x227)
)
result[0, 6, 3] = numpy.sum(
x70 * (x15 * (3.0 * x222 + x295 * x71) + x20 * x229 + x20 * x230 + x20 * x231)
)
result[0, 6, 4] = numpy.sum(
x79 * (x15 * x80 * (x293 + x294) + x20 * x232 + x20 * x233 + x20 * x234)
)
result[0, 6, 5] = numpy.sum(x70 * (x20 * x235 + x20 * x236 + x20 * x237 + x292 * x96))
result[0, 7, 0] = numpy.sum(
x121 * (x111 * x296 + x20 * x240 + x20 * x241 + x208 * x21)
)
result[0, 7, 1] = numpy.sum(
x136 * (x129 * x298 + x20 * x247 + x20 * x248 + x21 * x219)
)
result[0, 7, 2] = numpy.sum(
x136 * (x129 * x299 + x20 * x252 + x20 * x253 + x21 * x225)
)
result[0, 7, 3] = numpy.sum(
x121 * (x15 * (x245 * x50 + x298 * x71) + x20 * x256 + x20 * x257 + x21 * x229)
)
result[0, 7, 4] = numpy.sum(
x136 * (x15 * (x299 * x71 + x300) + x20 * x259 + x20 * x260 + x21 * x232)
)
result[0, 7, 5] = numpy.sum(
x121 * (x15 * (x228 + x299 * x80) + x20 * x262 + x20 * x263 + x21 * x235)
)
result[0, 8, 0] = numpy.sum(
x121 * (x111 * x301 + x20 * x267 + x21 * x239 + x21 * x240)
)
result[0, 8, 1] = numpy.sum(
x136 * (x129 * x302 + x20 * x275 + x21 * x246 + x21 * x247)
)
result[0, 8, 2] = numpy.sum(
x136 * (x129 * x303 + x20 * x280 + x21 * x251 + x21 * x252)
)
result[0, 8, 3] = numpy.sum(
x121 * (x15 * (x276 + x302 * x71) + x20 * x285 + x21 * x255 + x21 * x256)
)
result[0, 8, 4] = numpy.sum(
x136 * (x15 * (x281 + x303 * x71) + x20 * x288 + x21 * x258 + x21 * x259)
)
result[0, 8, 5] = numpy.sum(
x121 * (x15 * (x300 + x303 * x80) + x20 * x291 + x21 * x261 + x21 * x262)
)
result[0, 9, 0] = numpy.sum(
x70 * (x111 * x304 + x21 * x265 + x21 * x266 + x21 * x267)
)
result[0, 9, 1] = numpy.sum(
x79 * (x181 * x304 + x21 * x273 + x21 * x274 + x21 * x275)
)
result[0, 9, 2] = numpy.sum(
x79 * (x129 * x305 + x21 * x278 + x21 * x279 + x21 * x280)
)
result[0, 9, 3] = numpy.sum(x70 * (x21 * x283 + x21 * x284 + x21 * x285 + x304 * x86))
result[0, 9, 4] = numpy.sum(x79 * (x21 * x286 + x21 * x287 + x21 * x288 + x305 * x90))
result[0, 9, 5] = numpy.sum(
x70 * (x15 * (3.0 * x281 + x305 * x80) + x21 * x289 + x21 * x290 + x21 * x291)
)
return result
[docs]
def int3c2e3d_sph_033(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sf|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 10, 10), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = 0.5 / (ax + bx)
x6 = x4**2
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = x8**2
x10 = -x2 * (ax * A[2] + bx * B[2])
x11 = -x10 - C[2]
x12 = x11**2
x13 = cx + x1
x14 = x13 ** (-1.0)
x15 = x1 * x14
x16 = cx * x15 * (x12 + x6 + x9)
x17 = boys(4, x16)
x18 = x13 ** (-1.5)
x19 = 17.49341832762486
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2))
x23 = x19 * x22
x24 = x2 * x23
x25 = 2.0 * x18 * x24
x26 = x17 * x25
x27 = cx ** (-1.0)
x28 = x13 ** (-0.5)
x29 = boys(3, x16)
x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26)
x31 = -x3 - A[0]
x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4
x33 = -x32
x34 = boys(5, x16)
x35 = x25 * x34
x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4
x37 = cx * x14
x38 = x36 * x37
x39 = x30 + x31 * x33 - x38 * x4
x40 = x39 * x4
x41 = x33 * x5
x42 = 2.0 * x41
x43 = x40 + x42
x44 = x15 * x4
x45 = x33 * x4
x46 = 2.0 * x5
x47 = x27 * x29
x48 = x46 * x47
x49 = x24 * x28 * x48
x50 = x45 + x49
x51 = x15 * x46
x52 = x43 * x44 + x50 * x51
x53 = x23 * x48
x54 = x18 * x53
x55 = x4 * x54 + x44 * x50
x56 = x15 * (x44 * x52 + x51 * x55)
x57 = x1 * x13 ** (-2.5) * x53
x58 = x15 * (x44 * x55 + x57 * x6)
x59 = x0 * x58 + x56
x60 = x4**3
x61 = x1**2
x62 = 2.0 * x13 ** (-3.5) * x23 * x47 * x61
x63 = x0 * x62
x64 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35)
x65 = x25 * boys(6, x16)
x66 = x37 * x4
x67 = (
x31 * x39
- x46 * (x32 + x38)
- x66
* (
x31 * x36
+ x64
- x66 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x65)
)
)
x68 = x4 * x67
x69 = x39 * x5
x70 = 3.0 * x69
x71 = x15 * x5
x72 = 3.0 * x71
x73 = da * db * dc
x74 = 0.06666666666666667 * x73
x75 = x15 * x8
x76 = x75 * (x40 + x42)
x77 = x54 * x8
x78 = x45 * x75 + x77
x79 = x15 * (x44 * x76 + x51 * x78)
x80 = x4 * x8
x81 = x15 * (x44 * x78 + x57 * x80)
x82 = x0 * x81 + x79
x83 = x6 * x63
x84 = 2.23606797749979 * x74
x85 = x11 * x15
x86 = x85 * (x40 + x42)
x87 = x11 * x54
x88 = x45 * x85 + x87
x89 = x15 * (x44 * x86 + x51 * x88)
x90 = x11 * x57
x91 = x15 * (x4 * x90 + x44 * x88)
x92 = x0 * x91 + x89
x93 = x61 / x13**2
x94 = x9 * x93
x95 = x15 * x94 * (x40 + x42)
x96 = x57 * x9
x97 = x15 * (x45 * x94 + x96)
x98 = x0 * x97 + x95
x99 = x4 * x63
x100 = x8 * x93
x101 = x100 * x11
x102 = x101 * x15 * (x40 + x42)
x103 = x8 * x90
x104 = x15 * (x101 * x45 + x103)
x105 = x0 * x104 + x102
x106 = x11 * x80
x107 = 3.872983346207417 * x74
x108 = x12 * x93
x109 = x108 * x15 * (x40 + x42)
x110 = x12 * x57
x111 = x15 * (x108 * x45 + x110)
x112 = x0 * x111 + x109
x113 = x8**3
x114 = x1**3 / x13**3
x115 = x113 * x114
x116 = x115 * x39
x117 = x115 * x33
x118 = x0 * x117 + x116
x119 = x114 * x9
x120 = x11 * x119
x121 = x120 * x39
x122 = x120 * x33
x123 = x0 * x122 + x121
x124 = x11 * x9
x125 = x114 * x12
x126 = x125 * x8
x127 = x126 * x39
x128 = x126 * x33
x129 = x0 * x128 + x127
x130 = x12 * x8
x131 = x11**3
x132 = x114 * x131
x133 = x132 * x39
x134 = x132 * x33
x135 = x0 * x134 + x133
x136 = -x7 - A[1]
x137 = -2.0 * x136 * x19 * x2 * x22 * x27 * x28 * x29 + x26 * x8
x138 = -x137
x139 = x138 * x5
x140 = 2.0 * x136 * x17 * x19 * x2 * x22 * x27 * x28 - x35 * x8
x141 = x140 * x37
x142 = x138 * x31 - x141 * x4
x143 = x142 * x4
x144 = x139 + x143
x145 = x44 * (x139 + x144)
x146 = x6 * x93
x147 = x15 * (x139 * x146 + x145 * x44)
x148 = x147 + x20 * x58
x149 = x114 * x60
x150 = x138 * x149
x151 = x20 * x62
x152 = x150 + x151 * x60
x153 = -x5 * (x137 + x141)
x154 = 2.0 * x136 * x19 * x2 * x22 * x27 * x28 * x34 - x65 * x8
x155 = x142 * x31 + x153 - x66 * (x140 * x31 - x154 * x66)
x156 = x155 * x4
x157 = x142 * x5
x158 = 2.0 * x157
x159 = x138 * x8
x160 = x159 + x49
x161 = x15 * x160
x162 = x142 * x8
x163 = x162 + x41
x164 = x161 * x5 + x163 * x44
x165 = x4 * x93
x166 = x165 * x5
x167 = x15 * (x160 * x166 + x164 * x44)
x168 = x167 + x20 * x81
x169 = x114 * x6
x170 = x160 * x169
x171 = x151 * x6
x172 = x170 + x171 * x8
x173 = x155 * x8
x174 = x173 + x69
x175 = x163 * x51
x176 = 0.3333333333333333 * x73
x177 = x139 * x85
x178 = x143 * x85 + x177
x179 = x11 * x165
x180 = x15 * (x139 * x179 + x178 * x44)
x181 = x180 + x20 * x91
x182 = x11 * x169
x183 = x138 * x182
x184 = x11 * x171 + x183
x185 = x158 * x85
x186 = x161 * x8 + x77
x187 = x75 * (x163 + x41)
x188 = x15 * (x186 * x71 + x187 * x44)
x189 = x188 + x20 * x97
x190 = x165 * x186
x191 = x151 * x4
x192 = x190 + x191 * x9
x193 = x75 * (x174 + x69)
x194 = x187 * x51
x195 = x159 * x85 + x87
x196 = x41 * x85
x197 = x162 * x85 + x196
x198 = x15 * (x195 * x71 + x197 * x44)
x199 = x104 * x20 + x198
x200 = x165 * x195
x201 = x106 * x151 + x200
x202 = x69 * x85
x203 = x173 * x85 + x202
x204 = x197 * x51
x205 = 1.732050807568877 * x176
x206 = x108 * x139
x207 = x15 * (x108 * x143 + x206)
x208 = x111 * x20 + x207
x209 = x125 * x4
x210 = x138 * x209
x211 = x12 * x191 + x210
x212 = x108 * x158
x213 = x15 * (x187 * x75 + x41 * x94)
x214 = x117 * x20 + x213
x215 = x15 * (x186 * x75 + x96)
x216 = x113 * x151 + x215
x217 = x15 * (x101 * x41 + x197 * x75)
x218 = x122 * x20 + x217
x219 = x15 * (x103 + x195 * x75)
x220 = x124 * x151 + x219
x221 = x108 * x41
x222 = x15 * (x108 * x162 + x221)
x223 = x128 * x20 + x222
x224 = x15 * (x108 * x159 + x110)
x225 = x130 * x151 + x224
x226 = x108 * x69
x227 = x132 * x142
x228 = x134 * x20 + x227
x229 = x132 * x138
x230 = x131 * x151 + x229
x231 = -x10 - A[2]
x232 = x11 * x26 - 2.0 * x19 * x2 * x22 * x231 * x27 * x28 * x29
x233 = -x232
x234 = x233 * x5
x235 = -x11 * x35 + 2.0 * x17 * x19 * x2 * x22 * x231 * x27 * x28
x236 = x235 * x37
x237 = x233 * x31 - x236 * x4
x238 = x237 * x4
x239 = x234 + x238
x240 = x44 * (x234 + x239)
x241 = x15 * (x146 * x234 + x240 * x44)
x242 = x21 * x58 + x241
x243 = x149 * x233
x244 = x21 * x62
x245 = x243 + x244 * x60
x246 = -x5 * (x232 + x236)
x247 = -x11 * x65 + 2.0 * x19 * x2 * x22 * x231 * x27 * x28 * x34
x248 = x237 * x31 + x246 - x66 * (x235 * x31 - x247 * x66)
x249 = x248 * x4
x250 = x237 * x5
x251 = 2.0 * x250
x252 = x234 * x75
x253 = x238 * x75 + x252
x254 = x165 * x8
x255 = x15 * (x234 * x254 + x253 * x44)
x256 = x21 * x81 + x255
x257 = x169 * x8
x258 = x233 * x257
x259 = x244 * x6
x260 = x258 + x259 * x8
x261 = x11 * x233 + x49
x262 = x261 * x71
x263 = x11 * x237 + x41
x264 = x262 + x263 * x44
x265 = x15 * (x166 * x261 + x264 * x44)
x266 = x21 * x91 + x265
x267 = x169 * x261
x268 = x11 * x259 + x267
x269 = x11 * x248 + x69
x270 = x263 * x51
x271 = x234 * x94
x272 = x15 * (x238 * x94 + x271)
x273 = x21 * x97 + x272
x274 = x119 * x4
x275 = x233 * x274
x276 = x244 * x4
x277 = x275 + x276 * x9
x278 = x100 * x5
x279 = x261 * x278
x280 = x15 * (x254 * x263 + x279)
x281 = x104 * x21 + x280
x282 = x114 * x80
x283 = x261 * x282
x284 = x106 * x244 + x283
x285 = x261 * x85 + x87
x286 = x285 * x71
x287 = x196 + x263 * x85
x288 = x15 * (x286 + x287 * x44)
x289 = x111 * x21 + x288
x290 = x165 * x285
x291 = x12 * x276 + x290
x292 = x202 + x269 * x85
x293 = x287 * x51
x294 = x115 * x237
x295 = x117 * x21 + x294
x296 = x115 * x233
x297 = x113 * x244 + x296
x298 = x119 * x263
x299 = x122 * x21 + x298
x300 = x119 * x261
x301 = x124 * x244 + x300
x302 = x100 * x287
x303 = x128 * x21 + x302
x304 = x100 * x285
x305 = x130 * x244 + x304
x306 = x15 * (x221 + x287 * x85)
x307 = x134 * x21 + x306
x308 = x15 * (x110 + x285 * x85)
x309 = x131 * x244 + x308
x310 = x136 * x138 - x141 * x8 + x30
x311 = x149 * x310
x312 = x150 * x20 + x311
x313 = x152 * x20 + x312
x314 = x310 * x5
x315 = x37 * x8
x316 = x136 * x140 - x154 * x315 + x64
x317 = x31 * x310 - x316 * x66
x318 = x317 * x4
x319 = x310 * x8
x320 = 2.0 * x139
x321 = x319 + x320
x322 = x169 * x321
x323 = x170 * x20 + x322
x324 = x172 * x20 + x323
x325 = x321 * x71
x326 = x317 * x8
x327 = x158 + x326
x328 = x182 * x310
x329 = x183 * x20 + x328
x330 = x184 * x20 + x329
x331 = x314 * x85
x332 = x161 * x46 + x321 * x75
x333 = x165 * x332
x334 = x190 * x20 + x333
x335 = x192 * x20 + x334
x336 = x332 * x71
x337 = x175 + x327 * x75
x338 = x85 * (x319 + x320)
x339 = x165 * x338
x340 = x20 * x200 + x339
x341 = x20 * x201 + x340
x342 = x338 * x71
x343 = x185 + x326 * x85
x344 = x209 * x310
x345 = x20 * x210 + x344
x346 = x20 * x211 + x345
x347 = x108 * x314
x348 = x15 * (x186 * x51 + x332 * x75)
x349 = x20 * x215 + x348
x350 = x20 * x216 + x349
x351 = x15 * (x195 * x51 + x338 * x75)
x352 = x20 * x219 + x351
x353 = x20 * x220 + x352
x354 = x108 * x15 * (x319 + x320)
x355 = x20 * x224 + x354
x356 = x20 * x225 + x355
x357 = x132 * x310
x358 = x20 * x229 + x357
x359 = x20 * x230 + x358
x360 = x136 * x233 - x236 * x8
x361 = x149 * x360
x362 = x150 * x21 + x361
x363 = x20 * x245 + x362
x364 = x360 * x5
x365 = x136 * x235 - x247 * x315
x366 = x31 * x360 - x365 * x66
x367 = x234 + x360 * x8
x368 = x169 * x367
x369 = x170 * x21 + x368
x370 = x20 * x260 + x369
x371 = x250 + x366 * x8
x372 = x11 * x360 + x139
x373 = x169 * x372
x374 = x183 * x21 + x373
x375 = x20 * x268 + x374
x376 = x11 * x366 + x157
x377 = x252 + x367 * x75
x378 = x165 * x377
x379 = x190 * x21 + x378
x380 = x20 * x277 + x379
x381 = x75 * (x250 + x371)
x382 = x262 + x372 * x75
x383 = x165 * x382
x384 = x200 * x21 + x383
x385 = x20 * x284 + x384
x386 = x263 * x71 + x376 * x75
x387 = x177 + x372 * x85
x388 = x165 * x387
x389 = x21 * x210 + x388
x390 = x20 * x291 + x389
x391 = x85 * (x157 + x376)
x392 = x15 * (x271 + x377 * x75)
x393 = x21 * x215 + x392
x394 = x20 * x297 + x393
x395 = x15 * (x279 + x382 * x75)
x396 = x21 * x219 + x395
x397 = x20 * x301 + x396
x398 = x15 * (x286 + x387 * x75)
x399 = x21 * x224 + x398
x400 = x20 * x305 + x399
x401 = x15 * (x206 + x387 * x85)
x402 = x21 * x229 + x401
x403 = x20 * x309 + x402
x404 = -x11 * x236 + x231 * x233 + x30
x405 = x149 * x404
x406 = x21 * x243 + x405
x407 = x21 * x245 + x406
x408 = x404 * x5
x409 = x11 * x37
x410 = x231 * x235 - x247 * x409 + x64
x411 = x31 * x404 - x410 * x66
x412 = x4 * x411
x413 = x257 * x404
x414 = x21 * x258 + x413
x415 = x21 * x260 + x414
x416 = x408 * x75
x417 = x11 * x404 + 2.0 * x234
x418 = x169 * x417
x419 = x21 * x267 + x418
x420 = x21 * x268 + x419
x421 = x417 * x71
x422 = x11 * x411 + x251
x423 = x274 * x404
x424 = x21 * x275 + x423
x425 = x21 * x277 + x424
x426 = x408 * x94
x427 = x282 * x417
x428 = x21 * x283 + x427
x429 = x21 * x284 + x428
x430 = x278 * x417
x431 = x261 * x51 + x417 * x85
x432 = x165 * x431
x433 = x21 * x290 + x432
x434 = x21 * x291 + x433
x435 = x431 * x71
x436 = x270 + x422 * x85
x437 = x115 * x404
x438 = x21 * x296 + x437
x439 = x21 * x297 + x438
x440 = x119 * x417
x441 = x21 * x300 + x440
x442 = x21 * x301 + x441
x443 = x100 * x431
x444 = x21 * x304 + x443
x445 = x21 * x305 + x444
x446 = x15 * (x285 * x51 + x431 * x85)
x447 = x21 * x308 + x446
x448 = x21 * x309 + x447
x449 = x136 * x310 + 2.0 * x153 - x315 * x316
x450 = x449 * x8
x451 = 3.0 * x314
x452 = x450 + x451
x453 = 3.0 * x325 + x452 * x75
x454 = x85 * (x450 + x451)
x455 = x136 * x360 + x246 - x315 * x365
x456 = 2.0 * x364
x457 = x455 * x8 + x456
x458 = x11 * x455 + x314
x459 = x367 * x51 + x457 * x75
x460 = x372 * x51
x461 = x458 * x75 + x460
x462 = x331 + x458 * x85
x463 = x387 * x51
x464 = x136 * x404 - x315 * x410
x465 = x408 + x464 * x8
x466 = x11 * x464 + x456
x467 = x416 + x465 * x75
x468 = x421 + x466 * x75
x469 = x460 + x466 * x85
x470 = x231 * x404 + 2.0 * x246 - x409 * x410
x471 = x11 * x470 + 3.0 * x408
x472 = 3.0 * x421 + x471 * x85
# 100 item(s)
result[0, 0, 0] = numpy.sum(
x74
* (
x0 * x56
+ x0 * x59
+ x0 * (x0 * (x58 + x60 * x63) + x59)
+ x15 * (x44 * (x43 * x72 + x44 * (x68 + x70)) + x52 * x72)
)
)
result[0, 0, 1] = numpy.sum(
x84
* (
x0 * x79
+ x0 * x82
+ x0 * (x0 * (x8 * x83 + x81) + x82)
+ x15 * (x44 * x75 * (x68 + x70) + x72 * x76)
)
)
result[0, 0, 2] = numpy.sum(
x84
* (
x0 * x89
+ x0 * x92
+ x0 * (x0 * (x11 * x83 + x91) + x92)
+ x15 * (x44 * x85 * (x68 + x70) + x72 * x86)
)
)
result[0, 0, 3] = numpy.sum(
x84
* (
x0 * x95
+ x0 * x98
+ x0 * (x0 * (x9 * x99 + x97) + x98)
+ x15 * x94 * (x68 + x70)
)
)
result[0, 0, 4] = numpy.sum(
x107
* (
x0 * x102
+ x0 * x105
+ x0 * (x0 * (x104 + x106 * x63) + x105)
+ x101 * x15 * (x68 + x70)
)
)
result[0, 0, 5] = numpy.sum(
x84
* (
x0 * x109
+ x0 * x112
+ x0 * (x0 * (x111 + x12 * x99) + x112)
+ x108 * x15 * (x68 + x70)
)
)
result[0, 0, 6] = numpy.sum(
x74
* (x0 * x116 + x0 * x118 + x0 * (x0 * (x113 * x63 + x117) + x118) + x115 * x67)
)
result[0, 0, 7] = numpy.sum(
x84
* (x0 * x121 + x0 * x123 + x0 * (x0 * (x122 + x124 * x63) + x123) + x120 * x67)
)
result[0, 0, 8] = numpy.sum(
x84
* (x0 * x127 + x0 * x129 + x0 * (x0 * (x128 + x130 * x63) + x129) + x126 * x67)
)
result[0, 0, 9] = numpy.sum(
x74
* (x0 * x133 + x0 * x135 + x0 * (x0 * (x131 * x63 + x134) + x135) + x132 * x67)
)
result[0, 1, 0] = numpy.sum(
x84
* (
x0 * x148
+ x0 * (x0 * x152 + x148)
+ x15 * (x145 * x51 + x44 * (x144 * x51 + x44 * (x156 + x158)))
+ x20 * x56
)
)
result[0, 1, 1] = numpy.sum(
x176
* (
x0 * x168
+ x0 * (x0 * x172 + x168)
+ x15 * (x164 * x51 + x44 * (x174 * x44 + x175))
+ x20 * x79
)
)
result[0, 1, 2] = numpy.sum(
x176
* (
x0 * x181
+ x0 * (x0 * x184 + x181)
+ x15 * (x178 * x51 + x44 * (x156 * x85 + x185))
+ x20 * x89
)
)
result[0, 1, 3] = numpy.sum(
x176
* (x0 * x189 + x0 * (x0 * x192 + x189) + x15 * (x193 * x44 + x194) + x20 * x95)
)
result[0, 1, 4] = numpy.sum(
x205
* (x0 * x199 + x0 * (x0 * x201 + x199) + x102 * x20 + x15 * (x203 * x44 + x204))
)
result[0, 1, 5] = numpy.sum(
x176
* (x0 * x208 + x0 * (x0 * x211 + x208) + x109 * x20 + x15 * (x108 * x156 + x212))
)
result[0, 1, 6] = numpy.sum(
x84
* (
x0 * x214
+ x0 * (x0 * x216 + x214)
+ x116 * x20
+ x15 * (x193 * x75 + x69 * x94)
)
)
result[0, 1, 7] = numpy.sum(
x176
* (
x0 * x218
+ x0 * (x0 * x220 + x218)
+ x121 * x20
+ x15 * (x101 * x69 + x203 * x75)
)
)
result[0, 1, 8] = numpy.sum(
x176
* (x0 * x223 + x0 * (x0 * x225 + x223) + x127 * x20 + x15 * (x108 * x173 + x226))
)
result[0, 1, 9] = numpy.sum(
x84 * (x0 * x228 + x0 * (x0 * x230 + x228) + x132 * x155 + x133 * x20)
)
result[0, 2, 0] = numpy.sum(
x84
* (
x0 * x242
+ x0 * (x0 * x245 + x242)
+ x15 * (x240 * x51 + x44 * (x239 * x51 + x44 * (x249 + x251)))
+ x21 * x56
)
)
result[0, 2, 1] = numpy.sum(
x176
* (
x0 * x256
+ x0 * (x0 * x260 + x256)
+ x15 * (x253 * x51 + x44 * x75 * (x249 + x251))
+ x21 * x79
)
)
result[0, 2, 2] = numpy.sum(
x176
* (
x0 * x266
+ x0 * (x0 * x268 + x266)
+ x15 * (x264 * x51 + x44 * (x269 * x44 + x270))
+ x21 * x89
)
)
result[0, 2, 3] = numpy.sum(
x176
* (x0 * x273 + x0 * (x0 * x277 + x273) + x15 * x94 * (x249 + x251) + x21 * x95)
)
result[0, 2, 4] = numpy.sum(
x205
* (
x0 * x281
+ x0 * (x0 * x284 + x281)
+ x102 * x21
+ x15 * (x100 * x263 * x46 + x254 * x269)
)
)
result[0, 2, 5] = numpy.sum(
x176
* (x0 * x289 + x0 * (x0 * x291 + x289) + x109 * x21 + x15 * (x292 * x44 + x293))
)
result[0, 2, 6] = numpy.sum(
x84 * (x0 * x295 + x0 * (x0 * x297 + x295) + x115 * x248 + x116 * x21)
)
result[0, 2, 7] = numpy.sum(
x176 * (x0 * x299 + x0 * (x0 * x301 + x299) + x119 * x269 + x121 * x21)
)
result[0, 2, 8] = numpy.sum(
x176 * (x0 * x303 + x0 * (x0 * x305 + x303) + x100 * x292 + x127 * x21)
)
result[0, 2, 9] = numpy.sum(
x84
* (x0 * x307 + x0 * (x0 * x309 + x307) + x133 * x21 + x15 * (x226 + x292 * x85))
)
result[0, 3, 0] = numpy.sum(
x84
* (
x0 * x313
+ x147 * x20
+ x148 * x20
+ x15 * (x146 * x314 + x44**2 * (2.0 * x314 + x318))
)
)
result[0, 3, 1] = numpy.sum(
x176
* (
x0 * x324
+ x15 * (x166 * x321 + x44 * (x325 + x327 * x44))
+ x167 * x20
+ x168 * x20
)
)
result[0, 3, 2] = numpy.sum(
x176
* (
x0 * x330
+ x15 * (x179 * x314 + x44 * (x318 * x85 + x331))
+ x180 * x20
+ x181 * x20
)
)
result[0, 3, 3] = numpy.sum(
x176 * (x0 * x335 + x15 * (x336 + x337 * x44) + x188 * x20 + x189 * x20)
)
result[0, 3, 4] = numpy.sum(
x205 * (x0 * x341 + x15 * (x342 + x343 * x44) + x198 * x20 + x199 * x20)
)
result[0, 3, 5] = numpy.sum(
x176 * (x0 * x346 + x15 * (x108 * x318 + x347) + x20 * x207 + x20 * x208)
)
result[0, 3, 6] = numpy.sum(
x84 * (x0 * x350 + x15 * (x194 + x337 * x75) + x20 * x213 + x20 * x214)
)
result[0, 3, 7] = numpy.sum(
x176 * (x0 * x353 + x15 * (x204 + x343 * x75) + x20 * x217 + x20 * x218)
)
result[0, 3, 8] = numpy.sum(
x176 * (x0 * x356 + x15 * (x108 * x326 + x212) + x20 * x222 + x20 * x223)
)
result[0, 3, 9] = numpy.sum(x84 * (x0 * x359 + x132 * x317 + x20 * x227 + x20 * x228))
result[0, 4, 0] = numpy.sum(
x107
* (
x0 * x363
+ x147 * x21
+ x15 * (x146 * x364 + x44**2 * (2.0 * x364 + x366 * x4))
+ x20 * x242
)
)
result[0, 4, 1] = numpy.sum(
x205
* (
x0 * x370
+ x15 * (x166 * x367 + x44 * (x367 * x71 + x371 * x44))
+ x167 * x21
+ x20 * x256
)
)
result[0, 4, 2] = numpy.sum(
x205
* (
x0 * x375
+ x15 * (x166 * x372 + x44 * (x372 * x71 + x376 * x44))
+ x180 * x21
+ x20 * x266
)
)
result[0, 4, 3] = numpy.sum(
x205 * (x0 * x380 + x15 * (x377 * x71 + x381 * x44) + x188 * x21 + x20 * x273)
)
result[0, 4, 4] = numpy.sum(
x73 * (x0 * x385 + x15 * (x382 * x71 + x386 * x44) + x198 * x21 + x20 * x281)
)
result[0, 4, 5] = numpy.sum(
x205 * (x0 * x390 + x15 * (x387 * x71 + x391 * x44) + x20 * x289 + x207 * x21)
)
result[0, 4, 6] = numpy.sum(
x107 * (x0 * x394 + x15 * (x250 * x94 + x381 * x75) + x20 * x295 + x21 * x213)
)
result[0, 4, 7] = numpy.sum(
x205 * (x0 * x397 + x15 * (x263 * x278 + x386 * x75) + x20 * x299 + x21 * x217)
)
result[0, 4, 8] = numpy.sum(
x205 * (x0 * x400 + x15 * (x287 * x71 + x391 * x75) + x20 * x303 + x21 * x222)
)
result[0, 4, 9] = numpy.sum(
x107 * (x0 * x403 + x15 * (x108 * x157 + x391 * x85) + x20 * x307 + x21 * x227)
)
result[0, 5, 0] = numpy.sum(
x84
* (
x0 * x407
+ x15 * (x146 * x408 + x44**2 * (2.0 * x408 + x412))
+ x21 * x241
+ x21 * x242
)
)
result[0, 5, 1] = numpy.sum(
x176
* (
x0 * x415
+ x15 * (x254 * x408 + x44 * (x412 * x75 + x416))
+ x21 * x255
+ x21 * x256
)
)
result[0, 5, 2] = numpy.sum(
x176
* (
x0 * x420
+ x15 * (x166 * x417 + x44 * (x421 + x422 * x44))
+ x21 * x265
+ x21 * x266
)
)
result[0, 5, 3] = numpy.sum(
x176 * (x0 * x425 + x15 * (x412 * x94 + x426) + x21 * x272 + x21 * x273)
)
result[0, 5, 4] = numpy.sum(
x205 * (x0 * x429 + x15 * (x254 * x422 + x430) + x21 * x280 + x21 * x281)
)
result[0, 5, 5] = numpy.sum(
x176 * (x0 * x434 + x15 * (x435 + x436 * x44) + x21 * x288 + x21 * x289)
)
result[0, 5, 6] = numpy.sum(x84 * (x0 * x439 + x115 * x411 + x21 * x294 + x21 * x295))
result[0, 5, 7] = numpy.sum(
x176 * (x0 * x442 + x119 * x422 + x21 * x298 + x21 * x299)
)
result[0, 5, 8] = numpy.sum(
x176 * (x0 * x445 + x100 * x436 + x21 * x302 + x21 * x303)
)
result[0, 5, 9] = numpy.sum(
x84 * (x0 * x448 + x15 * (x293 + x436 * x85) + x21 * x306 + x21 * x307)
)
result[0, 6, 0] = numpy.sum(
x74 * (x149 * x449 + x20 * x311 + x20 * x312 + x20 * x313)
)
result[0, 6, 1] = numpy.sum(
x84 * (x169 * x452 + x20 * x322 + x20 * x323 + x20 * x324)
)
result[0, 6, 2] = numpy.sum(
x84 * (x182 * x449 + x20 * x328 + x20 * x329 + x20 * x330)
)
result[0, 6, 3] = numpy.sum(
x84 * (x165 * x453 + x20 * x333 + x20 * x334 + x20 * x335)
)
result[0, 6, 4] = numpy.sum(
x107 * (x165 * x454 + x20 * x339 + x20 * x340 + x20 * x341)
)
result[0, 6, 5] = numpy.sum(
x84 * (x20 * x344 + x20 * x345 + x20 * x346 + x209 * x449)
)
result[0, 6, 6] = numpy.sum(
x74 * (x15 * (3.0 * x336 + x453 * x75) + x20 * x348 + x20 * x349 + x20 * x350)
)
result[0, 6, 7] = numpy.sum(
x84 * (x15 * (3.0 * x342 + x454 * x75) + x20 * x351 + x20 * x352 + x20 * x353)
)
result[0, 6, 8] = numpy.sum(
x84 * (x108 * x15 * (x450 + x451) + x20 * x354 + x20 * x355 + x20 * x356)
)
result[0, 6, 9] = numpy.sum(
x74 * (x132 * x449 + x20 * x357 + x20 * x358 + x20 * x359)
)
result[0, 7, 0] = numpy.sum(
x84 * (x149 * x455 + x20 * x362 + x20 * x363 + x21 * x311)
)
result[0, 7, 1] = numpy.sum(
x176 * (x169 * x457 + x20 * x369 + x20 * x370 + x21 * x322)
)
result[0, 7, 2] = numpy.sum(
x176 * (x169 * x458 + x20 * x374 + x20 * x375 + x21 * x328)
)
result[0, 7, 3] = numpy.sum(
x176 * (x165 * x459 + x20 * x379 + x20 * x380 + x21 * x333)
)
result[0, 7, 4] = numpy.sum(
x205 * (x165 * x461 + x20 * x384 + x20 * x385 + x21 * x339)
)
result[0, 7, 5] = numpy.sum(
x176 * (x165 * x462 + x20 * x389 + x20 * x390 + x21 * x344)
)
result[0, 7, 6] = numpy.sum(
x84 * (x15 * (x377 * x51 + x459 * x75) + x20 * x393 + x20 * x394 + x21 * x348)
)
result[0, 7, 7] = numpy.sum(
x176 * (x15 * (x382 * x51 + x461 * x75) + x20 * x396 + x20 * x397 + x21 * x351)
)
result[0, 7, 8] = numpy.sum(
x176 * (x15 * (x462 * x75 + x463) + x20 * x399 + x20 * x400 + x21 * x354)
)
result[0, 7, 9] = numpy.sum(
x84 * (x15 * (x347 + x462 * x85) + x20 * x402 + x20 * x403 + x21 * x357)
)
result[0, 8, 0] = numpy.sum(
x84 * (x149 * x464 + x20 * x407 + x21 * x361 + x21 * x362)
)
result[0, 8, 1] = numpy.sum(
x176 * (x169 * x465 + x20 * x415 + x21 * x368 + x21 * x369)
)
result[0, 8, 2] = numpy.sum(
x176 * (x169 * x466 + x20 * x420 + x21 * x373 + x21 * x374)
)
result[0, 8, 3] = numpy.sum(
x176 * (x165 * x467 + x20 * x425 + x21 * x378 + x21 * x379)
)
result[0, 8, 4] = numpy.sum(
x205 * (x165 * x468 + x20 * x429 + x21 * x383 + x21 * x384)
)
result[0, 8, 5] = numpy.sum(
x176 * (x165 * x469 + x20 * x434 + x21 * x388 + x21 * x389)
)
result[0, 8, 6] = numpy.sum(
x84 * (x15 * (x426 + x467 * x75) + x20 * x439 + x21 * x392 + x21 * x393)
)
result[0, 8, 7] = numpy.sum(
x176 * (x15 * (x430 + x468 * x75) + x20 * x442 + x21 * x395 + x21 * x396)
)
result[0, 8, 8] = numpy.sum(
x176 * (x15 * (x435 + x469 * x75) + x20 * x445 + x21 * x398 + x21 * x399)
)
result[0, 8, 9] = numpy.sum(
x84 * (x15 * (x463 + x469 * x85) + x20 * x448 + x21 * x401 + x21 * x402)
)
result[0, 9, 0] = numpy.sum(
x74 * (x149 * x470 + x21 * x405 + x21 * x406 + x21 * x407)
)
result[0, 9, 1] = numpy.sum(
x84 * (x21 * x413 + x21 * x414 + x21 * x415 + x257 * x470)
)
result[0, 9, 2] = numpy.sum(
x84 * (x169 * x471 + x21 * x418 + x21 * x419 + x21 * x420)
)
result[0, 9, 3] = numpy.sum(
x84 * (x21 * x423 + x21 * x424 + x21 * x425 + x274 * x470)
)
result[0, 9, 4] = numpy.sum(
x107 * (x21 * x427 + x21 * x428 + x21 * x429 + x282 * x471)
)
result[0, 9, 5] = numpy.sum(
x84 * (x165 * x472 + x21 * x432 + x21 * x433 + x21 * x434)
)
result[0, 9, 6] = numpy.sum(
x74 * (x115 * x470 + x21 * x437 + x21 * x438 + x21 * x439)
)
result[0, 9, 7] = numpy.sum(
x84 * (x119 * x471 + x21 * x440 + x21 * x441 + x21 * x442)
)
result[0, 9, 8] = numpy.sum(
x84 * (x100 * x472 + x21 * x443 + x21 * x444 + x21 * x445)
)
result[0, 9, 9] = numpy.sum(
x74 * (x15 * (3.0 * x435 + x472 * x85) + x21 * x446 + x21 * x447 + x21 * x448)
)
return result
[docs]
def int3c2e3d_sph_034(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (sf|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1, 10, 15), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = 0.5 / (ax + bx)
x6 = x4**2
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = x8**2
x10 = -x2 * (ax * A[2] + bx * B[2])
x11 = -x10 - C[2]
x12 = x11**2
x13 = cx + x1
x14 = x13 ** (-1.0)
x15 = x1 * x14
x16 = cx * x15 * (x12 + x6 + x9)
x17 = boys(5, x16)
x18 = x13 ** (-1.5)
x19 = 17.49341832762486
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2))
x23 = x19 * x22
x24 = x2 * x23
x25 = 2.0 * x18 * x24
x26 = x17 * x25
x27 = cx ** (-1.0)
x28 = x13 ** (-0.5)
x29 = boys(4, x16)
x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26)
x31 = -x3 - A[0]
x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4
x33 = -x32
x34 = boys(6, x16)
x35 = x25 * x34
x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4
x37 = cx * x14
x38 = x36 * x37
x39 = x30 + x31 * x33 - x38 * x4
x40 = x39 * x4
x41 = x33 * x5
x42 = 2.0 * x41
x43 = x40 + x42
x44 = x15 * x4
x45 = x33 * x4
x46 = 2.0 * x5
x47 = x27 * x29
x48 = x46 * x47
x49 = x24 * x28 * x48
x50 = x45 + x49
x51 = x15 * x46
x52 = x43 * x44 + x50 * x51
x53 = x23 * x48
x54 = x18 * x53
x55 = x4 * x54 + x44 * x50
x56 = x44 * x52 + x51 * x55
x57 = x53 * x6
x58 = x1 * x13 ** (-2.5)
x59 = x44 * x55 + x57 * x58
x60 = x15 * (x44 * x56 + x51 * x59)
x61 = x4**3
x62 = x1**2
x63 = x13 ** (-3.5) * x62
x64 = x53 * x63
x65 = x15 * (x44 * x59 + x61 * x64)
x66 = x0 * x65 + x60
x67 = x4**4
x68 = x1**3
x69 = 2.0 * x13 ** (-4.5) * x23 * x47 * x68
x70 = x0 * x69
x71 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35)
x72 = x25 * boys(7, x16)
x73 = x37 * x4
x74 = (
x31 * x39
- x46 * (x32 + x38)
- x73
* (
x31 * x36
+ x71
- x73 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x72)
)
)
x75 = x4 * x74
x76 = x39 * x5
x77 = 3.0 * x76
x78 = x15 * x5
x79 = 3.0 * x78
x80 = da * db * dc
x81 = 0.009523809523809524 * x80
x82 = 2.645751311064591 * x81
x83 = x15 * x8
x84 = x83 * (x40 + x42)
x85 = x54 * x8
x86 = x45 * x83 + x85
x87 = x44 * x84 + x51 * x86
x88 = x53 * x58
x89 = x4 * x88
x90 = x44 * x86 + x8 * x89
x91 = x15 * (x44 * x87 + x51 * x90)
x92 = x57 * x63
x93 = x15 * (x44 * x90 + x8 * x92)
x94 = x0 * x93 + x91
x95 = x61 * x70
x96 = 0.06666666666666667 * x80
x97 = x11 * x15
x98 = x97 * (x40 + x42)
x99 = x11 * x54
x100 = x45 * x97 + x99
x101 = x100 * x51 + x44 * x98
x102 = x100 * x44 + x11 * x89
x103 = x15 * (x101 * x44 + x102 * x51)
x104 = x15 * (x102 * x44 + x11 * x92)
x105 = x0 * x104 + x103
x106 = x62 / x13**2
x107 = x106 * x9
x108 = x107 * (x40 + x42)
x109 = x88 * x9
x110 = x107 * x45 + x109
x111 = x15 * (x108 * x44 + x110 * x51)
x112 = x4 * x9
x113 = x15 * (x110 * x44 + x112 * x64)
x114 = x0 * x113 + x111
x115 = x6 * x9
x116 = 3.872983346207417
x117 = 0.02222222222222222 * x116 * x80
x118 = x106 * x8
x119 = x11 * x118
x120 = x119 * (x40 + x42)
x121 = x11 * x8
x122 = x121 * x88
x123 = x119 * x45 + x122
x124 = x15 * (x120 * x44 + x123 * x51)
x125 = x15 * (x121 * x4 * x64 + x123 * x44)
x126 = x0 * x125 + x124
x127 = x121 * x6
x128 = 2.23606797749979 * x96
x129 = x106 * x12
x130 = x129 * (x40 + x42)
x131 = x12 * x88
x132 = x129 * x45 + x131
x133 = x15 * (x130 * x44 + x132 * x51)
x134 = x12 * x4
x135 = x15 * (x132 * x44 + x134 * x64)
x136 = x0 * x135 + x133
x137 = x12 * x6
x138 = x8**3
x139 = x68 / x13**3
x140 = x138 * x139
x141 = x140 * x15 * (x40 + x42)
x142 = x138 * x64
x143 = x15 * (x140 * x45 + x142)
x144 = x0 * x143 + x141
x145 = x138 * x70
x146 = x139 * x9
x147 = x11 * x146
x148 = x147 * x15 * (x40 + x42)
x149 = x11 * x64 * x9
x150 = x15 * (x147 * x45 + x149)
x151 = x0 * x150 + x148
x152 = x11 * x112
x153 = x139 * x8
x154 = x12 * x153
x155 = x15 * x154 * (x40 + x42)
x156 = x12 * x64 * x8
x157 = x15 * (x154 * x45 + x156)
x158 = x0 * x157 + x155
x159 = x134 * x8
x160 = x11**3
x161 = x139 * x160
x162 = x15 * x161 * (x40 + x42)
x163 = x160 * x64
x164 = x15 * (x161 * x45 + x163)
x165 = x0 * x164 + x162
x166 = x160 * x4
x167 = x8**4
x168 = x1**4 / x13**4
x169 = x167 * x168
x170 = x169 * x39
x171 = x169 * x33
x172 = x0 * x171 + x170
x173 = x138 * x168
x174 = x11 * x173
x175 = x174 * x39
x176 = x174 * x33
x177 = x0 * x176 + x175
x178 = x168 * x39
x179 = x12 * x9
x180 = x178 * x179
x181 = x168 * x179
x182 = x181 * x33
x183 = x0 * x182 + x180
x184 = x160 * x8
x185 = x178 * x184
x186 = x168 * x184
x187 = x186 * x33
x188 = x0 * x187 + x185
x189 = x11**4
x190 = x168 * x189
x191 = x190 * x39
x192 = x190 * x33
x193 = x0 * x192 + x191
x194 = -x7 - A[1]
x195 = -2.0 * x19 * x194 * x2 * x22 * x27 * x28 * x29 + x26 * x8
x196 = -x195
x197 = x196 * x5
x198 = 2.0 * x17 * x19 * x194 * x2 * x22 * x27 * x28 - x35 * x8
x199 = x198 * x37
x200 = x196 * x31 - x199 * x4
x201 = x200 * x4
x202 = x197 + x201
x203 = x44 * (x197 + x202)
x204 = x106 * x6
x205 = x197 * x204 + x203 * x44
x206 = x139 * x61
x207 = x15 * (x197 * x206 + x205 * x44)
x208 = x20 * x65 + x207
x209 = x168 * x67
x210 = x196 * x209
x211 = x20 * x69
x212 = x210 + x211 * x67
x213 = -x5 * (x195 + x199)
x214 = 2.0 * x19 * x194 * x2 * x22 * x27 * x28 * x34 - x72 * x8
x215 = x200 * x31 + x213 - x73 * (x198 * x31 - x214 * x73)
x216 = x215 * x4
x217 = x200 * x5
x218 = 2.0 * x217
x219 = 5.916079783099616 * x81
x220 = x196 * x8
x221 = x220 + x49
x222 = x15 * x221
x223 = x200 * x8
x224 = x223 + x41
x225 = x222 * x5 + x224 * x44
x226 = x106 * x4
x227 = x221 * x5
x228 = x225 * x44 + x226 * x227
x229 = x139 * x6
x230 = x15 * (x227 * x229 + x228 * x44)
x231 = x20 * x93 + x230
x232 = x168 * x61
x233 = x221 * x232
x234 = x211 * x61
x235 = x233 + x234 * x8
x236 = x215 * x8
x237 = x236 + x76
x238 = x224 * x51
x239 = x197 * x97
x240 = x201 * x97 + x239
x241 = x11 * x197
x242 = x226 * x241 + x240 * x44
x243 = x15 * (x229 * x241 + x242 * x44)
x244 = x104 * x20 + x243
x245 = x11 * x232
x246 = x196 * x245
x247 = x11 * x234 + x246
x248 = x218 * x97
x249 = x222 * x8 + x85
x250 = x83 * (x224 + x41)
x251 = x249 * x78 + x250 * x44
x252 = x226 * x5
x253 = x15 * (x249 * x252 + x251 * x44)
x254 = x113 * x20 + x253
x255 = x229 * x249
x256 = x115 * x211 + x255
x257 = x83 * (x237 + x76)
x258 = x250 * x51
x259 = 1.732050807568877
x260 = 0.1111111111111111 * x259 * x80
x261 = x220 * x97 + x99
x262 = x41 * x97
x263 = x223 * x97 + x262
x264 = x261 * x78 + x263 * x44
x265 = x15 * (x252 * x261 + x264 * x44)
x266 = x125 * x20 + x265
x267 = x229 * x261
x268 = x127 * x211 + x267
x269 = x76 * x97
x270 = x236 * x97 + x269
x271 = x263 * x51
x272 = 0.3333333333333333 * x80
x273 = x129 * x197
x274 = x129 * x201 + x273
x275 = x134 * x139
x276 = x15 * (x197 * x275 + x274 * x44)
x277 = x135 * x20 + x276
x278 = x168 * x196
x279 = x137 * x278
x280 = x137 * x211 + x279
x281 = x129 * x218
x282 = x109 + x249 * x83
x283 = x107 * x41 + x250 * x83
x284 = x15 * (x282 * x78 + x283 * x44)
x285 = x143 * x20 + x284
x286 = x226 * x282
x287 = x138 * x211
x288 = x286 + x287 * x4
x289 = x107 * x76 + x257 * x83
x290 = x283 * x51
x291 = x122 + x261 * x83
x292 = x119 * x41 + x263 * x83
x293 = x15 * (x291 * x78 + x292 * x44)
x294 = x150 * x20 + x293
x295 = x226 * x291
x296 = x152 * x211 + x295
x297 = x119 * x76 + x270 * x83
x298 = x292 * x51
x299 = x129 * x220 + x131
x300 = x129 * x41
x301 = x129 * x223 + x300
x302 = x15 * (x299 * x78 + x301 * x44)
x303 = x157 * x20 + x302
x304 = x226 * x299
x305 = x159 * x211 + x304
x306 = x129 * x76
x307 = x129 * x236 + x306
x308 = x301 * x51
x309 = x161 * x197
x310 = x15 * (x161 * x201 + x309)
x311 = x164 * x20 + x310
x312 = x166 * x278
x313 = x166 * x211 + x312
x314 = x161 * x218
x315 = x15 * (x140 * x41 + x283 * x83)
x316 = x171 * x20 + x315
x317 = x15 * (x142 + x282 * x83)
x318 = x167 * x211 + x317
x319 = x15 * (x147 * x41 + x292 * x83)
x320 = x176 * x20 + x319
x321 = x15 * (x149 + x291 * x83)
x322 = x11 * x287 + x321
x323 = x15 * (x154 * x41 + x301 * x83)
x324 = x182 * x20 + x323
x325 = x15 * (x156 + x299 * x83)
x326 = x179 * x211 + x325
x327 = x161 * x41
x328 = x15 * (x161 * x223 + x327)
x329 = x187 * x20 + x328
x330 = x15 * (x161 * x220 + x163)
x331 = x184 * x211 + x330
x332 = x161 * x76
x333 = x190 * x200
x334 = x192 * x20 + x333
x335 = x190 * x196
x336 = x189 * x211 + x335
x337 = -x10 - A[2]
x338 = x11 * x26 - 2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x337
x339 = -x338
x340 = x339 * x5
x341 = -x11 * x35 + 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x337
x342 = x341 * x37
x343 = x31 * x339 - x342 * x4
x344 = x343 * x4
x345 = x340 + x344
x346 = x44 * (x340 + x345)
x347 = x204 * x340 + x346 * x44
x348 = x15 * (x206 * x340 + x347 * x44)
x349 = x21 * x65 + x348
x350 = x209 * x339
x351 = x21 * x69
x352 = x350 + x351 * x67
x353 = -x5 * (x338 + x342)
x354 = -x11 * x72 + 2.0 * x19 * x2 * x22 * x27 * x28 * x337 * x34
x355 = x31 * x343 + x353 - x73 * (x31 * x341 - x354 * x73)
x356 = x355 * x4
x357 = x343 * x5
x358 = 2.0 * x357
x359 = x340 * x83
x360 = x344 * x83 + x359
x361 = x226 * x8
x362 = x340 * x361 + x360 * x44
x363 = x229 * x8
x364 = x15 * (x340 * x363 + x362 * x44)
x365 = x21 * x93 + x364
x366 = x232 * x8
x367 = x339 * x366
x368 = x351 * x61
x369 = x367 + x368 * x8
x370 = x11 * x339 + x49
x371 = x370 * x78
x372 = x11 * x343 + x41
x373 = x371 + x372 * x44
x374 = x252 * x370 + x373 * x44
x375 = x370 * x5
x376 = x15 * (x229 * x375 + x374 * x44)
x377 = x104 * x21 + x376
x378 = x232 * x370
x379 = x11 * x368 + x378
x380 = x11 * x355 + x76
x381 = x372 * x51
x382 = x107 * x340
x383 = x107 * x344 + x382
x384 = x146 * x4
x385 = x15 * (x340 * x384 + x383 * x44)
x386 = x113 * x21 + x385
x387 = x168 * x6
x388 = x387 * x9
x389 = x339 * x388
x390 = x115 * x351 + x389
x391 = x118 * x375
x392 = x361 * x372 + x391
x393 = x153 * x4
x394 = x15 * (x375 * x393 + x392 * x44)
x395 = x125 * x21 + x394
x396 = x387 * x8
x397 = x370 * x396
x398 = x127 * x351 + x397
x399 = x372 * x46
x400 = x370 * x97 + x99
x401 = x400 * x78
x402 = x262 + x372 * x97
x403 = x401 + x402 * x44
x404 = x15 * (x252 * x400 + x403 * x44)
x405 = x135 * x21 + x404
x406 = x229 * x400
x407 = x137 * x351 + x406
x408 = x269 + x380 * x97
x409 = x402 * x51
x410 = x140 * x340
x411 = x15 * (x140 * x344 + x410)
x412 = x143 * x21 + x411
x413 = x173 * x4
x414 = x339 * x413
x415 = x138 * x351
x416 = x4 * x415 + x414
x417 = x146 * x375
x418 = x15 * (x372 * x384 + x417)
x419 = x150 * x21 + x418
x420 = x112 * x168
x421 = x370 * x420
x422 = x152 * x351 + x421
x423 = x118 * x5
x424 = x400 * x423
x425 = x15 * (x361 * x402 + x424)
x426 = x157 * x21 + x425
x427 = x393 * x400
x428 = x159 * x351 + x427
x429 = x131 + x400 * x97
x430 = x429 * x78
x431 = x300 + x402 * x97
x432 = x15 * (x430 + x431 * x44)
x433 = x164 * x21 + x432
x434 = x226 * x429
x435 = x166 * x351 + x434
x436 = x306 + x408 * x97
x437 = x431 * x51
x438 = x169 * x343
x439 = x171 * x21 + x438
x440 = x169 * x339
x441 = x167 * x351 + x440
x442 = x173 * x372
x443 = x176 * x21 + x442
x444 = x173 * x370
x445 = x11 * x415 + x444
x446 = x146 * x402
x447 = x182 * x21 + x446
x448 = x146 * x400
x449 = x179 * x351 + x448
x450 = x118 * x431
x451 = x187 * x21 + x450
x452 = x118 * x429
x453 = x184 * x351 + x452
x454 = x15 * (x327 + x431 * x97)
x455 = x192 * x21 + x454
x456 = x15 * (x163 + x429 * x97)
x457 = x189 * x351 + x456
x458 = x194 * x196 - x199 * x8 + x30
x459 = x209 * x458
x460 = x20 * x210 + x459
x461 = x20 * x212 + x460
x462 = x458 * x5
x463 = x37 * x8
x464 = x194 * x198 - x214 * x463 + x71
x465 = x31 * x458 - x464 * x73
x466 = x4 * x465
x467 = x458 * x8
x468 = 2.0 * x197
x469 = x467 + x468
x470 = x232 * x469
x471 = x20 * x233 + x470
x472 = x20 * x235 + x471
x473 = x469 * x78
x474 = x465 * x8
x475 = x218 + x474
x476 = x229 * x5
x477 = x245 * x458
x478 = x20 * x246 + x477
x479 = x20 * x247 + x478
x480 = x462 * x97
x481 = x11 * x462
x482 = x222 * x46 + x469 * x83
x483 = x229 * x482
x484 = x20 * x255 + x483
x485 = x20 * x256 + x484
x486 = x482 * x78
x487 = x238 + x475 * x83
x488 = x97 * (x467 + x468)
x489 = x229 * x488
x490 = x20 * x267 + x489
x491 = x20 * x268 + x490
x492 = x488 * x78
x493 = x248 + x474 * x97
x494 = x168 * x458
x495 = x137 * x494
x496 = x20 * x279 + x495
x497 = x20 * x280 + x496
x498 = x129 * x462
x499 = x249 * x51 + x482 * x83
x500 = x226 * x499
x501 = x20 * x286 + x500
x502 = x20 * x288 + x501
x503 = x499 * x78
x504 = x258 + x487 * x83
x505 = x261 * x51 + x488 * x83
x506 = x226 * x505
x507 = x20 * x295 + x506
x508 = x20 * x296 + x507
x509 = x505 * x78
x510 = x271 + x493 * x83
x511 = x129 * (x467 + x468)
x512 = x226 * x511
x513 = x20 * x304 + x512
x514 = x20 * x305 + x513
x515 = x511 * x78
x516 = x129 * x474 + x281
x517 = x166 * x494
x518 = x20 * x312 + x517
x519 = x20 * x313 + x518
x520 = x161 * x462
x521 = x15 * (x282 * x51 + x499 * x83)
x522 = x20 * x317 + x521
x523 = x20 * x318 + x522
x524 = x15 * (x291 * x51 + x505 * x83)
x525 = x20 * x321 + x524
x526 = x20 * x322 + x525
x527 = x15 * (x299 * x51 + x511 * x83)
x528 = x20 * x325 + x527
x529 = x20 * x326 + x528
x530 = x15 * x161 * (x467 + x468)
x531 = x20 * x330 + x530
x532 = x20 * x331 + x531
x533 = x190 * x458
x534 = x20 * x335 + x533
x535 = x20 * x336 + x534
x536 = x194 * x339 - x342 * x8
x537 = x209 * x536
x538 = x21 * x210 + x537
x539 = x20 * x352 + x538
x540 = x5 * x536
x541 = x194 * x341 - x354 * x463
x542 = x31 * x536 - x541 * x73
x543 = 10.2469507659596 * x81
x544 = x340 + x536 * x8
x545 = x232 * x544
x546 = x21 * x233 + x545
x547 = x20 * x369 + x546
x548 = x357 + x542 * x8
x549 = x116 * x96
x550 = x11 * x536 + x197
x551 = x232 * x550
x552 = x21 * x246 + x551
x553 = x20 * x379 + x552
x554 = x11 * x542 + x217
x555 = x359 + x544 * x83
x556 = x229 * x555
x557 = x21 * x255 + x556
x558 = x20 * x390 + x557
x559 = x83 * (x357 + x548)
x560 = x371 + x550 * x83
x561 = x229 * x560
x562 = x21 * x267 + x561
x563 = x20 * x398 + x562
x564 = x372 * x78 + x554 * x83
x565 = x259 * x272
x566 = x239 + x550 * x97
x567 = x229 * x566
x568 = x21 * x279 + x567
x569 = x20 * x407 + x568
x570 = x97 * (x217 + x554)
x571 = x382 + x555 * x83
x572 = x226 * x571
x573 = x21 * x286 + x572
x574 = x20 * x416 + x573
x575 = x107 * x357 + x559 * x83
x576 = x391 + x560 * x83
x577 = x226 * x576
x578 = x21 * x295 + x577
x579 = x20 * x422 + x578
x580 = x372 * x423 + x564 * x83
x581 = x401 + x566 * x83
x582 = x226 * x581
x583 = x21 * x304 + x582
x584 = x20 * x428 + x583
x585 = x402 * x78 + x570 * x83
x586 = x273 + x566 * x97
x587 = x226 * x586
x588 = x21 * x312 + x587
x589 = x20 * x435 + x588
x590 = x129 * x217 + x570 * x97
x591 = x15 * (x410 + x571 * x83)
x592 = x21 * x317 + x591
x593 = x20 * x441 + x592
x594 = x15 * (x417 + x576 * x83)
x595 = x21 * x321 + x594
x596 = x20 * x445 + x595
x597 = x146 * x5
x598 = x15 * (x424 + x581 * x83)
x599 = x21 * x325 + x598
x600 = x20 * x449 + x599
x601 = x15 * (x430 + x586 * x83)
x602 = x21 * x330 + x601
x603 = x20 * x453 + x602
x604 = x15 * (x309 + x586 * x97)
x605 = x21 * x335 + x604
x606 = x20 * x457 + x605
x607 = -x11 * x342 + x30 + x337 * x339
x608 = x209 * x607
x609 = x21 * x350 + x608
x610 = x21 * x352 + x609
x611 = x5 * x607
x612 = x11 * x37
x613 = x337 * x341 - x354 * x612 + x71
x614 = x31 * x607 - x613 * x73
x615 = x4 * x614
x616 = x366 * x607
x617 = x21 * x367 + x616
x618 = x21 * x369 + x617
x619 = x611 * x83
x620 = x11 * x607 + 2.0 * x340
x621 = x232 * x620
x622 = x21 * x378 + x621
x623 = x21 * x379 + x622
x624 = x620 * x78
x625 = x11 * x614 + x358
x626 = x388 * x607
x627 = x21 * x389 + x626
x628 = x21 * x390 + x627
x629 = x107 * x611
x630 = x396 * x620
x631 = x21 * x397 + x630
x632 = x21 * x398 + x631
x633 = x423 * x620
x634 = x370 * x51 + x620 * x97
x635 = x229 * x634
x636 = x21 * x406 + x635
x637 = x21 * x407 + x636
x638 = x634 * x78
x639 = x381 + x625 * x97
x640 = x413 * x607
x641 = x21 * x414 + x640
x642 = x21 * x416 + x641
x643 = x140 * x611
x644 = x420 * x620
x645 = x21 * x421 + x644
x646 = x21 * x422 + x645
x647 = x597 * x620
x648 = x393 * x634
x649 = x21 * x427 + x648
x650 = x21 * x428 + x649
x651 = x423 * x634
x652 = x400 * x51 + x634 * x97
x653 = x226 * x652
x654 = x21 * x434 + x653
x655 = x21 * x435 + x654
x656 = x652 * x78
x657 = x409 + x639 * x97
x658 = x169 * x607
x659 = x21 * x440 + x658
x660 = x21 * x441 + x659
x661 = x173 * x620
x662 = x21 * x444 + x661
x663 = x21 * x445 + x662
x664 = x146 * x634
x665 = x21 * x448 + x664
x666 = x21 * x449 + x665
x667 = x118 * x652
x668 = x21 * x452 + x667
x669 = x21 * x453 + x668
x670 = x15 * (x429 * x51 + x652 * x97)
x671 = x21 * x456 + x670
x672 = x21 * x457 + x671
x673 = x194 * x458 + 2.0 * x213 - x463 * x464
x674 = x673 * x8
x675 = 3.0 * x462
x676 = x674 + x675
x677 = 3.0 * x473 + x676 * x83
x678 = x97 * (x674 + x675)
x679 = x168 * x673
x680 = 3.0 * x486 + x677 * x83
x681 = 3.0 * x492 + x678 * x83
x682 = x129 * (x674 + x675)
x683 = x194 * x536 + x353 - x463 * x541
x684 = 2.0 * x540
x685 = x683 * x8 + x684
x686 = x11 * x683 + x462
x687 = x51 * x544 + x685 * x83
x688 = x51 * x550
x689 = x686 * x83 + x688
x690 = x480 + x686 * x97
x691 = x51 * x555 + x687 * x83
x692 = x51 * x560 + x689 * x83
x693 = x51 * x566
x694 = x690 * x83 + x693
x695 = x498 + x690 * x97
x696 = x51 * x586
x697 = x194 * x607 - x463 * x613
x698 = x611 + x697 * x8
x699 = x11 * x697 + x684
x700 = x619 + x698 * x83
x701 = x624 + x699 * x83
x702 = x688 + x699 * x97
x703 = x629 + x700 * x83
x704 = x633 + x701 * x83
x705 = x638 + x702 * x83
x706 = x693 + x702 * x97
x707 = x337 * x607 + 2.0 * x353 - x612 * x613
x708 = x11 * x707 + 3.0 * x611
x709 = 3.0 * x624 + x708 * x97
x710 = 3.0 * x638 + x709 * x97
# 150 item(s)
result[0, 0, 0] = numpy.sum(
x82
* (
x0 * x60
+ x0 * x66
+ x0 * (x0 * (x65 + x67 * x70) + x66)
+ x15
* (x44 * (x44 * (x43 * x79 + x44 * (x75 + x77)) + x52 * x79) + x56 * x79)
)
)
result[0, 0, 1] = numpy.sum(
x96
* (
x0 * x91
+ x0 * x94
+ x0 * (x0 * (x8 * x95 + x93) + x94)
+ x15 * (x44 * (x44 * x83 * (x75 + x77) + x79 * x84) + x79 * x87)
)
)
result[0, 0, 2] = numpy.sum(
x96
* (
x0 * x103
+ x0 * x105
+ x0 * (x0 * (x104 + x11 * x95) + x105)
+ x15 * (x101 * x79 + x44 * (x44 * x97 * (x75 + x77) + x79 * x98))
)
)
result[0, 0, 3] = numpy.sum(
x117
* (
x0 * x111
+ x0 * x114
+ x0 * (x0 * (x113 + x115 * x70) + x114)
+ x15 * (x107 * x44 * (x75 + x77) + x108 * x79)
)
)
result[0, 0, 4] = numpy.sum(
x128
* (
x0 * x124
+ x0 * x126
+ x0 * (x0 * (x125 + x127 * x70) + x126)
+ x15 * (x119 * x44 * (x75 + x77) + x120 * x79)
)
)
result[0, 0, 5] = numpy.sum(
x117
* (
x0 * x133
+ x0 * x136
+ x0 * (x0 * (x135 + x137 * x70) + x136)
+ x15 * (x129 * x44 * (x75 + x77) + x130 * x79)
)
)
result[0, 0, 6] = numpy.sum(
x96
* (
x0 * x141
+ x0 * x144
+ x0 * (x0 * (x143 + x145 * x4) + x144)
+ x140 * x15 * (x75 + x77)
)
)
result[0, 0, 7] = numpy.sum(
x128
* (
x0 * x148
+ x0 * x151
+ x0 * (x0 * (x150 + x152 * x70) + x151)
+ x147 * x15 * (x75 + x77)
)
)
result[0, 0, 8] = numpy.sum(
x128
* (
x0 * x155
+ x0 * x158
+ x0 * (x0 * (x157 + x159 * x70) + x158)
+ x15 * x154 * (x75 + x77)
)
)
result[0, 0, 9] = numpy.sum(
x96
* (
x0 * x162
+ x0 * x165
+ x0 * (x0 * (x164 + x166 * x70) + x165)
+ x15 * x161 * (x75 + x77)
)
)
result[0, 0, 10] = numpy.sum(
x82
* (x0 * x170 + x0 * x172 + x0 * (x0 * (x167 * x70 + x171) + x172) + x169 * x74)
)
result[0, 0, 11] = numpy.sum(
x96
* (x0 * x175 + x0 * x177 + x0 * (x0 * (x11 * x145 + x176) + x177) + x174 * x74)
)
result[0, 0, 12] = numpy.sum(
x117
* (x0 * x180 + x0 * x183 + x0 * (x0 * (x179 * x70 + x182) + x183) + x181 * x74)
)
result[0, 0, 13] = numpy.sum(
x96
* (x0 * x185 + x0 * x188 + x0 * (x0 * (x184 * x70 + x187) + x188) + x186 * x74)
)
result[0, 0, 14] = numpy.sum(
x82
* (x0 * x191 + x0 * x193 + x0 * (x0 * (x189 * x70 + x192) + x193) + x190 * x74)
)
result[0, 1, 0] = numpy.sum(
x219
* (
x0 * x208
+ x0 * (x0 * x212 + x208)
+ x15
* (x205 * x51 + x44 * (x203 * x51 + x44 * (x202 * x51 + x44 * (x216 + x218))))
+ x20 * x60
)
)
result[0, 1, 1] = numpy.sum(
x128
* (
x0 * x231
+ x0 * (x0 * x235 + x231)
+ x15 * (x228 * x51 + x44 * (x225 * x51 + x44 * (x237 * x44 + x238)))
+ x20 * x91
)
)
result[0, 1, 2] = numpy.sum(
x128
* (
x0 * x244
+ x0 * (x0 * x247 + x244)
+ x103 * x20
+ x15 * (x242 * x51 + x44 * (x240 * x51 + x44 * (x216 * x97 + x248)))
)
)
result[0, 1, 3] = numpy.sum(
x260
* (
x0 * x254
+ x0 * (x0 * x256 + x254)
+ x111 * x20
+ x15 * (x251 * x51 + x44 * (x257 * x44 + x258))
)
)
result[0, 1, 4] = numpy.sum(
x272
* (
x0 * x266
+ x0 * (x0 * x268 + x266)
+ x124 * x20
+ x15 * (x264 * x51 + x44 * (x270 * x44 + x271))
)
)
result[0, 1, 5] = numpy.sum(
x260
* (
x0 * x277
+ x0 * (x0 * x280 + x277)
+ x133 * x20
+ x15 * (x274 * x51 + x44 * (x129 * x216 + x281))
)
)
result[0, 1, 6] = numpy.sum(
x128
* (x0 * x285 + x0 * (x0 * x288 + x285) + x141 * x20 + x15 * (x289 * x44 + x290))
)
result[0, 1, 7] = numpy.sum(
x272
* (x0 * x294 + x0 * (x0 * x296 + x294) + x148 * x20 + x15 * (x297 * x44 + x298))
)
result[0, 1, 8] = numpy.sum(
x272
* (x0 * x303 + x0 * (x0 * x305 + x303) + x15 * (x307 * x44 + x308) + x155 * x20)
)
result[0, 1, 9] = numpy.sum(
x128
* (x0 * x311 + x0 * (x0 * x313 + x311) + x15 * (x161 * x216 + x314) + x162 * x20)
)
result[0, 1, 10] = numpy.sum(
x219
* (
x0 * x316
+ x0 * (x0 * x318 + x316)
+ x15 * (x140 * x76 + x289 * x83)
+ x170 * x20
)
)
result[0, 1, 11] = numpy.sum(
x128
* (
x0 * x320
+ x0 * (x0 * x322 + x320)
+ x15 * (x147 * x76 + x297 * x83)
+ x175 * x20
)
)
result[0, 1, 12] = numpy.sum(
x260
* (
x0 * x324
+ x0 * (x0 * x326 + x324)
+ x15 * (x154 * x76 + x307 * x83)
+ x180 * x20
)
)
result[0, 1, 13] = numpy.sum(
x128
* (x0 * x329 + x0 * (x0 * x331 + x329) + x15 * (x161 * x236 + x332) + x185 * x20)
)
result[0, 1, 14] = numpy.sum(
x219 * (x0 * x334 + x0 * (x0 * x336 + x334) + x190 * x215 + x191 * x20)
)
result[0, 2, 0] = numpy.sum(
x219
* (
x0 * x349
+ x0 * (x0 * x352 + x349)
+ x15
* (x347 * x51 + x44 * (x346 * x51 + x44 * (x345 * x51 + x44 * (x356 + x358))))
+ x21 * x60
)
)
result[0, 2, 1] = numpy.sum(
x128
* (
x0 * x365
+ x0 * (x0 * x369 + x365)
+ x15 * (x362 * x51 + x44 * (x360 * x51 + x44 * x83 * (x356 + x358)))
+ x21 * x91
)
)
result[0, 2, 2] = numpy.sum(
x128
* (
x0 * x377
+ x0 * (x0 * x379 + x377)
+ x103 * x21
+ x15 * (x374 * x51 + x44 * (x373 * x51 + x44 * (x380 * x44 + x381)))
)
)
result[0, 2, 3] = numpy.sum(
x260
* (
x0 * x386
+ x0 * (x0 * x390 + x386)
+ x111 * x21
+ x15 * (x107 * x44 * (x356 + x358) + x383 * x51)
)
)
result[0, 2, 4] = numpy.sum(
x272
* (
x0 * x395
+ x0 * (x0 * x398 + x395)
+ x124 * x21
+ x15 * (x392 * x51 + x44 * (x118 * x399 + x361 * x380))
)
)
result[0, 2, 5] = numpy.sum(
x260
* (
x0 * x405
+ x0 * (x0 * x407 + x405)
+ x133 * x21
+ x15 * (x403 * x51 + x44 * (x408 * x44 + x409))
)
)
result[0, 2, 6] = numpy.sum(
x128
* (x0 * x412 + x0 * (x0 * x416 + x412) + x140 * x15 * (x356 + x358) + x141 * x21)
)
result[0, 2, 7] = numpy.sum(
x272
* (
x0 * x419
+ x0 * (x0 * x422 + x419)
+ x148 * x21
+ x15 * (x146 * x399 + x380 * x384)
)
)
result[0, 2, 8] = numpy.sum(
x272
* (
x0 * x426
+ x0 * (x0 * x428 + x426)
+ x15 * (x118 * x402 * x46 + x361 * x408)
+ x155 * x21
)
)
result[0, 2, 9] = numpy.sum(
x128
* (x0 * x433 + x0 * (x0 * x435 + x433) + x15 * (x436 * x44 + x437) + x162 * x21)
)
result[0, 2, 10] = numpy.sum(
x219 * (x0 * x439 + x0 * (x0 * x441 + x439) + x169 * x355 + x170 * x21)
)
result[0, 2, 11] = numpy.sum(
x128 * (x0 * x443 + x0 * (x0 * x445 + x443) + x173 * x380 + x175 * x21)
)
result[0, 2, 12] = numpy.sum(
x260 * (x0 * x447 + x0 * (x0 * x449 + x447) + x146 * x408 + x180 * x21)
)
result[0, 2, 13] = numpy.sum(
x128 * (x0 * x451 + x0 * (x0 * x453 + x451) + x118 * x436 + x185 * x21)
)
result[0, 2, 14] = numpy.sum(
x219
* (x0 * x455 + x0 * (x0 * x457 + x455) + x15 * (x332 + x436 * x97) + x191 * x21)
)
result[0, 3, 0] = numpy.sum(
x219
* (
x0 * x461
+ x15 * (x206 * x462 + x44 * (x204 * x462 + x44**2 * (2.0 * x462 + x466)))
+ x20 * x207
+ x20 * x208
)
)
result[0, 3, 1] = numpy.sum(
x128
* (
x0 * x472
+ x15 * (x44 * (x252 * x469 + x44 * (x44 * x475 + x473)) + x469 * x476)
+ x20 * x230
+ x20 * x231
)
)
result[0, 3, 2] = numpy.sum(
x128
* (
x0 * x479
+ x15 * (x229 * x481 + x44 * (x226 * x481 + x44 * (x466 * x97 + x480)))
+ x20 * x243
+ x20 * x244
)
)
result[0, 3, 3] = numpy.sum(
x260
* (
x0 * x485
+ x15 * (x252 * x482 + x44 * (x44 * x487 + x486))
+ x20 * x253
+ x20 * x254
)
)
result[0, 3, 4] = numpy.sum(
x272
* (
x0 * x491
+ x15 * (x252 * x488 + x44 * (x44 * x493 + x492))
+ x20 * x265
+ x20 * x266
)
)
result[0, 3, 5] = numpy.sum(
x260
* (
x0 * x497
+ x15 * (x275 * x462 + x44 * (x129 * x466 + x498))
+ x20 * x276
+ x20 * x277
)
)
result[0, 3, 6] = numpy.sum(
x128 * (x0 * x502 + x15 * (x44 * x504 + x503) + x20 * x284 + x20 * x285)
)
result[0, 3, 7] = numpy.sum(
x272 * (x0 * x508 + x15 * (x44 * x510 + x509) + x20 * x293 + x20 * x294)
)
result[0, 3, 8] = numpy.sum(
x272 * (x0 * x514 + x15 * (x44 * x516 + x515) + x20 * x302 + x20 * x303)
)
result[0, 3, 9] = numpy.sum(
x128 * (x0 * x519 + x15 * (x161 * x466 + x520) + x20 * x310 + x20 * x311)
)
result[0, 3, 10] = numpy.sum(
x219 * (x0 * x523 + x15 * (x290 + x504 * x83) + x20 * x315 + x20 * x316)
)
result[0, 3, 11] = numpy.sum(
x128 * (x0 * x526 + x15 * (x298 + x510 * x83) + x20 * x319 + x20 * x320)
)
result[0, 3, 12] = numpy.sum(
x260 * (x0 * x529 + x15 * (x308 + x516 * x83) + x20 * x323 + x20 * x324)
)
result[0, 3, 13] = numpy.sum(
x128 * (x0 * x532 + x15 * (x161 * x474 + x314) + x20 * x328 + x20 * x329)
)
result[0, 3, 14] = numpy.sum(
x219 * (x0 * x535 + x190 * x465 + x20 * x333 + x20 * x334)
)
result[0, 4, 0] = numpy.sum(
x543
* (
x0 * x539
+ x15
* (x206 * x540 + x44 * (x204 * x540 + x44**2 * (x4 * x542 + 2.0 * x540)))
+ x20 * x349
+ x207 * x21
)
)
result[0, 4, 1] = numpy.sum(
x549
* (
x0 * x547
+ x15 * (x44 * (x252 * x544 + x44 * (x44 * x548 + x544 * x78)) + x476 * x544)
+ x20 * x365
+ x21 * x230
)
)
result[0, 4, 2] = numpy.sum(
x549
* (
x0 * x553
+ x15 * (x44 * (x252 * x550 + x44 * (x44 * x554 + x550 * x78)) + x476 * x550)
+ x20 * x377
+ x21 * x243
)
)
result[0, 4, 3] = numpy.sum(
x272
* (
x0 * x558
+ x15 * (x252 * x555 + x44 * (x44 * x559 + x555 * x78))
+ x20 * x386
+ x21 * x253
)
)
result[0, 4, 4] = numpy.sum(
x565
* (
x0 * x563
+ x15 * (x252 * x560 + x44 * (x44 * x564 + x560 * x78))
+ x20 * x395
+ x21 * x265
)
)
result[0, 4, 5] = numpy.sum(
x272
* (
x0 * x569
+ x15 * (x252 * x566 + x44 * (x44 * x570 + x566 * x78))
+ x20 * x405
+ x21 * x276
)
)
result[0, 4, 6] = numpy.sum(
x549 * (x0 * x574 + x15 * (x44 * x575 + x571 * x78) + x20 * x412 + x21 * x284)
)
result[0, 4, 7] = numpy.sum(
x565 * (x0 * x579 + x15 * (x44 * x580 + x576 * x78) + x20 * x419 + x21 * x293)
)
result[0, 4, 8] = numpy.sum(
x565 * (x0 * x584 + x15 * (x44 * x585 + x581 * x78) + x20 * x426 + x21 * x302)
)
result[0, 4, 9] = numpy.sum(
x549 * (x0 * x589 + x15 * (x44 * x590 + x586 * x78) + x20 * x433 + x21 * x310)
)
result[0, 4, 10] = numpy.sum(
x543 * (x0 * x593 + x15 * (x140 * x357 + x575 * x83) + x20 * x439 + x21 * x315)
)
result[0, 4, 11] = numpy.sum(
x549 * (x0 * x596 + x15 * (x372 * x597 + x580 * x83) + x20 * x443 + x21 * x319)
)
result[0, 4, 12] = numpy.sum(
x272 * (x0 * x600 + x15 * (x402 * x423 + x585 * x83) + x20 * x447 + x21 * x323)
)
result[0, 4, 13] = numpy.sum(
x549 * (x0 * x603 + x15 * (x431 * x78 + x590 * x83) + x20 * x451 + x21 * x328)
)
result[0, 4, 14] = numpy.sum(
x543 * (x0 * x606 + x15 * (x161 * x217 + x590 * x97) + x20 * x455 + x21 * x333)
)
result[0, 5, 0] = numpy.sum(
x219
* (
x0 * x610
+ x15 * (x206 * x611 + x44 * (x204 * x611 + x44**2 * (2.0 * x611 + x615)))
+ x21 * x348
+ x21 * x349
)
)
result[0, 5, 1] = numpy.sum(
x128
* (
x0 * x618
+ x15 * (x363 * x611 + x44 * (x361 * x611 + x44 * (x615 * x83 + x619)))
+ x21 * x364
+ x21 * x365
)
)
result[0, 5, 2] = numpy.sum(
x128
* (
x0 * x623
+ x15 * (x44 * (x252 * x620 + x44 * (x44 * x625 + x624)) + x476 * x620)
+ x21 * x376
+ x21 * x377
)
)
result[0, 5, 3] = numpy.sum(
x260
* (
x0 * x628
+ x15 * (x384 * x611 + x44 * (x107 * x615 + x629))
+ x21 * x385
+ x21 * x386
)
)
result[0, 5, 4] = numpy.sum(
x272
* (
x0 * x632
+ x15 * (x393 * x5 * x620 + x44 * (x361 * x625 + x633))
+ x21 * x394
+ x21 * x395
)
)
result[0, 5, 5] = numpy.sum(
x260
* (
x0 * x637
+ x15 * (x252 * x634 + x44 * (x44 * x639 + x638))
+ x21 * x404
+ x21 * x405
)
)
result[0, 5, 6] = numpy.sum(
x128 * (x0 * x642 + x15 * (x140 * x615 + x643) + x21 * x411 + x21 * x412)
)
result[0, 5, 7] = numpy.sum(
x272 * (x0 * x646 + x15 * (x384 * x625 + x647) + x21 * x418 + x21 * x419)
)
result[0, 5, 8] = numpy.sum(
x272 * (x0 * x650 + x15 * (x361 * x639 + x651) + x21 * x425 + x21 * x426)
)
result[0, 5, 9] = numpy.sum(
x128 * (x0 * x655 + x15 * (x44 * x657 + x656) + x21 * x432 + x21 * x433)
)
result[0, 5, 10] = numpy.sum(
x219 * (x0 * x660 + x169 * x614 + x21 * x438 + x21 * x439)
)
result[0, 5, 11] = numpy.sum(
x128 * (x0 * x663 + x173 * x625 + x21 * x442 + x21 * x443)
)
result[0, 5, 12] = numpy.sum(
x260 * (x0 * x666 + x146 * x639 + x21 * x446 + x21 * x447)
)
result[0, 5, 13] = numpy.sum(
x128 * (x0 * x669 + x118 * x657 + x21 * x450 + x21 * x451)
)
result[0, 5, 14] = numpy.sum(
x219 * (x0 * x672 + x15 * (x437 + x657 * x97) + x21 * x454 + x21 * x455)
)
result[0, 6, 0] = numpy.sum(
x82 * (x20 * x459 + x20 * x460 + x20 * x461 + x209 * x673)
)
result[0, 6, 1] = numpy.sum(
x96 * (x20 * x470 + x20 * x471 + x20 * x472 + x232 * x676)
)
result[0, 6, 2] = numpy.sum(
x96 * (x20 * x477 + x20 * x478 + x20 * x479 + x245 * x673)
)
result[0, 6, 3] = numpy.sum(
x117 * (x20 * x483 + x20 * x484 + x20 * x485 + x229 * x677)
)
result[0, 6, 4] = numpy.sum(
x128 * (x20 * x489 + x20 * x490 + x20 * x491 + x229 * x678)
)
result[0, 6, 5] = numpy.sum(
x117 * (x137 * x679 + x20 * x495 + x20 * x496 + x20 * x497)
)
result[0, 6, 6] = numpy.sum(
x96 * (x20 * x500 + x20 * x501 + x20 * x502 + x226 * x680)
)
result[0, 6, 7] = numpy.sum(
x128 * (x20 * x506 + x20 * x507 + x20 * x508 + x226 * x681)
)
result[0, 6, 8] = numpy.sum(
x128 * (x20 * x512 + x20 * x513 + x20 * x514 + x226 * x682)
)
result[0, 6, 9] = numpy.sum(
x96 * (x166 * x679 + x20 * x517 + x20 * x518 + x20 * x519)
)
result[0, 6, 10] = numpy.sum(
x82 * (x15 * (3.0 * x503 + x680 * x83) + x20 * x521 + x20 * x522 + x20 * x523)
)
result[0, 6, 11] = numpy.sum(
x96 * (x15 * (3.0 * x509 + x681 * x83) + x20 * x524 + x20 * x525 + x20 * x526)
)
result[0, 6, 12] = numpy.sum(
x117 * (x15 * (3.0 * x515 + x682 * x83) + x20 * x527 + x20 * x528 + x20 * x529)
)
result[0, 6, 13] = numpy.sum(
x96 * (x15 * x161 * (x674 + x675) + x20 * x530 + x20 * x531 + x20 * x532)
)
result[0, 6, 14] = numpy.sum(
x82 * (x190 * x673 + x20 * x533 + x20 * x534 + x20 * x535)
)
result[0, 7, 0] = numpy.sum(
x219 * (x20 * x538 + x20 * x539 + x209 * x683 + x21 * x459)
)
result[0, 7, 1] = numpy.sum(
x128 * (x20 * x546 + x20 * x547 + x21 * x470 + x232 * x685)
)
result[0, 7, 2] = numpy.sum(
x128 * (x20 * x552 + x20 * x553 + x21 * x477 + x232 * x686)
)
result[0, 7, 3] = numpy.sum(
x260 * (x20 * x557 + x20 * x558 + x21 * x483 + x229 * x687)
)
result[0, 7, 4] = numpy.sum(
x272 * (x20 * x562 + x20 * x563 + x21 * x489 + x229 * x689)
)
result[0, 7, 5] = numpy.sum(
x260 * (x20 * x568 + x20 * x569 + x21 * x495 + x229 * x690)
)
result[0, 7, 6] = numpy.sum(
x128 * (x20 * x573 + x20 * x574 + x21 * x500 + x226 * x691)
)
result[0, 7, 7] = numpy.sum(
x272 * (x20 * x578 + x20 * x579 + x21 * x506 + x226 * x692)
)
result[0, 7, 8] = numpy.sum(
x272 * (x20 * x583 + x20 * x584 + x21 * x512 + x226 * x694)
)
result[0, 7, 9] = numpy.sum(
x128 * (x20 * x588 + x20 * x589 + x21 * x517 + x226 * x695)
)
result[0, 7, 10] = numpy.sum(
x219 * (x15 * (x51 * x571 + x691 * x83) + x20 * x592 + x20 * x593 + x21 * x521)
)
result[0, 7, 11] = numpy.sum(
x128 * (x15 * (x51 * x576 + x692 * x83) + x20 * x595 + x20 * x596 + x21 * x524)
)
result[0, 7, 12] = numpy.sum(
x260 * (x15 * (x51 * x581 + x694 * x83) + x20 * x599 + x20 * x600 + x21 * x527)
)
result[0, 7, 13] = numpy.sum(
x128 * (x15 * (x695 * x83 + x696) + x20 * x602 + x20 * x603 + x21 * x530)
)
result[0, 7, 14] = numpy.sum(
x219 * (x15 * (x520 + x695 * x97) + x20 * x605 + x20 * x606 + x21 * x533)
)
result[0, 8, 0] = numpy.sum(
x219 * (x20 * x610 + x209 * x697 + x21 * x537 + x21 * x538)
)
result[0, 8, 1] = numpy.sum(
x128 * (x20 * x618 + x21 * x545 + x21 * x546 + x232 * x698)
)
result[0, 8, 2] = numpy.sum(
x128 * (x20 * x623 + x21 * x551 + x21 * x552 + x232 * x699)
)
result[0, 8, 3] = numpy.sum(
x260 * (x20 * x628 + x21 * x556 + x21 * x557 + x229 * x700)
)
result[0, 8, 4] = numpy.sum(
x272 * (x20 * x632 + x21 * x561 + x21 * x562 + x229 * x701)
)
result[0, 8, 5] = numpy.sum(
x260 * (x20 * x637 + x21 * x567 + x21 * x568 + x229 * x702)
)
result[0, 8, 6] = numpy.sum(
x128 * (x20 * x642 + x21 * x572 + x21 * x573 + x226 * x703)
)
result[0, 8, 7] = numpy.sum(
x272 * (x20 * x646 + x21 * x577 + x21 * x578 + x226 * x704)
)
result[0, 8, 8] = numpy.sum(
x272 * (x20 * x650 + x21 * x582 + x21 * x583 + x226 * x705)
)
result[0, 8, 9] = numpy.sum(
x128 * (x20 * x655 + x21 * x587 + x21 * x588 + x226 * x706)
)
result[0, 8, 10] = numpy.sum(
x219 * (x15 * (x643 + x703 * x83) + x20 * x660 + x21 * x591 + x21 * x592)
)
result[0, 8, 11] = numpy.sum(
x128 * (x15 * (x647 + x704 * x83) + x20 * x663 + x21 * x594 + x21 * x595)
)
result[0, 8, 12] = numpy.sum(
x260 * (x15 * (x651 + x705 * x83) + x20 * x666 + x21 * x598 + x21 * x599)
)
result[0, 8, 13] = numpy.sum(
x128 * (x15 * (x656 + x706 * x83) + x20 * x669 + x21 * x601 + x21 * x602)
)
result[0, 8, 14] = numpy.sum(
x219 * (x15 * (x696 + x706 * x97) + x20 * x672 + x21 * x604 + x21 * x605)
)
result[0, 9, 0] = numpy.sum(
x82 * (x209 * x707 + x21 * x608 + x21 * x609 + x21 * x610)
)
result[0, 9, 1] = numpy.sum(
x96 * (x21 * x616 + x21 * x617 + x21 * x618 + x366 * x707)
)
result[0, 9, 2] = numpy.sum(
x96 * (x21 * x621 + x21 * x622 + x21 * x623 + x232 * x708)
)
result[0, 9, 3] = numpy.sum(
x117 * (x21 * x626 + x21 * x627 + x21 * x628 + x388 * x707)
)
result[0, 9, 4] = numpy.sum(
x128 * (x21 * x630 + x21 * x631 + x21 * x632 + x396 * x708)
)
result[0, 9, 5] = numpy.sum(
x117 * (x21 * x635 + x21 * x636 + x21 * x637 + x229 * x709)
)
result[0, 9, 6] = numpy.sum(
x96 * (x21 * x640 + x21 * x641 + x21 * x642 + x413 * x707)
)
result[0, 9, 7] = numpy.sum(
x128 * (x21 * x644 + x21 * x645 + x21 * x646 + x420 * x708)
)
result[0, 9, 8] = numpy.sum(
x128 * (x21 * x648 + x21 * x649 + x21 * x650 + x393 * x709)
)
result[0, 9, 9] = numpy.sum(
x96 * (x21 * x653 + x21 * x654 + x21 * x655 + x226 * x710)
)
result[0, 9, 10] = numpy.sum(
x82 * (x169 * x707 + x21 * x658 + x21 * x659 + x21 * x660)
)
result[0, 9, 11] = numpy.sum(
x96 * (x173 * x708 + x21 * x661 + x21 * x662 + x21 * x663)
)
result[0, 9, 12] = numpy.sum(
x117 * (x146 * x709 + x21 * x664 + x21 * x665 + x21 * x666)
)
result[0, 9, 13] = numpy.sum(
x96 * (x118 * x710 + x21 * x667 + x21 * x668 + x21 * x669)
)
result[0, 9, 14] = numpy.sum(
x82 * (x15 * (3.0 * x656 + x710 * x97) + x21 * x670 + x21 * x671 + x21 * x672)
)
return result
[docs]
def int3c2e3d_sph_100(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ps|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 1, 1), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = cx + x0
x5 = x4 ** (-1.0)
x6 = -x1 * (ax * A[1] + bx * B[1])
x7 = x6 + C[1]
x8 = -x1 * (ax * A[2] + bx * B[2])
x9 = x8 + C[2]
x10 = cx * x0 * x5 * (x3**2 + x7**2 + x9**2)
x11 = x5 * boys(1, x10)
x12 = cx ** (-1.0)
x13 = boys(0, x10)
x14 = (
34.98683665524972
* da
* db
* dc
* x1
* x4 ** (-0.5)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
)
# 3 item(s)
result[0, 0, 0] = numpy.sum(x14 * (x11 * x3 - x12 * x13 * (x2 + A[0])))
result[1, 0, 0] = numpy.sum(x14 * (x11 * x7 - x12 * x13 * (x6 + A[1])))
result[2, 0, 0] = numpy.sum(x14 * (x11 * x9 - x12 * x13 * (x8 + A[2])))
return result
[docs]
def int3c2e3d_sph_101(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ps|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 1, 3), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = cx + x0
x5 = x4 ** (-1.0)
x6 = -x1 * (ax * A[1] + bx * B[1])
x7 = x6 + C[1]
x8 = -x1 * (ax * A[2] + bx * B[2])
x9 = x8 + C[2]
x10 = cx * x0 * x5 * (x3**2 + x7**2 + x9**2)
x11 = x5 * boys(2, x10)
x12 = cx ** (-1.0)
x13 = boys(1, x10)
x14 = -2.0 * x11 * x3 + 2.0 * x12 * x13 * (x2 + A[0])
x15 = x1 * x12 * x13
x16 = (
17.49341832762486
* da
* db
* dc
* x4 ** (-1.5)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
)
x17 = x14 * x16
x18 = -2.0 * x11 * x7 + 2.0 * x12 * x13 * (x6 + A[1])
x19 = x16 * x18
x20 = -2.0 * x11 * x9 + 2.0 * x12 * x13 * (x8 + A[2])
x21 = x16 * x20
# 9 item(s)
result[0, 0, 0] = numpy.sum(x16 * (x14 * x3 + x15))
result[0, 0, 1] = numpy.sum(x17 * x7)
result[0, 0, 2] = numpy.sum(x17 * x9)
result[1, 0, 0] = numpy.sum(x19 * x3)
result[1, 0, 1] = numpy.sum(x16 * (x15 + x18 * x7))
result[1, 0, 2] = numpy.sum(x19 * x9)
result[2, 0, 0] = numpy.sum(x21 * x3)
result[2, 0, 1] = numpy.sum(x21 * x7)
result[2, 0, 2] = numpy.sum(x16 * (x15 + x20 * x9))
return result
[docs]
def int3c2e3d_sph_102(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ps|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 1, 6), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = -x3
x5 = cx + x0
x6 = x5 ** (-1.0)
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x0 * x6
x14 = x13 * (x12**2 + x4**2 + x9**2)
x15 = x6 * boys(3, x14)
x16 = x2 + A[0]
x17 = cx ** (-1.0)
x18 = x17 * boys(2, x14)
x19 = 2.0 * x3
x20 = x19 * (x15 * x4 + x16 * x18)
x21 = x3**2
x22 = x8**2
x23 = x11**2
x24 = x13 * (x21 + x22 + x23)
x25 = boys(2, x24)
x26 = x1 * x17 * x25
x27 = 2.0 * x26
x28 = (
17.49341832762486
* da
* db
* dc
* x0
* x5 ** (-2.5)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
)
x29 = x28 * x3
x30 = 1.732050807568877
x31 = 0.3333333333333333 * x30
x32 = x28 * (x20 + x26)
x33 = x6 * boys(3, x24)
x34 = x16 * x17 * x25 - x3 * x33
x35 = 0.6666666666666667 * x28 * x30
x36 = x34 * x35
x37 = 2.0 * x8
x38 = x11 * x28
x39 = x7 + A[1]
x40 = x17 * x25 * x39 - x33 * x8
x41 = x35 * x40
x42 = x37 * (x15 * x9 + x18 * x39)
x43 = x28 * x8
x44 = x10 + A[2]
x45 = -x11 * x33 + x17 * x25 * x44
x46 = x35 * x45
x47 = 2.0 * x11
x48 = x26 + x45 * x47
# 18 item(s)
result[0, 0, 0] = numpy.sum(-x29 * x31 * (x20 + x27))
result[0, 0, 1] = numpy.sum(-x32 * x8)
result[0, 0, 2] = numpy.sum(-x11 * x32)
result[0, 0, 3] = numpy.sum(-x22 * x36)
result[0, 0, 4] = numpy.sum(-x34 * x37 * x38)
result[0, 0, 5] = numpy.sum(-x23 * x36)
result[1, 0, 0] = numpy.sum(-x21 * x41)
result[1, 0, 1] = numpy.sum(-x29 * (x26 + x37 * x40))
result[1, 0, 2] = numpy.sum(-x19 * x38 * x40)
result[1, 0, 3] = numpy.sum(-x31 * x43 * (x27 + x42))
result[1, 0, 4] = numpy.sum(-x38 * (x26 + x42))
result[1, 0, 5] = numpy.sum(-x23 * x41)
result[2, 0, 0] = numpy.sum(-x21 * x46)
result[2, 0, 1] = numpy.sum(-x19 * x43 * x45)
result[2, 0, 2] = numpy.sum(-x29 * x48)
result[2, 0, 3] = numpy.sum(-x22 * x46)
result[2, 0, 4] = numpy.sum(-x43 * x48)
result[2, 0, 5] = numpy.sum(-x31 * x38 * (x27 + x47 * (x12 * x15 + x18 * x44)))
return result
[docs]
def int3c2e3d_sph_103(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ps|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 1, 10), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = cx + x0
x5 = x4 ** (-1.5)
x6 = x3 * x5
x7 = x3**2
x8 = -x1 * (ax * A[1] + bx * B[1])
x9 = -x8 - C[1]
x10 = x9**2
x11 = -x1 * (ax * A[2] + bx * B[2])
x12 = -x11 - C[2]
x13 = x12**2
x14 = x0 / x4
x15 = cx * x14 * (x10 + x13 + x7)
x16 = 17.49341832762486
x17 = numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
x18 = 2.0 * x16 * x17
x19 = x1 * x18
x20 = x19 * boys(4, x15)
x21 = cx ** (-1.0)
x22 = x4 ** (-0.5)
x23 = boys(3, x15)
x24 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x2 + A[0]) - x20 * x6
x25 = x24 * x3
x26 = 0.5 / (ax + bx)
x27 = x21 * x23
x28 = x19 * x22 * x26 * x27
x29 = x14 * x3
x30 = x18 * x26 * x27
x31 = x0 * x30 * x4 ** (-2.5)
x32 = da * db * dc
x33 = x14 * x32
x34 = 0.2581988897471611
x35 = x33 * x34
x36 = x14 * x9
x37 = x30 * x5
x38 = x37 * x9
x39 = x3 * x31
x40 = 0.5773502691896258
x41 = x33 * x40
x42 = x12 * x14
x43 = x12 * x37
x44 = x0**2 / x4**2
x45 = x25 * x44
x46 = x10 * x31
x47 = x12 * x9
x48 = x31 * x47
x49 = x13 * x31
x50 = x9**3
x51 = x0**3 / x4**3
x52 = x32 * x51
x53 = x34 * x52
x54 = x24 * x53
x55 = x10 * x40
x56 = x24 * x52
x57 = x40 * x9
x58 = x12**3
x59 = x3**3
x60 = x20 * x5
x61 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x8 + A[1]) - x60 * x9
x62 = x53 * x61
x63 = x61 * x9
x64 = x28 + x63
x65 = x40 * x7
x66 = x52 * x65
x67 = x36 * x64 + x38
x68 = x3 * x32
x69 = x44 * x68
x70 = x40 * x69
x71 = x42 * x63 + x43
x72 = x51 * x68
x73 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x11 + A[2]) - x12 * x60
x74 = x53 * x73
x75 = x12 * x73 + x28
x76 = x51 * x75
x77 = x32 * x76
x78 = x42 * x75 + x43
# 30 item(s)
result[0, 0, 0] = numpy.sum(x35 * (x29 * (x29 * (x25 + x28) + x30 * x6) + x31 * x7))
result[0, 0, 1] = numpy.sum(x41 * (x29 * (x25 * x36 + x38) + x39 * x9))
result[0, 0, 2] = numpy.sum(x41 * (x12 * x39 + x29 * (x25 * x42 + x43)))
result[0, 0, 3] = numpy.sum(x41 * (x10 * x45 + x46))
result[0, 0, 4] = numpy.sum(x33 * (x45 * x47 + x48))
result[0, 0, 5] = numpy.sum(x41 * (x13 * x45 + x49))
result[0, 0, 6] = numpy.sum(x50 * x54)
result[0, 0, 7] = numpy.sum(x12 * x55 * x56)
result[0, 0, 8] = numpy.sum(x13 * x56 * x57)
result[0, 0, 9] = numpy.sum(x54 * x58)
result[1, 0, 0] = numpy.sum(x59 * x62)
result[1, 0, 1] = numpy.sum(x64 * x66)
result[1, 0, 2] = numpy.sum(x12 * x61 * x66)
result[1, 0, 3] = numpy.sum(x67 * x70)
result[1, 0, 4] = numpy.sum(x69 * x71)
result[1, 0, 5] = numpy.sum(x13 * x40 * x61 * x72)
result[1, 0, 6] = numpy.sum(x35 * (x36 * x67 + x46))
result[1, 0, 7] = numpy.sum(x41 * (x36 * x71 + x48))
result[1, 0, 8] = numpy.sum(x41 * (x13 * x44 * x63 + x49))
result[1, 0, 9] = numpy.sum(x58 * x62)
result[2, 0, 0] = numpy.sum(x59 * x74)
result[2, 0, 1] = numpy.sum(x66 * x73 * x9)
result[2, 0, 2] = numpy.sum(x65 * x77)
result[2, 0, 3] = numpy.sum(x55 * x72 * x73)
result[2, 0, 4] = numpy.sum(x68 * x76 * x9)
result[2, 0, 5] = numpy.sum(x70 * x78)
result[2, 0, 6] = numpy.sum(x50 * x74)
result[2, 0, 7] = numpy.sum(x55 * x77)
result[2, 0, 8] = numpy.sum(x32 * x44 * x57 * x78)
result[2, 0, 9] = numpy.sum(x35 * (x42 * x78 + x49))
return result
[docs]
def int3c2e3d_sph_104(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ps|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 1, 15), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = cx + x0
x5 = x4 ** (-1.5)
x6 = x3 * x5
x7 = x3**2
x8 = -x1 * (ax * A[1] + bx * B[1])
x9 = -x8 - C[1]
x10 = x9**2
x11 = -x1 * (ax * A[2] + bx * B[2])
x12 = -x11 - C[2]
x13 = x12**2
x14 = x0 / x4
x15 = cx * x14 * (x10 + x13 + x7)
x16 = 17.49341832762486
x17 = numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
x18 = 2.0 * x16 * x17
x19 = x1 * x18
x20 = x19 * boys(5, x15)
x21 = cx ** (-1.0)
x22 = x4 ** (-0.5)
x23 = boys(4, x15)
x24 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x2 + A[0]) - x20 * x6
x25 = x24 * x3
x26 = 0.5 / (ax + bx)
x27 = x21 * x23
x28 = x19 * x22 * x26 * x27
x29 = x14 * x3
x30 = x18 * x26 * x27
x31 = x30 * x7
x32 = x0 * x4 ** (-2.5)
x33 = x3**3
x34 = x0**2
x35 = x34 * x4 ** (-3.5)
x36 = x30 * x35
x37 = da * db * dc
x38 = x14 * x37
x39 = 0.09759000729485332
x40 = x38 * x39
x41 = x14 * x9
x42 = x30 * x5
x43 = x42 * x9
x44 = x30 * x32
x45 = x3 * x44
x46 = x31 * x35
x47 = 0.2581988897471611
x48 = x38 * x47
x49 = x12 * x14
x50 = x12 * x42
x51 = x34 / x4**2
x52 = x10 * x25
x53 = x10 * x44
x54 = x3 * x36
x55 = 0.3333333333333333 * x38
x56 = x51 * x9
x57 = x12 * x9
x58 = x44 * x57
x59 = 1.732050807568877
x60 = x55 * x59
x61 = x13 * x51
x62 = x13 * x44
x63 = x9**3
x64 = x0**3 / x4**3
x65 = x25 * x64
x66 = x36 * x63
x67 = x10 * x12 * x36
x68 = x13 * x9
x69 = x36 * x68
x70 = x12**3
x71 = x36 * x70
x72 = x9**4
x73 = x0**4 / x4**4
x74 = x24 * x73
x75 = x37 * x39
x76 = x74 * x75
x77 = x37 * x47
x78 = x74 * x77
x79 = 0.3333333333333333 * x37
x80 = x13 * x79
x81 = x12**4
x82 = x3**4
x83 = x20 * x5
x84 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x8 + A[1]) - x83 * x9
x85 = x73 * x84
x86 = x75 * x85
x87 = x84 * x9
x88 = x28 + x87
x89 = x73 * x77
x90 = x33 * x89
x91 = x77 * x85
x92 = x41 * x88 + x43
x93 = x64 * x79
x94 = x7 * x93
x95 = x49 * x87 + x50
x96 = x41 * x92 + x53
x97 = x3 * x51
x98 = x77 * x97
x99 = x41 * x95 + x58
x100 = x59 * x79
x101 = x100 * x97
x102 = x61 * x87 + x62
x103 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x11 + A[2]) - x12 * x83
x104 = x103 * x73
x105 = x104 * x75
x106 = x103 * x12 + x28
x107 = x100 * x106 * x73
x108 = x106 * x49 + x50
x109 = x63 * x89
x110 = x108 * x93
x111 = x108 * x49 + x62
# 45 item(s)
result[0, 0, 0] = numpy.sum(
x40 * (x29 * (x29 * (x29 * (x25 + x28) + x30 * x6) + x31 * x32) + x33 * x36)
)
result[0, 0, 1] = numpy.sum(
x48 * (x29 * (x29 * (x25 * x41 + x43) + x45 * x9) + x46 * x9)
)
result[0, 0, 2] = numpy.sum(
x48 * (x12 * x46 + x29 * (x12 * x45 + x29 * (x25 * x49 + x50)))
)
result[0, 0, 3] = numpy.sum(x55 * (x10 * x54 + x29 * (x51 * x52 + x53)))
result[0, 0, 4] = numpy.sum(x60 * (x29 * (x12 * x25 * x56 + x58) + x54 * x57))
result[0, 0, 5] = numpy.sum(x55 * (x13 * x54 + x29 * (x25 * x61 + x62)))
result[0, 0, 6] = numpy.sum(x48 * (x63 * x65 + x66))
result[0, 0, 7] = numpy.sum(x60 * (x12 * x52 * x64 + x67))
result[0, 0, 8] = numpy.sum(x60 * (x65 * x68 + x69))
result[0, 0, 9] = numpy.sum(x48 * (x65 * x70 + x71))
result[0, 0, 10] = numpy.sum(x72 * x76)
result[0, 0, 11] = numpy.sum(x12 * x63 * x78)
result[0, 0, 12] = numpy.sum(x10 * x74 * x80)
result[0, 0, 13] = numpy.sum(x70 * x78 * x9)
result[0, 0, 14] = numpy.sum(x76 * x81)
result[1, 0, 0] = numpy.sum(x82 * x86)
result[1, 0, 1] = numpy.sum(x88 * x90)
result[1, 0, 2] = numpy.sum(x12 * x33 * x91)
result[1, 0, 3] = numpy.sum(x92 * x94)
result[1, 0, 4] = numpy.sum(x59 * x94 * x95)
result[1, 0, 5] = numpy.sum(x7 * x80 * x85)
result[1, 0, 6] = numpy.sum(x96 * x98)
result[1, 0, 7] = numpy.sum(x101 * x99)
result[1, 0, 8] = numpy.sum(x101 * x102)
result[1, 0, 9] = numpy.sum(x3 * x70 * x91)
result[1, 0, 10] = numpy.sum(x40 * (x41 * x96 + x66))
result[1, 0, 11] = numpy.sum(x48 * (x41 * x99 + x67))
result[1, 0, 12] = numpy.sum(x55 * (x102 * x41 + x69))
result[1, 0, 13] = numpy.sum(x48 * (x64 * x70 * x87 + x71))
result[1, 0, 14] = numpy.sum(x81 * x86)
result[2, 0, 0] = numpy.sum(x105 * x82)
result[2, 0, 1] = numpy.sum(x103 * x9 * x90)
result[2, 0, 2] = numpy.sum(x106 * x90)
result[2, 0, 3] = numpy.sum(x10 * x104 * x7 * x79)
result[2, 0, 4] = numpy.sum(x107 * x7 * x9)
result[2, 0, 5] = numpy.sum(x108 * x94)
result[2, 0, 6] = numpy.sum(x103 * x109 * x3)
result[2, 0, 7] = numpy.sum(x10 * x107 * x3)
result[2, 0, 8] = numpy.sum(x110 * x3 * x59 * x9)
result[2, 0, 9] = numpy.sum(x111 * x98)
result[2, 0, 10] = numpy.sum(x105 * x72)
result[2, 0, 11] = numpy.sum(x106 * x109)
result[2, 0, 12] = numpy.sum(x10 * x110)
result[2, 0, 13] = numpy.sum(x111 * x56 * x77)
result[2, 0, 14] = numpy.sum(x40 * (x111 * x49 + x71))
return result
[docs]
def int3c2e3d_sph_110(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pp|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 3, 1), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = cx + x0
x3 = x2 ** (-1.0)
x4 = -x1 * (ax * A[0] + bx * B[0])
x5 = x4 + C[0]
x6 = -x5
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x3
x14 = x0 * x13 * (x12**2 + x6**2 + x9**2)
x15 = boys(1, x14)
x16 = x15 * x3
x17 = cx ** (-1.0)
x18 = x17 * boys(0, x14)
x19 = x1 * (x16 - x18)
x20 = x4 + A[0]
x21 = -x20
x22 = x16 * x6 - x18 * x21
x23 = 2.0 * x22
x24 = A[0] - B[0]
x25 = x3 * boys(2, x14)
x26 = x15 * x17
x27 = x13 * x5
x28 = A[1] - B[1]
x29 = A[2] - B[2]
x30 = (
17.49341832762486
* da
* db
* dc
* x1
* x2 ** (-0.5)
* numpy.exp(-ax * bx * x1 * (x24**2 + x28**2 + x29**2))
)
x31 = x7 + A[1]
x32 = -x31
x33 = x16 * x9 - x18 * x32
x34 = x25 * x9 - x26 * x32
x35 = -x20 * x33 + x27 * x34
x36 = 2.0 * x30
x37 = x10 + A[2]
x38 = -x37
x39 = x12 * x16 - x18 * x38
x40 = x12 * x25 - x26 * x38
x41 = -x20 * x39 + x27 * x40
x42 = 2.0 * x33
x43 = x13 * x8
x44 = -x31 * x39 + x40 * x43
x45 = 2.0 * x39
# 9 item(s)
result[0, 0, 0] = numpy.sum(
-x30 * (x19 - x20 * x23 + x23 * x24 - 2.0 * x27 * (x21 * x26 - x25 * x6))
)
result[0, 1, 0] = numpy.sum(-x36 * (x22 * x28 + x35))
result[0, 2, 0] = numpy.sum(-x36 * (x22 * x29 + x41))
result[1, 0, 0] = numpy.sum(-x36 * (x24 * x33 + x35))
result[1, 1, 0] = numpy.sum(x30 * (-x19 - x28 * x42 + x31 * x42 - 2.0 * x34 * x43))
result[1, 2, 0] = numpy.sum(-x36 * (x29 * x33 + x44))
result[2, 0, 0] = numpy.sum(-x36 * (x24 * x39 + x41))
result[2, 1, 0] = numpy.sum(-x36 * (x28 * x39 + x44))
result[2, 2, 0] = numpy.sum(
x30 * (-2.0 * x11 * x13 * x40 - x19 - x29 * x45 + x37 * x45)
)
return result
[docs]
def int3c2e3d_sph_111(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pp|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 3, 3), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = cx + x0
x5 = x4 ** (-1.0)
x6 = -x3
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x5
x14 = x0 * x13
x15 = x14 * (x12**2 + x6**2 + x9**2)
x16 = boys(2, x15)
x17 = x16 * x5
x18 = cx ** (-1.0)
x19 = x18 * boys(1, x15)
x20 = x1 * (x17 - x19)
x21 = x2 + A[0]
x22 = -x21
x23 = 2.0 * x17 * x6 - 2.0 * x19 * x22
x24 = x5 * boys(3, x15)
x25 = x16 * x18
x26 = x13 * x3
x27 = x20 - x21 * x23 - 2.0 * x26 * (x22 * x25 - x24 * x6)
x28 = A[0] - B[0]
x29 = x14 * (x11**2 + x3**2 + x8**2)
x30 = x5 * boys(2, x29)
x31 = boys(1, x29)
x32 = x18 * x21 * x31 - x3 * x30
x33 = 2.0 * x32
x34 = x1 * x18 * x31
x35 = x3 * x33 + x34
x36 = A[1] - B[1]
x37 = A[2] - B[2]
x38 = (
17.49341832762486
* da
* db
* dc
* x4 ** (-1.5)
* numpy.exp(-ax * bx * x1 * (x28**2 + x36**2 + x37**2))
)
x39 = x38 * (x27 + x28 * x33)
x40 = x7 + A[1]
x41 = x18 * x31 * x40 - x30 * x8
x42 = -x1 * x41
x43 = -x40
x44 = x17 * x9 - x19 * x43
x45 = x24 * x9 - x25 * x43
x46 = -x21 * x44 + x26 * x45
x47 = 2.0 * x46
x48 = x3 * x47 + x42
x49 = x32 * x36
x50 = 2.0 * x8
x51 = -x1 * x32
x52 = x47 * x8 + x51
x53 = 2.0 * x11
x54 = x38 * x53
x55 = x10 + A[2]
x56 = -x11 * x30 + x18 * x31 * x55
x57 = -x1 * x56
x58 = -x55
x59 = x12 * x17 - x19 * x58
x60 = x12 * x24 - x25 * x58
x61 = -x21 * x59 + x26 * x60
x62 = 2.0 * x61
x63 = x3 * x62 + x57
x64 = x32 * x37
x65 = x38 * x50
x66 = x11 * x62 + x51
x67 = x28 * x41
x68 = 2.0 * x3
x69 = 2.0 * x41
x70 = x34 + x69 * x8
x71 = 2.0 * x44
x72 = x13 * x45 * x50 + x20 - x40 * x71
x73 = x38 * (x36 * x69 + x72)
x74 = x37 * x41
x75 = x13 * x60
x76 = -x40 * x59 + x75 * x8
x77 = x38 * x68
x78 = 2.0 * x76
x79 = x57 + x78 * x8
x80 = x11 * x78 + x42
x81 = x28 * x56
x82 = 2.0 * x56
x83 = x11 * x82 + x34
x84 = x36 * x56
x85 = 2.0 * x59
x86 = x20 + x53 * x75 - x55 * x85
x87 = x38 * (x37 * x82 + x86)
# 27 item(s)
result[0, 0, 0] = numpy.sum(x38 * (-x1 * x23 + x27 * x3 + x28 * x35))
result[0, 0, 1] = numpy.sum(x39 * x8)
result[0, 0, 2] = numpy.sum(x11 * x39)
result[0, 1, 0] = numpy.sum(x38 * (x35 * x36 + x48))
result[0, 1, 1] = numpy.sum(x38 * (x49 * x50 + x52))
result[0, 1, 2] = numpy.sum(x54 * (x46 + x49))
result[0, 2, 0] = numpy.sum(x38 * (x35 * x37 + x63))
result[0, 2, 1] = numpy.sum(x65 * (x61 + x64))
result[0, 2, 2] = numpy.sum(x38 * (x53 * x64 + x66))
result[1, 0, 0] = numpy.sum(x38 * (x48 + x67 * x68))
result[1, 0, 1] = numpy.sum(x38 * (x28 * x70 + x52))
result[1, 0, 2] = numpy.sum(x54 * (x46 + x67))
result[1, 1, 0] = numpy.sum(x3 * x73)
result[1, 1, 1] = numpy.sum(x38 * (-x1 * x71 + x36 * x70 + x72 * x8))
result[1, 1, 2] = numpy.sum(x11 * x73)
result[1, 2, 0] = numpy.sum(x77 * (x74 + x76))
result[1, 2, 1] = numpy.sum(x38 * (x37 * x70 + x79))
result[1, 2, 2] = numpy.sum(x38 * (x53 * x74 + x80))
result[2, 0, 0] = numpy.sum(x38 * (x63 + x68 * x81))
result[2, 0, 1] = numpy.sum(x65 * (x61 + x81))
result[2, 0, 2] = numpy.sum(x38 * (x28 * x83 + x66))
result[2, 1, 0] = numpy.sum(x77 * (x76 + x84))
result[2, 1, 1] = numpy.sum(x38 * (x50 * x84 + x79))
result[2, 1, 2] = numpy.sum(x38 * (x36 * x83 + x80))
result[2, 2, 0] = numpy.sum(x3 * x87)
result[2, 2, 1] = numpy.sum(x8 * x87)
result[2, 2, 2] = numpy.sum(x38 * (-x1 * x85 + x11 * x86 + x37 * x83))
return result
[docs]
def int3c2e3d_sph_112(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pp|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 3, 6), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = -x3
x5 = cx + x0
x6 = x5 ** (-1.0)
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x6
x14 = x0 * x13
x15 = x14 * (x12**2 + x4**2 + x9**2)
x16 = boys(3, x15)
x17 = x16 * x6
x18 = x2 + A[0]
x19 = -x18
x20 = cx ** (-1.0)
x21 = boys(2, x15)
x22 = x20 * x21
x23 = x17 * x4 - x19 * x22
x24 = x23 * x3
x25 = x3**2
x26 = x8**2
x27 = x11**2
x28 = x14 * (x25 + x26 + x27)
x29 = boys(2, x28)
x30 = x1 * x20 * x29
x31 = 2.0 * x24 + x30
x32 = x1 * (x17 - x22)
x33 = 2.0 * x23
x34 = x6 * boys(4, x15)
x35 = 2.0 * x3
x36 = -x13 * x35 * (x16 * x19 * x20 - x34 * x4) - x18 * x33 + x32
x37 = x1 * x23
x38 = A[0] - B[0]
x39 = x24 + x30
x40 = 1.732050807568877
x41 = A[1] - B[1]
x42 = A[2] - B[2]
x43 = (
17.49341832762486
* da
* db
* dc
* x0
* x5 ** (-2.5)
* numpy.exp(-ax * bx * x1 * (x38**2 + x41**2 + x42**2))
)
x44 = x40 * x43
x45 = 0.3333333333333333 * x44
x46 = x6 * boys(3, x28)
x47 = -x43 * (-2.0 * x1 * (x18 * x20 * x29 - x3 * x46) + x3 * x36 + x31 * x38)
x48 = x33 * x38 + x36
x49 = x45 * x48
x50 = x11 * x43
x51 = x7 + A[1]
x52 = -x51
x53 = x17 * x9 - x20 * x21 * x52
x54 = x1 * x53
x55 = -x54
x56 = -x16 * x20 * x52 + x34 * x9
x57 = x13 * x4
x58 = x19 * x53 - x56 * x57
x59 = x3 * x58
x60 = x55 + x59
x61 = x3 * x43
x62 = 0.6666666666666667 * x40
x63 = x61 * x62
x64 = x31 * x41
x65 = -x37
x66 = x58 * x8
x67 = x65 + 2.0 * x66
x68 = x53 * x8
x69 = x30 + 2.0 * x68
x70 = x1 * x69
x71 = x3 * x67 - 0.5 * x70
x72 = x55 + 2.0 * x59
x73 = x23 * x41
x74 = x73 * x8
x75 = x65 + x66
x76 = x43 * x8
x77 = x62 * x76
x78 = 0.6666666666666667 * x44
x79 = x27 * x78
x80 = x10 + A[2]
x81 = -x80
x82 = x12 * x17 - x20 * x21 * x81
x83 = -x82
x84 = x12 * x34 - x16 * x20 * x81
x85 = -x84
x86 = -x19 * x83 + x57 * x85
x87 = x3 * x86
x88 = x1 * x82
x89 = -x88
x90 = x87 + x89
x91 = x31 * x42
x92 = 2.0 * x87 + x89
x93 = x11 * x86
x94 = x65 + 2.0 * x93
x95 = x11 * x82
x96 = x30 + 2.0 * x95
x97 = x1 * x96
x98 = -0.5 * x97
x99 = x3 * x94 + x98
x100 = x23 * x42
x101 = x26 * x78
x102 = x100 * x11
x103 = x65 + x93
x104 = x50 * x62
x105 = x38 * x53
x106 = x105 * x3
x107 = x38 * x69
x108 = x30 + x68
x109 = 2.0 * x53
x110 = 2.0 * x8
x111 = -x109 * x51 + x110 * x13 * x56 + x32
x112 = x109 * x41 + x111
x113 = x112 * x45
x114 = x41 * x69
x115 = -x111 * x8 + 2.0 * x54
x116 = x42 * x53
x117 = x13 * x85 * x9 - x52 * x83
x118 = x25 * x78
x119 = x42 * x69
x120 = x117 * x8
x121 = 2.0 * x120 + x89
x122 = x11 * x116
x123 = x11 * x117
x124 = 2.0 * x123 + x55
x125 = x120 + x89
x126 = x124 * x8 + x98
x127 = x123 + x55
x128 = x38 * x82
x129 = x128 * x3
x130 = x38 * x96
x131 = x30 + x95
x132 = x41 * x82
x133 = x132 * x8
x134 = x41 * x96
x135 = 2.0 * x82
x136 = 2.0 * x11
x137 = x13 * x136 * x84 - x135 * x80 + x32
x138 = x135 * x42 + x137
x139 = x138 * x45
x140 = -x11 * x137 + 2.0 * x88
x141 = -x140 + x42 * x96
# 54 item(s)
result[0, 0, 0] = numpy.sum(
-x45 * (-x1 * x31 + x3 * (x3 * x36 - 2.0 * x37) + x35 * x38 * x39)
)
result[0, 0, 1] = numpy.sum(x47 * x8)
result[0, 0, 2] = numpy.sum(x11 * x47)
result[0, 0, 3] = numpy.sum(-x26 * x49)
result[0, 0, 4] = numpy.sum(-x48 * x50 * x8)
result[0, 0, 5] = numpy.sum(-x27 * x49)
result[0, 1, 0] = numpy.sum(-x63 * (x39 * x41 + x60))
result[0, 1, 1] = numpy.sum(-x43 * (x64 * x8 + x71))
result[0, 1, 2] = numpy.sum(-x50 * (x64 + x72))
result[0, 1, 3] = numpy.sum(-x77 * (x74 + x75))
result[0, 1, 4] = numpy.sum(-x50 * (x67 + 2.0 * x74))
result[0, 1, 5] = numpy.sum(-x79 * (x58 + x73))
result[0, 2, 0] = numpy.sum(-x63 * (x39 * x42 + x90))
result[0, 2, 1] = numpy.sum(-x76 * (x91 + x92))
result[0, 2, 2] = numpy.sum(-x43 * (x11 * x91 + x99))
result[0, 2, 3] = numpy.sum(-x101 * (x100 + x86))
result[0, 2, 4] = numpy.sum(-x76 * (2.0 * x102 + x94))
result[0, 2, 5] = numpy.sum(-x104 * (x102 + x103))
result[1, 0, 0] = numpy.sum(-x63 * (x106 + x60))
result[1, 0, 1] = numpy.sum(-x43 * (x107 * x3 + x71))
result[1, 0, 2] = numpy.sum(-x50 * (2.0 * x106 + x72))
result[1, 0, 3] = numpy.sum(-x77 * (x108 * x38 + x75))
result[1, 0, 4] = numpy.sum(-x50 * (x107 + x67))
result[1, 0, 5] = numpy.sum(-x79 * (x105 + x58))
result[1, 1, 0] = numpy.sum(-x113 * x25)
result[1, 1, 1] = numpy.sum(x61 * (-x114 + x115))
result[1, 1, 2] = numpy.sum(-x112 * x3 * x50)
result[1, 1, 3] = numpy.sum(x45 * (-x108 * x110 * x41 + x115 * x8 + x70))
result[1, 1, 4] = numpy.sum(
-x50 * (-2.0 * x1 * (x20 * x29 * x51 - x46 * x8) + x111 * x8 + x114)
)
result[1, 1, 5] = numpy.sum(-x113 * x27)
result[1, 2, 0] = numpy.sum(-x118 * (x116 + x117))
result[1, 2, 1] = numpy.sum(-x61 * (x119 + x121))
result[1, 2, 2] = numpy.sum(-x61 * (2.0 * x122 + x124))
result[1, 2, 3] = numpy.sum(-x77 * (x108 * x42 + x125))
result[1, 2, 4] = numpy.sum(-x43 * (x11 * x119 + x126))
result[1, 2, 5] = numpy.sum(-x104 * (x122 + x127))
result[2, 0, 0] = numpy.sum(-x63 * (x129 + x90))
result[2, 0, 1] = numpy.sum(-x76 * (2.0 * x129 + x92))
result[2, 0, 2] = numpy.sum(-x43 * (x130 * x3 + x99))
result[2, 0, 3] = numpy.sum(-x101 * (x128 + x86))
result[2, 0, 4] = numpy.sum(-x76 * (x130 + x94))
result[2, 0, 5] = numpy.sum(-x104 * (x103 + x131 * x38))
result[2, 1, 0] = numpy.sum(-x118 * (x117 + x132))
result[2, 1, 1] = numpy.sum(-x61 * (x121 + 2.0 * x133))
result[2, 1, 2] = numpy.sum(-x61 * (x124 + x134))
result[2, 1, 3] = numpy.sum(-x77 * (x125 + x133))
result[2, 1, 4] = numpy.sum(-x43 * (x126 + x134 * x8))
result[2, 1, 5] = numpy.sum(-x104 * (x127 + x131 * x41))
result[2, 2, 0] = numpy.sum(-x139 * x25)
result[2, 2, 1] = numpy.sum(-x138 * x3 * x76)
result[2, 2, 2] = numpy.sum(-x141 * x61)
result[2, 2, 3] = numpy.sum(-x139 * x26)
result[2, 2, 4] = numpy.sum(-x141 * x76)
result[2, 2, 5] = numpy.sum(x45 * (x11 * x140 - x131 * x136 * x42 + x97))
return result
[docs]
def int3c2e3d_sph_113(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pp|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 3, 10), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = 0.5 / (ax + bx)
x5 = x3**2
x6 = -x1 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = x7**2
x9 = -x1 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = x10**2
x12 = cx + x0
x13 = x12 ** (-1.0)
x14 = x0 * x13
x15 = cx * x14 * (x11 + x5 + x8)
x16 = boys(4, x15)
x17 = x12 ** (-1.5)
x18 = 17.49341832762486
x19 = A[0] - B[0]
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = numpy.exp(-ax * bx * x1 * (x19**2 + x20**2 + x21**2))
x23 = 2.0 * x18 * x22
x24 = x1 * x23
x25 = x17 * x24
x26 = x16 * x25
x27 = cx ** (-1.0)
x28 = x12 ** (-0.5)
x29 = boys(3, x15)
x30 = x4 * (2.0 * x1 * x18 * x22 * x27 * x28 * x29 - x26)
x31 = -x2 - A[0]
x32 = 2.0 * x1 * x18 * x22 * x27 * x28 * x29 * x31 - x26 * x3
x33 = x25 * boys(5, x15)
x34 = cx * x13
x35 = x3 * x34
x36 = (
x30 + x31 * x32 - x35 * (2.0 * x1 * x16 * x18 * x22 * x27 * x28 * x31 - x3 * x33)
)
x37 = x3 * x36
x38 = x32 * x4
x39 = 2.0 * x38
x40 = x14 * x3
x41 = x3 * x32
x42 = x27 * x29
x43 = x24 * x28 * x4 * x42
x44 = x41 + x43
x45 = x14 * x4
x46 = 2.0 * x45
x47 = x23 * x4 * x42
x48 = x17 * x47
x49 = x3 * x48 + x40 * x44
x50 = x0 * x12 ** (-2.5) * x47
x51 = x40 * x49 + x5 * x50
x52 = x14 * x19
x53 = da * db * dc
x54 = 0.2581988897471611 * x53
x55 = x14 * x7
x56 = x48 * x7
x57 = x41 * x55 + x56
x58 = x3 * x50
x59 = x40 * x57 + x58 * x7
x60 = 0.5773502691896258 * x53
x61 = x10 * x14
x62 = x10 * x48
x63 = x41 * x61 + x62
x64 = x10 * x58 + x40 * x63
x65 = x0**2 / x12**2
x66 = x65 * x8
x67 = x50 * x8
x68 = x41 * x66 + x67
x69 = x65 * x7
x70 = x10 * x69
x71 = x10 * x50 * x7
x72 = x41 * x70 + x71
x73 = x11 * x65
x74 = x11 * x50
x75 = x41 * x73 + x74
x76 = x7**3
x77 = x0**3 / x12**3
x78 = x36 * x77
x79 = x76 * x77
x80 = x19 * x32
x81 = x77 * x8
x82 = x10 * x81
x83 = x11 * x7
x84 = x77 * x83
x85 = x10**3
x86 = x77 * x85
x87 = -x6 - A[1]
x88 = 2.0 * x1 * x18 * x22 * x27 * x28 * x29 * x87 - x26 * x7
x89 = x4 * x88
x90 = 2.0 * x1 * x16 * x18 * x22 * x27 * x28 * x87 - x33 * x7
x91 = x31 * x88 - x35 * x90
x92 = x3 * x91
x93 = x5 * x65
x94 = x14 * (x40**2 * (2.0 * x89 + x92) + x89 * x93)
x95 = x14 * x20
x96 = x7 * x88
x97 = x43 + x96
x98 = x14 * x97
x99 = x4 * x98
x100 = x7 * x91
x101 = x100 + x38
x102 = x3 * x65
x103 = x102 * x4
x104 = x14 * (x103 * x97 + x40 * (x101 * x40 + x99))
x105 = x61 * x89
x106 = x14 * (x10 * x102 * x89 + x40 * (x105 + x61 * x92))
x107 = x56 + x7 * x98
x108 = x107 * x45
x109 = x55 * (x101 + x38)
x110 = x14 * (x108 + x109 * x40)
x111 = x61 * x96 + x62
x112 = x111 * x45
x113 = x38 * x61
x114 = x100 * x61 + x113
x115 = x14 * (x112 + x114 * x40)
x116 = x73 * x89
x117 = x14 * (x116 + x73 * x92)
x118 = x14 * (x109 * x55 + x38 * x66)
x119 = x20 * x32
x120 = x14 * (x114 * x55 + x38 * x70)
x121 = x38 * x73
x122 = x14 * (x100 * x73 + x121)
x123 = x86 * x91
x124 = -x9 - A[2]
x125 = 2.0 * x1 * x124 * x18 * x22 * x27 * x28 * x29 - x10 * x26
x126 = x125 * x4
x127 = 2.0 * x1 * x124 * x16 * x18 * x22 * x27 * x28 - x10 * x33
x128 = x125 * x31 - x127 * x35
x129 = x128 * x3
x130 = x14 * (x126 * x93 + x40**2 * (2.0 * x126 + x129))
x131 = x14 * x21
x132 = x126 * x55
x133 = x3 * x69
x134 = x14 * (x126 * x133 + x40 * (x129 * x55 + x132))
x135 = x10 * x125 + x43
x136 = x135 * x45
x137 = x10 * x128 + x38
x138 = x14 * (x103 * x135 + x40 * (x136 + x137 * x40))
x139 = x126 * x66
x140 = x14 * (x129 * x66 + x139)
x141 = x135 * x4 * x69
x142 = x14 * (x133 * x137 + x141)
x143 = x135 * x61 + x62
x144 = x143 * x45
x145 = x113 + x137 * x61
x146 = x14 * (x144 + x145 * x40)
x147 = x128 * x79
x148 = x21 * x32
x149 = x137 * x81
x150 = x145 * x69
x151 = x14 * (x121 + x145 * x61)
x152 = x3**3 * x77
x153 = x19 * x88
x154 = x5 * x77
x155 = x154 * x97
x156 = x10 * x154
x157 = x102 * x19
x158 = x3 * x77
x159 = x11 * x158
x160 = x107 * x55 + x67
x161 = x111 * x55 + x71
x162 = x73 * x96 + x74
x163 = x34 * x7
x164 = -x163 * x90 + x30 + x87 * x88
x165 = x20 * x88
x166 = x164 * x7
x167 = 2.0 * x89
x168 = x166 + x167
x169 = x168 * x55 + 2.0 * x99
x170 = x102 * x20
x171 = x61 * (x166 + x167)
x172 = x125 * x87 - x127 * x163
x173 = x152 * x172
x174 = x21 * x88
x175 = x126 + x172 * x7
x176 = x154 * x175
x177 = x10 * x172 + x89
x178 = x154 * x177
x179 = x132 + x175 * x55
x180 = x102 * x179
x181 = x102 * x21
x182 = x136 + x177 * x55
x183 = x102 * x182
x184 = x105 + x177 * x61
x185 = x102 * x184
x186 = x14 * (x139 + x179 * x55)
x187 = x14 * (x141 + x182 * x55)
x188 = x14 * (x144 + x184 * x55)
x189 = x14 * (x116 + x184 * x61)
x190 = x125 * x19
x191 = x154 * x7
x192 = x135 * x19
x193 = x3 * x81
x194 = x158 * x7
x195 = x143 * x69
x196 = x143 * x61 + x74
x197 = x125 * x20
x198 = x135 * x20
x199 = -x10 * x127 * x34 + x124 * x125 + x30
x200 = x125 * x21
x201 = x10 * x199 + 2.0 * x126
x202 = x135 * x21
x203 = 2.0 * x136 + x201 * x61
# 90 item(s)
result[0, 0, 0] = numpy.sum(
x54 * (x14 * (x40 * (x40 * (x37 + x39) + x44 * x46) + x46 * x49) + x51 * x52)
)
result[0, 0, 1] = numpy.sum(
x60 * (x14 * (x40 * x55 * (x37 + x39) + x46 * x57) + x52 * x59)
)
result[0, 0, 2] = numpy.sum(
x60 * (x14 * (x40 * x61 * (x37 + x39) + x46 * x63) + x52 * x64)
)
result[0, 0, 3] = numpy.sum(x60 * (x14 * x66 * (x37 + x39) + x52 * x68))
result[0, 0, 4] = numpy.sum(x53 * (x14 * x70 * (x37 + x39) + x52 * x72))
result[0, 0, 5] = numpy.sum(x60 * (x14 * x73 * (x37 + x39) + x52 * x75))
result[0, 0, 6] = numpy.sum(x54 * (x76 * x78 + x79 * x80))
result[0, 0, 7] = numpy.sum(x60 * (x10 * x78 * x8 + x80 * x82))
result[0, 0, 8] = numpy.sum(x60 * (x78 * x83 + x80 * x84))
result[0, 0, 9] = numpy.sum(x54 * (x78 * x85 + x80 * x86))
result[0, 1, 0] = numpy.sum(x54 * (x51 * x95 + x94))
result[0, 1, 1] = numpy.sum(x60 * (x104 + x59 * x95))
result[0, 1, 2] = numpy.sum(x60 * (x106 + x64 * x95))
result[0, 1, 3] = numpy.sum(x60 * (x110 + x68 * x95))
result[0, 1, 4] = numpy.sum(x53 * (x115 + x72 * x95))
result[0, 1, 5] = numpy.sum(x60 * (x117 + x75 * x95))
result[0, 1, 6] = numpy.sum(x54 * (x118 + x119 * x79))
result[0, 1, 7] = numpy.sum(x60 * (x119 * x82 + x120))
result[0, 1, 8] = numpy.sum(x60 * (x119 * x84 + x122))
result[0, 1, 9] = numpy.sum(x54 * (x119 * x86 + x123))
result[0, 2, 0] = numpy.sum(x54 * (x130 + x131 * x51))
result[0, 2, 1] = numpy.sum(x60 * (x131 * x59 + x134))
result[0, 2, 2] = numpy.sum(x60 * (x131 * x64 + x138))
result[0, 2, 3] = numpy.sum(x60 * (x131 * x68 + x140))
result[0, 2, 4] = numpy.sum(x53 * (x131 * x72 + x142))
result[0, 2, 5] = numpy.sum(x60 * (x131 * x75 + x146))
result[0, 2, 6] = numpy.sum(x54 * (x147 + x148 * x79))
result[0, 2, 7] = numpy.sum(x60 * (x148 * x82 + x149))
result[0, 2, 8] = numpy.sum(x60 * (x148 * x84 + x150))
result[0, 2, 9] = numpy.sum(x54 * (x148 * x86 + x151))
result[1, 0, 0] = numpy.sum(x54 * (x152 * x153 + x94))
result[1, 0, 1] = numpy.sum(x60 * (x104 + x155 * x19))
result[1, 0, 2] = numpy.sum(x60 * (x106 + x153 * x156))
result[1, 0, 3] = numpy.sum(x60 * (x107 * x157 + x110))
result[1, 0, 4] = numpy.sum(x53 * (x111 * x157 + x115))
result[1, 0, 5] = numpy.sum(x60 * (x117 + x153 * x159))
result[1, 0, 6] = numpy.sum(x54 * (x118 + x160 * x52))
result[1, 0, 7] = numpy.sum(x60 * (x120 + x161 * x52))
result[1, 0, 8] = numpy.sum(x60 * (x122 + x162 * x52))
result[1, 0, 9] = numpy.sum(x54 * (x123 + x153 * x86))
result[1, 1, 0] = numpy.sum(x152 * x54 * (x164 + x165))
result[1, 1, 1] = numpy.sum(x60 * (x154 * x168 + x155 * x20))
result[1, 1, 2] = numpy.sum(x156 * x60 * (x164 + x165))
result[1, 1, 3] = numpy.sum(x60 * (x102 * x169 + x107 * x170))
result[1, 1, 4] = numpy.sum(x53 * (x102 * x171 + x111 * x170))
result[1, 1, 5] = numpy.sum(x159 * x60 * (x164 + x165))
result[1, 1, 6] = numpy.sum(x54 * (x14 * (2.0 * x108 + x169 * x55) + x160 * x95))
result[1, 1, 7] = numpy.sum(x60 * (x14 * (2.0 * x112 + x171 * x55) + x161 * x95))
result[1, 1, 8] = numpy.sum(x60 * (x14 * x73 * (x166 + x167) + x162 * x95))
result[1, 1, 9] = numpy.sum(x54 * x86 * (x164 + x165))
result[1, 2, 0] = numpy.sum(x54 * (x152 * x174 + x173))
result[1, 2, 1] = numpy.sum(x60 * (x155 * x21 + x176))
result[1, 2, 2] = numpy.sum(x60 * (x156 * x174 + x178))
result[1, 2, 3] = numpy.sum(x60 * (x107 * x181 + x180))
result[1, 2, 4] = numpy.sum(x53 * (x111 * x181 + x183))
result[1, 2, 5] = numpy.sum(x60 * (x159 * x174 + x185))
result[1, 2, 6] = numpy.sum(x54 * (x131 * x160 + x186))
result[1, 2, 7] = numpy.sum(x60 * (x131 * x161 + x187))
result[1, 2, 8] = numpy.sum(x60 * (x131 * x162 + x188))
result[1, 2, 9] = numpy.sum(x54 * (x174 * x86 + x189))
result[2, 0, 0] = numpy.sum(x54 * (x130 + x152 * x190))
result[2, 0, 1] = numpy.sum(x60 * (x134 + x190 * x191))
result[2, 0, 2] = numpy.sum(x60 * (x138 + x154 * x192))
result[2, 0, 3] = numpy.sum(x60 * (x140 + x190 * x193))
result[2, 0, 4] = numpy.sum(x53 * (x142 + x192 * x194))
result[2, 0, 5] = numpy.sum(x60 * (x143 * x157 + x146))
result[2, 0, 6] = numpy.sum(x54 * (x147 + x190 * x79))
result[2, 0, 7] = numpy.sum(x60 * (x149 + x192 * x81))
result[2, 0, 8] = numpy.sum(x60 * (x150 + x19 * x195))
result[2, 0, 9] = numpy.sum(x54 * (x151 + x196 * x52))
result[2, 1, 0] = numpy.sum(x54 * (x152 * x197 + x173))
result[2, 1, 1] = numpy.sum(x60 * (x176 + x191 * x197))
result[2, 1, 2] = numpy.sum(x60 * (x154 * x198 + x178))
result[2, 1, 3] = numpy.sum(x60 * (x180 + x193 * x197))
result[2, 1, 4] = numpy.sum(x53 * (x183 + x194 * x198))
result[2, 1, 5] = numpy.sum(x60 * (x143 * x170 + x185))
result[2, 1, 6] = numpy.sum(x54 * (x186 + x197 * x79))
result[2, 1, 7] = numpy.sum(x60 * (x187 + x198 * x81))
result[2, 1, 8] = numpy.sum(x60 * (x188 + x195 * x20))
result[2, 1, 9] = numpy.sum(x54 * (x189 + x196 * x95))
result[2, 2, 0] = numpy.sum(x152 * x54 * (x199 + x200))
result[2, 2, 1] = numpy.sum(x191 * x60 * (x199 + x200))
result[2, 2, 2] = numpy.sum(x154 * x60 * (x201 + x202))
result[2, 2, 3] = numpy.sum(x193 * x60 * (x199 + x200))
result[2, 2, 4] = numpy.sum(x194 * x53 * (x201 + x202))
result[2, 2, 5] = numpy.sum(x60 * (x102 * x203 + x143 * x181))
result[2, 2, 6] = numpy.sum(x54 * x79 * (x199 + x200))
result[2, 2, 7] = numpy.sum(x60 * x81 * (x201 + x202))
result[2, 2, 8] = numpy.sum(x60 * (x195 * x21 + x203 * x69))
result[2, 2, 9] = numpy.sum(x54 * (x131 * x196 + x14 * (2.0 * x144 + x203 * x61)))
return result
[docs]
def int3c2e3d_sph_114(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pp|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 3, 15), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = 0.5 / (ax + bx)
x5 = x3**2
x6 = -x1 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = x7**2
x9 = -x1 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = x10**2
x12 = cx + x0
x13 = x12 ** (-1.0)
x14 = x0 * x13
x15 = cx * x14 * (x11 + x5 + x8)
x16 = boys(5, x15)
x17 = x12 ** (-1.5)
x18 = 17.49341832762486
x19 = A[0] - B[0]
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = numpy.exp(-ax * bx * x1 * (x19**2 + x20**2 + x21**2))
x23 = 2.0 * x18 * x22
x24 = x1 * x23
x25 = x17 * x24
x26 = x16 * x25
x27 = cx ** (-1.0)
x28 = x12 ** (-0.5)
x29 = boys(4, x15)
x30 = x4 * (2.0 * x1 * x18 * x22 * x27 * x28 * x29 - x26)
x31 = -x2 - A[0]
x32 = 2.0 * x1 * x18 * x22 * x27 * x28 * x29 * x31 - x26 * x3
x33 = x25 * boys(6, x15)
x34 = cx * x13
x35 = x3 * x34
x36 = (
x30 + x31 * x32 - x35 * (2.0 * x1 * x16 * x18 * x22 * x27 * x28 * x31 - x3 * x33)
)
x37 = x3 * x36
x38 = x32 * x4
x39 = 2.0 * x38
x40 = x14 * x3
x41 = x3 * x32
x42 = x27 * x29
x43 = x24 * x28 * x4 * x42
x44 = x41 + x43
x45 = x14 * x4
x46 = 2.0 * x45
x47 = x23 * x4 * x42
x48 = x17 * x47
x49 = x3 * x48 + x40 * x44
x50 = x47 * x5
x51 = x0 * x12 ** (-2.5)
x52 = x40 * x49 + x50 * x51
x53 = x3**3
x54 = x0**2
x55 = x12 ** (-3.5) * x54
x56 = x47 * x55
x57 = x40 * x52 + x53 * x56
x58 = x14 * x19
x59 = da * db * dc
x60 = 0.09759000729485332 * x59
x61 = x14 * x7
x62 = x48 * x7
x63 = x41 * x61 + x62
x64 = x47 * x51
x65 = x3 * x64
x66 = x40 * x63 + x65 * x7
x67 = x50 * x55
x68 = x40 * x66 + x67 * x7
x69 = 0.2581988897471611 * x59
x70 = x10 * x14
x71 = x10 * x48
x72 = x41 * x70 + x71
x73 = x10 * x65 + x40 * x72
x74 = x10 * x67 + x40 * x73
x75 = x54 / x12**2
x76 = x75 * x8
x77 = x64 * x8
x78 = x41 * x76 + x77
x79 = x3 * x8
x80 = x40 * x78 + x56 * x79
x81 = 0.3333333333333333 * x59
x82 = x7 * x75
x83 = x10 * x82
x84 = x10 * x7
x85 = x64 * x84
x86 = x41 * x83 + x85
x87 = x3 * x56 * x84 + x40 * x86
x88 = 1.732050807568877 * x81
x89 = x11 * x75
x90 = x11 * x64
x91 = x41 * x89 + x90
x92 = x11 * x3
x93 = x40 * x91 + x56 * x92
x94 = x7**3
x95 = x0**3 / x12**3
x96 = x94 * x95
x97 = x56 * x94
x98 = x41 * x96 + x97
x99 = x8 * x95
x100 = x10 * x99
x101 = x10 * x56 * x8
x102 = x100 * x41 + x101
x103 = x7 * x95
x104 = x103 * x11
x105 = x11 * x56 * x7
x106 = x104 * x41 + x105
x107 = x10**3
x108 = x107 * x95
x109 = x107 * x56
x110 = x108 * x41 + x109
x111 = x7**4
x112 = x0**4 / x12**4
x113 = x112 * x36
x114 = x111 * x112
x115 = x19 * x32
x116 = x112 * x94
x117 = x10 * x116
x118 = x11 * x8
x119 = x112 * x115
x120 = x107 * x7
x121 = x10**4
x122 = x112 * x121
x123 = -x6 - A[1]
x124 = 2.0 * x1 * x123 * x18 * x22 * x27 * x28 * x29 - x26 * x7
x125 = x124 * x4
x126 = 2.0 * x1 * x123 * x16 * x18 * x22 * x27 * x28 - x33 * x7
x127 = x124 * x31 - x126 * x35
x128 = x127 * x3
x129 = x5 * x75
x130 = x53 * x95
x131 = x14 * (x125 * x130 + x40 * (x125 * x129 + x40**2 * (2.0 * x125 + x128)))
x132 = x14 * x20
x133 = x124 * x7
x134 = x133 + x43
x135 = x134 * x14
x136 = x135 * x4
x137 = x127 * x7
x138 = x137 + x38
x139 = x3 * x75
x140 = x134 * x4
x141 = x5 * x95
x142 = x14 * (x140 * x141 + x40 * (x139 * x140 + x40 * (x136 + x138 * x40)))
x143 = x125 * x70
x144 = x10 * x125
x145 = x14 * (x141 * x144 + x40 * (x139 * x144 + x40 * (x128 * x70 + x143)))
x146 = x135 * x7 + x62
x147 = x146 * x45
x148 = x61 * (x138 + x38)
x149 = x139 * x4
x150 = x14 * (x146 * x149 + x40 * (x147 + x148 * x40))
x151 = x133 * x70 + x71
x152 = x151 * x45
x153 = x38 * x70
x154 = x137 * x70 + x153
x155 = x14 * (x149 * x151 + x40 * (x152 + x154 * x40))
x156 = x125 * x89
x157 = x14 * (x125 * x92 * x95 + x40 * (x128 * x89 + x156))
x158 = x146 * x61 + x77
x159 = x158 * x45
x160 = x148 * x61 + x38 * x76
x161 = x14 * (x159 + x160 * x40)
x162 = x151 * x61 + x85
x163 = x162 * x45
x164 = x154 * x61 + x38 * x83
x165 = x14 * (x163 + x164 * x40)
x166 = x133 * x89 + x90
x167 = x166 * x45
x168 = x38 * x89
x169 = x137 * x89 + x168
x170 = x14 * (x167 + x169 * x40)
x171 = x108 * x125
x172 = x14 * (x108 * x128 + x171)
x173 = x14 * (x160 * x61 + x38 * x96)
x174 = x20 * x32
x175 = x14 * (x100 * x38 + x164 * x61)
x176 = x14 * (x104 * x38 + x169 * x61)
x177 = x112 * x174
x178 = x108 * x38
x179 = x14 * (x108 * x137 + x178)
x180 = x122 * x127
x181 = -x9 - A[2]
x182 = 2.0 * x1 * x18 * x181 * x22 * x27 * x28 * x29 - x10 * x26
x183 = x182 * x4
x184 = 2.0 * x1 * x16 * x18 * x181 * x22 * x27 * x28 - x10 * x33
x185 = x182 * x31 - x184 * x35
x186 = x185 * x3
x187 = x14 * (x130 * x183 + x40 * (x129 * x183 + x40**2 * (2.0 * x183 + x186)))
x188 = x14 * x21
x189 = x183 * x61
x190 = x3 * x82
x191 = x14 * (x141 * x183 * x7 + x40 * (x183 * x190 + x40 * (x186 * x61 + x189)))
x192 = x10 * x182 + x43
x193 = x192 * x45
x194 = x10 * x185 + x38
x195 = x192 * x4
x196 = x14 * (x141 * x195 + x40 * (x149 * x192 + x40 * (x193 + x194 * x40)))
x197 = x183 * x76
x198 = x14 * (x183 * x3 * x99 + x40 * (x186 * x76 + x197))
x199 = x195 * x82
x200 = x194 * x3
x201 = x103 * x3
x202 = x14 * (x195 * x201 + x40 * (x199 + x200 * x82))
x203 = x192 * x70 + x71
x204 = x203 * x45
x205 = x153 + x194 * x70
x206 = x14 * (x149 * x203 + x40 * (x204 + x205 * x40))
x207 = x183 * x96
x208 = x14 * (x186 * x96 + x207)
x209 = x195 * x99
x210 = x14 * (x200 * x99 + x209)
x211 = x203 * x4 * x82
x212 = x14 * (x190 * x205 + x211)
x213 = x203 * x70 + x90
x214 = x213 * x45
x215 = x168 + x205 * x70
x216 = x14 * (x214 + x215 * x40)
x217 = x114 * x185
x218 = x21 * x32
x219 = x116 * x194
x220 = x205 * x99
x221 = x112 * x218
x222 = x215 * x82
x223 = x14 * (x178 + x215 * x70)
x224 = x112 * x3**4
x225 = x124 * x19
x226 = x112 * x53
x227 = x134 * x226
x228 = x10 * x226
x229 = x141 * x19
x230 = x11 * x5
x231 = x112 * x225
x232 = x139 * x19
x233 = x107 * x3
x234 = x158 * x61 + x97
x235 = x101 + x162 * x61
x236 = x105 + x166 * x61
x237 = x108 * x133 + x109
x238 = x34 * x7
x239 = x123 * x124 - x126 * x238 + x30
x240 = x124 * x20
x241 = x239 * x7
x242 = 2.0 * x125
x243 = x241 + x242
x244 = 2.0 * x136 + x243 * x61
x245 = x141 * x20
x246 = x70 * (x241 + x242)
x247 = x112 * x239
x248 = x112 * x240
x249 = 2.0 * x147 + x244 * x61
x250 = x139 * x20
x251 = 2.0 * x152 + x246 * x61
x252 = x89 * (x241 + x242)
x253 = x123 * x182 - x184 * x238
x254 = x224 * x253
x255 = x124 * x21
x256 = x183 + x253 * x7
x257 = x226 * x256
x258 = x10 * x253 + x125
x259 = x226 * x258
x260 = x189 + x256 * x61
x261 = x141 * x260
x262 = x141 * x21
x263 = x193 + x258 * x61
x264 = x141 * x263
x265 = x143 + x258 * x70
x266 = x141 * x265
x267 = x112 * x255
x268 = x197 + x260 * x61
x269 = x139 * x268
x270 = x139 * x21
x271 = x199 + x263 * x61
x272 = x139 * x271
x273 = x204 + x265 * x61
x274 = x139 * x273
x275 = x156 + x265 * x70
x276 = x139 * x275
x277 = x14 * (x207 + x268 * x61)
x278 = x14 * (x209 + x271 * x61)
x279 = x14 * (x211 + x273 * x61)
x280 = x14 * (x214 + x275 * x61)
x281 = x14 * (x171 + x275 * x70)
x282 = x182 * x19
x283 = x226 * x7
x284 = x19 * x192
x285 = x112 * x5
x286 = x285 * x8
x287 = x285 * x7
x288 = x116 * x3
x289 = x112 * x79
x290 = x201 * x203
x291 = x203 * x99
x292 = x213 * x82
x293 = x109 + x213 * x70
x294 = x182 * x20
x295 = x192 * x20
x296 = -x10 * x184 * x34 + x181 * x182 + x30
x297 = x182 * x21
x298 = x10 * x296 + 2.0 * x183
x299 = x192 * x21
x300 = 2.0 * x193 + x298 * x70
x301 = 2.0 * x204 + x300 * x70
# 135 item(s)
result[0, 0, 0] = numpy.sum(
x60
* (
x14 * (x40 * (x40 * (x40 * (x37 + x39) + x44 * x46) + x46 * x49) + x46 * x52)
+ x57 * x58
)
)
result[0, 0, 1] = numpy.sum(
x69
* (x14 * (x40 * (x40 * x61 * (x37 + x39) + x46 * x63) + x46 * x66) + x58 * x68)
)
result[0, 0, 2] = numpy.sum(
x69
* (x14 * (x40 * (x40 * x70 * (x37 + x39) + x46 * x72) + x46 * x73) + x58 * x74)
)
result[0, 0, 3] = numpy.sum(
x81 * (x14 * (x40 * x76 * (x37 + x39) + x46 * x78) + x58 * x80)
)
result[0, 0, 4] = numpy.sum(
x88 * (x14 * (x40 * x83 * (x37 + x39) + x46 * x86) + x58 * x87)
)
result[0, 0, 5] = numpy.sum(
x81 * (x14 * (x40 * x89 * (x37 + x39) + x46 * x91) + x58 * x93)
)
result[0, 0, 6] = numpy.sum(x69 * (x14 * x96 * (x37 + x39) + x58 * x98))
result[0, 0, 7] = numpy.sum(x88 * (x100 * x14 * (x37 + x39) + x102 * x58))
result[0, 0, 8] = numpy.sum(x88 * (x104 * x14 * (x37 + x39) + x106 * x58))
result[0, 0, 9] = numpy.sum(x69 * (x108 * x14 * (x37 + x39) + x110 * x58))
result[0, 0, 10] = numpy.sum(x60 * (x111 * x113 + x114 * x115))
result[0, 0, 11] = numpy.sum(x69 * (x10 * x113 * x94 + x115 * x117))
result[0, 0, 12] = numpy.sum(x118 * x81 * (x113 + x119))
result[0, 0, 13] = numpy.sum(x120 * x69 * (x113 + x119))
result[0, 0, 14] = numpy.sum(x60 * (x113 * x121 + x115 * x122))
result[0, 1, 0] = numpy.sum(x60 * (x131 + x132 * x57))
result[0, 1, 1] = numpy.sum(x69 * (x132 * x68 + x142))
result[0, 1, 2] = numpy.sum(x69 * (x132 * x74 + x145))
result[0, 1, 3] = numpy.sum(x81 * (x132 * x80 + x150))
result[0, 1, 4] = numpy.sum(x88 * (x132 * x87 + x155))
result[0, 1, 5] = numpy.sum(x81 * (x132 * x93 + x157))
result[0, 1, 6] = numpy.sum(x69 * (x132 * x98 + x161))
result[0, 1, 7] = numpy.sum(x88 * (x102 * x132 + x165))
result[0, 1, 8] = numpy.sum(x88 * (x106 * x132 + x170))
result[0, 1, 9] = numpy.sum(x69 * (x110 * x132 + x172))
result[0, 1, 10] = numpy.sum(x60 * (x114 * x174 + x173))
result[0, 1, 11] = numpy.sum(x69 * (x117 * x174 + x175))
result[0, 1, 12] = numpy.sum(x81 * (x118 * x177 + x176))
result[0, 1, 13] = numpy.sum(x69 * (x120 * x177 + x179))
result[0, 1, 14] = numpy.sum(x60 * (x122 * x174 + x180))
result[0, 2, 0] = numpy.sum(x60 * (x187 + x188 * x57))
result[0, 2, 1] = numpy.sum(x69 * (x188 * x68 + x191))
result[0, 2, 2] = numpy.sum(x69 * (x188 * x74 + x196))
result[0, 2, 3] = numpy.sum(x81 * (x188 * x80 + x198))
result[0, 2, 4] = numpy.sum(x88 * (x188 * x87 + x202))
result[0, 2, 5] = numpy.sum(x81 * (x188 * x93 + x206))
result[0, 2, 6] = numpy.sum(x69 * (x188 * x98 + x208))
result[0, 2, 7] = numpy.sum(x88 * (x102 * x188 + x210))
result[0, 2, 8] = numpy.sum(x88 * (x106 * x188 + x212))
result[0, 2, 9] = numpy.sum(x69 * (x110 * x188 + x216))
result[0, 2, 10] = numpy.sum(x60 * (x114 * x218 + x217))
result[0, 2, 11] = numpy.sum(x69 * (x117 * x218 + x219))
result[0, 2, 12] = numpy.sum(x81 * (x118 * x221 + x220))
result[0, 2, 13] = numpy.sum(x69 * (x120 * x221 + x222))
result[0, 2, 14] = numpy.sum(x60 * (x122 * x218 + x223))
result[1, 0, 0] = numpy.sum(x60 * (x131 + x224 * x225))
result[1, 0, 1] = numpy.sum(x69 * (x142 + x19 * x227))
result[1, 0, 2] = numpy.sum(x69 * (x145 + x225 * x228))
result[1, 0, 3] = numpy.sum(x81 * (x146 * x229 + x150))
result[1, 0, 4] = numpy.sum(x88 * (x151 * x229 + x155))
result[1, 0, 5] = numpy.sum(x81 * (x157 + x230 * x231))
result[1, 0, 6] = numpy.sum(x69 * (x158 * x232 + x161))
result[1, 0, 7] = numpy.sum(x88 * (x162 * x232 + x165))
result[1, 0, 8] = numpy.sum(x88 * (x166 * x232 + x170))
result[1, 0, 9] = numpy.sum(x69 * (x172 + x231 * x233))
result[1, 0, 10] = numpy.sum(x60 * (x173 + x234 * x58))
result[1, 0, 11] = numpy.sum(x69 * (x175 + x235 * x58))
result[1, 0, 12] = numpy.sum(x81 * (x176 + x236 * x58))
result[1, 0, 13] = numpy.sum(x69 * (x179 + x237 * x58))
result[1, 0, 14] = numpy.sum(x60 * (x122 * x225 + x180))
result[1, 1, 0] = numpy.sum(x224 * x60 * (x239 + x240))
result[1, 1, 1] = numpy.sum(x69 * (x20 * x227 + x226 * x243))
result[1, 1, 2] = numpy.sum(x228 * x69 * (x239 + x240))
result[1, 1, 3] = numpy.sum(x81 * (x141 * x244 + x146 * x245))
result[1, 1, 4] = numpy.sum(x88 * (x141 * x246 + x151 * x245))
result[1, 1, 5] = numpy.sum(x230 * x81 * (x247 + x248))
result[1, 1, 6] = numpy.sum(x69 * (x139 * x249 + x158 * x250))
result[1, 1, 7] = numpy.sum(x88 * (x139 * x251 + x162 * x250))
result[1, 1, 8] = numpy.sum(x88 * (x139 * x252 + x166 * x250))
result[1, 1, 9] = numpy.sum(x233 * x69 * (x247 + x248))
result[1, 1, 10] = numpy.sum(x60 * (x132 * x234 + x14 * (2.0 * x159 + x249 * x61)))
result[1, 1, 11] = numpy.sum(x69 * (x132 * x235 + x14 * (2.0 * x163 + x251 * x61)))
result[1, 1, 12] = numpy.sum(x81 * (x132 * x236 + x14 * (2.0 * x167 + x252 * x61)))
result[1, 1, 13] = numpy.sum(x69 * (x108 * x14 * (x241 + x242) + x132 * x237))
result[1, 1, 14] = numpy.sum(x122 * x60 * (x239 + x240))
result[1, 2, 0] = numpy.sum(x60 * (x224 * x255 + x254))
result[1, 2, 1] = numpy.sum(x69 * (x21 * x227 + x257))
result[1, 2, 2] = numpy.sum(x69 * (x228 * x255 + x259))
result[1, 2, 3] = numpy.sum(x81 * (x146 * x262 + x261))
result[1, 2, 4] = numpy.sum(x88 * (x151 * x262 + x264))
result[1, 2, 5] = numpy.sum(x81 * (x230 * x267 + x266))
result[1, 2, 6] = numpy.sum(x69 * (x158 * x270 + x269))
result[1, 2, 7] = numpy.sum(x88 * (x162 * x270 + x272))
result[1, 2, 8] = numpy.sum(x88 * (x166 * x270 + x274))
result[1, 2, 9] = numpy.sum(x69 * (x233 * x267 + x276))
result[1, 2, 10] = numpy.sum(x60 * (x188 * x234 + x277))
result[1, 2, 11] = numpy.sum(x69 * (x188 * x235 + x278))
result[1, 2, 12] = numpy.sum(x81 * (x188 * x236 + x279))
result[1, 2, 13] = numpy.sum(x69 * (x188 * x237 + x280))
result[1, 2, 14] = numpy.sum(x60 * (x122 * x255 + x281))
result[2, 0, 0] = numpy.sum(x60 * (x187 + x224 * x282))
result[2, 0, 1] = numpy.sum(x69 * (x191 + x282 * x283))
result[2, 0, 2] = numpy.sum(x69 * (x196 + x226 * x284))
result[2, 0, 3] = numpy.sum(x81 * (x198 + x282 * x286))
result[2, 0, 4] = numpy.sum(x88 * (x202 + x284 * x287))
result[2, 0, 5] = numpy.sum(x81 * (x203 * x229 + x206))
result[2, 0, 6] = numpy.sum(x69 * (x208 + x282 * x288))
result[2, 0, 7] = numpy.sum(x88 * (x210 + x284 * x289))
result[2, 0, 8] = numpy.sum(x88 * (x19 * x290 + x212))
result[2, 0, 9] = numpy.sum(x69 * (x213 * x232 + x216))
result[2, 0, 10] = numpy.sum(x60 * (x114 * x282 + x217))
result[2, 0, 11] = numpy.sum(x69 * (x116 * x284 + x219))
result[2, 0, 12] = numpy.sum(x81 * (x19 * x291 + x220))
result[2, 0, 13] = numpy.sum(x69 * (x19 * x292 + x222))
result[2, 0, 14] = numpy.sum(x60 * (x223 + x293 * x58))
result[2, 1, 0] = numpy.sum(x60 * (x224 * x294 + x254))
result[2, 1, 1] = numpy.sum(x69 * (x257 + x283 * x294))
result[2, 1, 2] = numpy.sum(x69 * (x226 * x295 + x259))
result[2, 1, 3] = numpy.sum(x81 * (x261 + x286 * x294))
result[2, 1, 4] = numpy.sum(x88 * (x264 + x287 * x295))
result[2, 1, 5] = numpy.sum(x81 * (x203 * x245 + x266))
result[2, 1, 6] = numpy.sum(x69 * (x269 + x288 * x294))
result[2, 1, 7] = numpy.sum(x88 * (x272 + x289 * x295))
result[2, 1, 8] = numpy.sum(x88 * (x20 * x290 + x274))
result[2, 1, 9] = numpy.sum(x69 * (x213 * x250 + x276))
result[2, 1, 10] = numpy.sum(x60 * (x114 * x294 + x277))
result[2, 1, 11] = numpy.sum(x69 * (x116 * x295 + x278))
result[2, 1, 12] = numpy.sum(x81 * (x20 * x291 + x279))
result[2, 1, 13] = numpy.sum(x69 * (x20 * x292 + x280))
result[2, 1, 14] = numpy.sum(x60 * (x132 * x293 + x281))
result[2, 2, 0] = numpy.sum(x224 * x60 * (x296 + x297))
result[2, 2, 1] = numpy.sum(x283 * x69 * (x296 + x297))
result[2, 2, 2] = numpy.sum(x226 * x69 * (x298 + x299))
result[2, 2, 3] = numpy.sum(x286 * x81 * (x296 + x297))
result[2, 2, 4] = numpy.sum(x287 * x88 * (x298 + x299))
result[2, 2, 5] = numpy.sum(x81 * (x141 * x300 + x203 * x262))
result[2, 2, 6] = numpy.sum(x288 * x69 * (x296 + x297))
result[2, 2, 7] = numpy.sum(x289 * x88 * (x298 + x299))
result[2, 2, 8] = numpy.sum(x88 * (x201 * x300 + x21 * x290))
result[2, 2, 9] = numpy.sum(x69 * (x139 * x301 + x213 * x270))
result[2, 2, 10] = numpy.sum(x114 * x60 * (x296 + x297))
result[2, 2, 11] = numpy.sum(x116 * x69 * (x298 + x299))
result[2, 2, 12] = numpy.sum(x81 * (x21 * x291 + x300 * x99))
result[2, 2, 13] = numpy.sum(x69 * (x21 * x292 + x301 * x82))
result[2, 2, 14] = numpy.sum(x60 * (x14 * (2.0 * x214 + x301 * x70) + x188 * x293))
return result
[docs]
def int3c2e3d_sph_120(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pd|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 6, 1), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = cx + x1
x4 = x3 ** (-1.0)
x5 = -x2 * (ax * A[0] + bx * B[0])
x6 = x5 + C[0]
x7 = -x6
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = x8 + C[1]
x10 = -x9
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = x11 + C[2]
x13 = -x12
x14 = cx * x4
x15 = x1 * x14
x16 = x15 * (x10**2 + x13**2 + x7**2)
x17 = boys(1, x16)
x18 = x17 * x4
x19 = cx ** (-1.0)
x20 = x19 * boys(0, x16)
x21 = x2 * (x18 - x20)
x22 = x5 + A[0]
x23 = -x22
x24 = x18 * x7 - x20 * x23
x25 = 2.0 * x24
x26 = boys(2, x16)
x27 = x26 * x4
x28 = x17 * x19
x29 = -x23 * x28 + x27 * x7
x30 = x14 * x29
x31 = x21 - x22 * x25 + 2.0 * x30 * x6
x32 = x15 * (x12**2 + x6**2 + x9**2)
x33 = x4 * boys(1, x32)
x34 = boys(0, x32)
x35 = 2.0 * x2
x36 = x2 * (x27 - x28)
x37 = 2.0 * x22
x38 = x4 * boys(3, x16)
x39 = x19 * x26
x40 = x14 * x6
x41 = 2.0 * x40
x42 = A[1] - B[1]
x43 = A[2] - B[2]
x44 = (
17.49341832762486
* da
* db
* dc
* x3 ** (-0.5)
* numpy.exp(-ax * bx * x2 * (x0**2 + x42**2 + x43**2))
)
x45 = x2 * x44
x46 = 0.5773502691896258 * x45
x47 = x8 + A[1]
x48 = -x47
x49 = x10 * x27 - x28 * x48
x50 = x14 * x49
x51 = x2 * (x19 * x34 * x47 - x33 * x9 - x50)
x52 = x10 * x18 - x20 * x48
x53 = -x22 * x52 + x50 * x6
x54 = x24 * x42 + x53
x55 = 2.0 * x0
x56 = x10 * x38 - x39 * x48
x57 = x11 + A[2]
x58 = -x57
x59 = x13 * x27 - x28 * x58
x60 = x14 * x59
x61 = x2 * (-x12 * x33 + x19 * x34 * x57 - x60)
x62 = x13 * x18 - x20 * x58
x63 = -x22 * x62 + x6 * x60
x64 = x24 * x43 + x63
x65 = x13 * x38 - x39 * x58
x66 = 2.0 * x42
x67 = 2.0 * x47
x68 = x21 + 2.0 * x50 * x9 - x52 * x67
x69 = x14 * x9
x70 = 2.0 * x69
x71 = x36 - x49 * x67 + x56 * x70
x72 = -x22 * x68 + x40 * x71 + x53 * x66
x73 = -x49
x74 = x14 * x73
x75 = x23 * x52 + x7 * x74
x76 = -x62
x77 = -x59
x78 = x14 * x77
x79 = x10 * x78 - x48 * x76
x80 = -x14 * x65
x81 = x10 * x80 - x48 * x77
x82 = -x22 * x79 + x40 * x81
x83 = x43 * x75 + x82
x84 = x35 * x44
x85 = 2.0 * x43
x86 = 2.0 * x57
x87 = 2.0 * x12 * x60 + x21 - x62 * x86
x88 = x12 * x14
x89 = x36 - x59 * x86 + 2.0 * x65 * x88
x90 = -x22 * x87 + x40 * x89 + x63 * x85
x91 = x52 * x66 + x68
x92 = -x47 * x62 + x60 * x9
x93 = x43 * x52 + x92
x94 = -x47 * x87 + x69 * x89 + x85 * x92
x95 = x2 * (x62 + x78)
x96 = -x23 * x76 + x7 * x78
x97 = -x42 * x62 - x92
x98 = x62 * x85 + x87
# 18 item(s)
result[0, 0, 0] = numpy.sum(
x46
* (
-x0 * x31
- x0 * (x0 * x25 + x31)
+ x22 * x31
+ x35 * (-x19 * x22 * x34 + x30 + x33 * x6)
+ x40 * (x29 * x37 - x36 + x41 * (x23 * x39 - x38 * x7))
)
)
result[0, 1, 0] = numpy.sum(
-x45
* (-2.0 * x22 * x53 + x31 * x42 - x41 * (x22 * x49 - x40 * x56) + x51 + x54 * x55)
)
result[0, 2, 0] = numpy.sum(
-x45
* (-2.0 * x22 * x63 + x31 * x43 - x41 * (x22 * x59 - x40 * x65) + x55 * x64 + x61)
)
result[0, 3, 0] = numpy.sum(-x46 * (x54 * x66 + x72))
result[0, 4, 0] = numpy.sum(-x84 * (x42 * x64 + x83))
result[0, 5, 0] = numpy.sum(-x46 * (x64 * x85 + x90))
result[1, 0, 0] = numpy.sum(
-x46
* (
x2 * (x52 + x74)
- x37 * x75
- x41 * (x14 * x56 * x7 + x23 * x73)
+ x55 * x75
+ x55 * (x0 * x52 + x53)
)
)
result[1, 1, 0] = numpy.sum(-x45 * (x0 * x91 + x72))
result[1, 2, 0] = numpy.sum(-x84 * (x0 * x93 + x83))
result[1, 3, 0] = numpy.sum(
x46 * (-x42 * x68 - x42 * x91 + x47 * x68 - 2.0 * x51 - x69 * x71)
)
result[1, 4, 0] = numpy.sum(
-x45
* (x43 * x68 - 2.0 * x47 * x92 + x61 + x66 * x93 - x70 * (x47 * x59 - x65 * x69))
)
result[1, 5, 0] = numpy.sum(-x46 * (x85 * x93 + x94))
result[2, 0, 0] = numpy.sum(
-x46
* (
-x37 * x96
- x41 * (x23 * x77 - x7 * x80)
+ x55 * x96
+ x55 * (x0 * x62 + x63)
+ x95
)
)
result[2, 1, 0] = numpy.sum(x84 * (x0 * x97 - x42 * x96 - x82))
result[2, 2, 0] = numpy.sum(-x45 * (x0 * x98 + x90))
result[2, 3, 0] = numpy.sum(
x46 * (-x66 * x79 + x66 * x97 + x67 * x79 - x70 * x81 - x95)
)
result[2, 4, 0] = numpy.sum(-x45 * (x42 * x98 + x94))
result[2, 5, 0] = numpy.sum(
x46 * (-x43 * x87 - x43 * x98 + x57 * x87 - 2.0 * x61 - x88 * x89)
)
return result
[docs]
def int3c2e3d_sph_121(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pd|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 6, 3), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = x3 + C[0]
x5 = cx + x1
x6 = x5 ** (-1.0)
x7 = -x4
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = x8 + C[1]
x10 = -x9
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = x11 + C[2]
x13 = -x12
x14 = cx * x6
x15 = x1 * x14
x16 = x15 * (x10**2 + x13**2 + x7**2)
x17 = boys(2, x16)
x18 = x17 * x6
x19 = cx ** (-1.0)
x20 = x19 * boys(1, x16)
x21 = x2 * (x18 - x20)
x22 = x3 + A[0]
x23 = -x22
x24 = x18 * x7 - x20 * x23
x25 = 2.0 * x24
x26 = boys(3, x16)
x27 = x26 * x6
x28 = x17 * x19
x29 = -x23 * x28 + x27 * x7
x30 = 2.0 * x4
x31 = x14 * x30
x32 = x21 - x22 * x25 + x29 * x31
x33 = -x32
x34 = x2 * x25 + x33 * x4
x35 = 2.0 * x2
x36 = x2 * (x27 - x28)
x37 = x6 * boys(4, x16)
x38 = (
-cx * x4 * x6 * (2.0 * x22 * x29 + x31 * (x19 * x23 * x26 - x37 * x7) - x36)
+ x22 * x33
- x35 * (x14 * x29 - x24)
)
x39 = x15 * (x12**2 + x4**2 + x9**2)
x40 = x6 * boys(2, x39)
x41 = boys(1, x39)
x42 = x19 * x22 * x41 - x4 * x40
x43 = x19 * x2 * x41
x44 = x30 * x42 + x43
x45 = A[1] - B[1]
x46 = A[2] - B[2]
x47 = (
17.49341832762486
* da
* db
* dc
* x5 ** (-1.5)
* numpy.exp(-ax * bx * x2 * (x0**2 + x45**2 + x46**2))
)
x48 = 0.5773502691896258
x49 = x47 * x48
x50 = x47 * x9
x51 = -x48 * (-x0 * x33 + x0 * (x0 * x25 + x32) + x38)
x52 = x12 * x47
x53 = x8 + A[1]
x54 = -x53
x55 = x10 * x27 - x28 * x54
x56 = -x55
x57 = x14 * x56
x58 = x10 * x18 - x20 * x54
x59 = x2 * (x57 + x58)
x60 = x23 * x58 + x57 * x7
x61 = 2.0 * x22
x62 = x10 * x37 - x19 * x26 * x54
x63 = x14 * x7
x64 = -x31 * (x23 * x56 + x62 * x63) + x59 - x60 * x61
x65 = -x64
x66 = x4 * x65
x67 = x19 * x41 * x53 - x40 * x9
x68 = -x2 * x67
x69 = x14 * x4
x70 = -x22 * x58 + x55 * x69
x71 = x30 * x70 + x68
x72 = x44 * x45 + x71
x73 = x35 * x60
x74 = x42 * x45
x75 = 2.0 * x9
x76 = -x2 * x42
x77 = 2.0 * x70
x78 = x76 + x77 * x9
x79 = x74 * x75 + x78
x80 = x45 * x9
x81 = 0.5 * x2 * x33
x82 = -x65 * x9 + x81
x83 = 2.0 * x0
x84 = x11 + A[2]
x85 = -x84
x86 = x13 * x27 - x28 * x85
x87 = -x86
x88 = x14 * x87
x89 = x13 * x18 - x20 * x85
x90 = x2 * (x88 + x89)
x91 = -x89
x92 = -x23 * x91 + x7 * x88
x93 = x13 * x37 - x19 * x26 * x85
x94 = -x93
x95 = -x31 * (x23 * x87 - x63 * x94) - x61 * x92 + x90
x96 = -x95
x97 = x4 * x96
x98 = -x12 * x40 + x19 * x41 * x84
x99 = -x2 * x98
x100 = -x22 * x89 + x69 * x86
x101 = x100 * x30 + x99
x102 = x101 + x44 * x46
x103 = x35 * x92
x104 = x42 * x46
x105 = 2.0 * x12
x106 = x100 * x105 + x76
x107 = x104 * x105 + x106
x108 = x12 * x46
x109 = -x12 * x96 + x81
x110 = 2.0 * x53
x111 = x14 * x75
x112 = -x110 * x58 + x111 * x55 + x21
x113 = -x112
x114 = -x111 * x62 - x36 + 2.0 * x53 * x55
x115 = x114 * x69
x116 = x113 * x22 - x115
x117 = 0.5 * x2
x118 = -x112 * x117 + x116 * x4 + x45 * x71
x119 = x2 * x70
x120 = x116 * x9 - 2.0 * x119 + x45 * x78
x121 = 2.0 * x45
x122 = x113 * x22 - x115 + x45 * x77
x123 = x48 * x52
x124 = x14 * x9
x125 = x124 * x86 - x53 * x89
x126 = x125 * x2
x127 = x10 * x88 - x54 * x91
x128 = x10 * x14 * x94 - x54 * x87
x129 = -x127 * x22 + x128 * x69
x130 = -x126 + x129 * x30
x131 = x130 + x46 * x71
x132 = x100 + x104
x133 = 2.0 * x80
x134 = x100 * x2
x135 = x129 * x75 - x134
x136 = x135 + x46 * x78
x137 = x105 * x129 - x119
x138 = x108 * x77 + x137
x139 = x105 * x14
x140 = x139 * x86 + x21 - 2.0 * x84 * x89
x141 = -x140
x142 = -x139 * x93 - x36 + 2.0 * x84 * x86
x143 = x142 * x69
x144 = x141 * x22 - x143
x145 = -x117 * x140
x146 = x101 * x46 + x144 * x4 + x145
x147 = 2.0 * x46
x148 = x100 * x147 + x141 * x22 - x143
x149 = x48 * x50
x150 = x106 * x46 + x12 * x144 - 2.0 * x134
x151 = x0 * x67
x152 = x43 + x67 * x75
x153 = x0 * (x112 + x121 * x67)
x154 = x113 * x9 + x35 * x58
x155 = x152 * x45 - x154
x156 = x46 * x67
x157 = x125 + x156
x158 = x0 * x30
x159 = x125 * x75 + x99
x160 = x152 * x46 + x159
x161 = x105 * x125 + x68
x162 = x105 * x156 + x161
x163 = -cx * x114 * x6 * x9 + x113 * x53 + 2.0 * x59
x164 = x113 * x45 - x163 - x45 * (x112 + x121 * x58)
x165 = x4 * x47
x166 = x165 * x48
x167 = -x110 * x127 + x111 * x128 + x90
x168 = -x167
x169 = x168 * x9
x170 = x127 * x35
x171 = x113 * x117 - x12 * x168
x172 = x124 * x142
x173 = x125 * x147 + x141 * x53 - x172
x174 = x141 * x53 - x172
x175 = x145 + x159 * x46 + x174 * x9
x176 = x12 * x174 - 2.0 * x126 + x161 * x46
x177 = x0 * x98
x178 = x105 * x98 + x43
x179 = x45 * x98
x180 = x125 + x179
x181 = x159 + x179 * x75
x182 = x161 + x178 * x45
x183 = x140 + x147 * x98
x184 = x0 * x183
x185 = x12 * x141 + x35 * x89
x186 = x178 * x46 - x185
x187 = x183 * x45
x188 = -cx * x12 * x142 * x6 + x141 * x84 + 2.0 * x90
x189 = x141 * x46 - x188 - x46 * (x140 + x147 * x89)
# 54 item(s)
result[0, 0, 0] = numpy.sum(
0.5
* x49
* (2.0 * x0**2 * x44 - 4.0 * x0 * x34 + 3.0 * x2 * x33 + 2.0 * x38 * x4)
)
result[0, 0, 1] = numpy.sum(-x50 * x51)
result[0, 0, 2] = numpy.sum(-x51 * x52)
result[0, 1, 0] = numpy.sum(x47 * (x0 * x72 - x34 * x45 - x66 - x73))
result[0, 1, 1] = numpy.sum(x47 * (x0 * x79 + x32 * x80 + x82))
result[0, 1, 2] = numpy.sum(x52 * (-x33 * x45 + x64 + x83 * (x24 * x45 + x60)))
result[0, 2, 0] = numpy.sum(x47 * (x0 * x102 - x103 - x34 * x46 - x97))
result[0, 2, 1] = numpy.sum(x50 * (-x33 * x46 + x83 * (x24 * x46 + x92) + x95))
result[0, 2, 2] = numpy.sum(x47 * (x0 * x107 + x108 * x32 + x109))
result[0, 3, 0] = numpy.sum(x49 * (x118 + x45 * x72))
result[0, 3, 1] = numpy.sum(x49 * (x120 + x45 * x79))
result[0, 3, 2] = numpy.sum(x123 * (x121 * (x70 + x74) + x122))
result[0, 4, 0] = numpy.sum(x47 * (x102 * x45 + x131))
result[0, 4, 1] = numpy.sum(x47 * (x132 * x133 + x136))
result[0, 4, 2] = numpy.sum(x47 * (x107 * x45 + x138))
result[0, 5, 0] = numpy.sum(x49 * (x102 * x46 + x146))
result[0, 5, 1] = numpy.sum(x149 * (x132 * x147 + x148))
result[0, 5, 2] = numpy.sum(x49 * (x107 * x46 + x150))
result[1, 0, 0] = numpy.sum(x49 * (x0 * x71 + x0 * (x151 * x30 + x71) - x66 - x73))
result[1, 0, 1] = numpy.sum(x49 * (x0 * x78 + x0 * (x0 * x152 + x78) + x82))
result[1, 0, 2] = numpy.sum(x123 * (x0 * x77 + x64 + x83 * (x151 + x70)))
result[1, 1, 0] = numpy.sum(x47 * (x118 + x153 * x4))
result[1, 1, 1] = numpy.sum(x47 * (x0 * x155 + x120))
result[1, 1, 2] = numpy.sum(x52 * (x122 + x153))
result[1, 2, 0] = numpy.sum(x47 * (x131 + x157 * x158))
result[1, 2, 1] = numpy.sum(x47 * (x0 * x160 + x136))
result[1, 2, 2] = numpy.sum(x47 * (x0 * x162 + x138))
result[1, 3, 0] = numpy.sum(-x164 * x166)
result[1, 3, 1] = numpy.sum(
0.5
* x49
* (3.0 * x113 * x2 - 2.0 * x154 * x45 + 2.0 * x155 * x45 + 2.0 * x163 * x9)
)
result[1, 3, 2] = numpy.sum(-x123 * x164)
result[1, 4, 0] = numpy.sum(x165 * (-x113 * x46 + x121 * (x127 + x46 * x58) + x167))
result[1, 4, 1] = numpy.sum(x47 * (-x154 * x46 + x160 * x45 - x169 - x170))
result[1, 4, 2] = numpy.sum(x47 * (x108 * x112 + x162 * x45 + x171))
result[1, 5, 0] = numpy.sum(x166 * (x147 * x157 + x173))
result[1, 5, 1] = numpy.sum(x49 * (x160 * x46 + x175))
result[1, 5, 2] = numpy.sum(x49 * (x162 * x46 + x176))
result[2, 0, 0] = numpy.sum(x49 * (x0 * x101 + x0 * (x101 + x177 * x30) - x103 - x97))
result[2, 0, 1] = numpy.sum(x149 * (x100 * x83 + x83 * (x100 + x177) + x95))
result[2, 0, 2] = numpy.sum(x49 * (x0 * x106 + x0 * (x0 * x178 + x106) + x109))
result[2, 1, 0] = numpy.sum(x47 * (x101 * x45 + x130 + x158 * x180))
result[2, 1, 1] = numpy.sum(x47 * (x0 * x181 + x100 * x133 + x135))
result[2, 1, 2] = numpy.sum(x47 * (x0 * x182 + x106 * x45 + x137))
result[2, 2, 0] = numpy.sum(x47 * (x146 + x184 * x4))
result[2, 2, 1] = numpy.sum(x50 * (x148 + x184))
result[2, 2, 2] = numpy.sum(x47 * (x0 * x186 + x150))
result[2, 3, 0] = numpy.sum(x166 * (x121 * x125 + x121 * x180 + x167))
result[2, 3, 1] = numpy.sum(x49 * (x159 * x45 - x169 - x170 + x181 * x45))
result[2, 3, 2] = numpy.sum(x49 * (x161 * x45 + x171 + x182 * x45))
result[2, 4, 0] = numpy.sum(x165 * (x173 + x187))
result[2, 4, 1] = numpy.sum(x47 * (x175 + x187 * x9))
result[2, 4, 2] = numpy.sum(x47 * (x176 + x186 * x45))
result[2, 5, 0] = numpy.sum(-x166 * x189)
result[2, 5, 1] = numpy.sum(-x149 * x189)
result[2, 5, 2] = numpy.sum(
0.5
* x49
* (2.0 * x12 * x188 + 3.0 * x141 * x2 - 2.0 * x185 * x46 + 2.0 * x186 * x46)
)
return result
[docs]
def int3c2e3d_sph_122(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pd|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 6, 6), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = x3 + C[0]
x5 = -x4
x6 = cx + x1
x7 = x6 ** (-1.0)
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = x8 + C[1]
x10 = -x9
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = x11 + C[2]
x13 = -x12
x14 = cx * x7
x15 = x1 * x14
x16 = x15 * (x10**2 + x13**2 + x5**2)
x17 = boys(3, x16)
x18 = x17 * x7
x19 = x3 + A[0]
x20 = -x19
x21 = cx ** (-1.0)
x22 = x21 * boys(2, x16)
x23 = x18 * x5 - x20 * x22
x24 = x23 * x4
x25 = x4**2
x26 = x9**2
x27 = x12**2
x28 = x15 * (x25 + x26 + x27)
x29 = boys(2, x28)
x30 = x2 * x21 * x29
x31 = 2.0 * x24 + x30
x32 = x18 - x22
x33 = x2 * x32
x34 = 2.0 * x19
x35 = boys(4, x16)
x36 = x35 * x7
x37 = x17 * x21
x38 = -x20 * x37 + x36 * x5
x39 = 2.0 * x4
x40 = x14 * x39
x41 = -x23 * x34 + x33 + x38 * x40
x42 = -x41
x43 = x2 * x23
x44 = x4 * x42 + 2.0 * x43
x45 = x2 * x31 + x4 * x44
x46 = x24 + x30
x47 = x0 * x39
x48 = 1.5 * x2
x49 = x36 - x37
x50 = x2 * x49
x51 = x7 * boys(5, x16)
x52 = x14 * x4
x53 = (
x19 * x42
- 2.0 * x2 * (x14 * x38 - x23)
- x52 * (2.0 * x19 * x38 + x40 * (x20 * x21 * x35 - x5 * x51) - x50)
)
x54 = 0.5 * x4
x55 = A[1] - B[1]
x56 = A[2] - B[2]
x57 = (
17.49341832762486
* da
* db
* dc
* x1
* x6 ** (-2.5)
* numpy.exp(-ax * bx * x2 * (x0**2 + x55**2 + x56**2))
)
x58 = 0.3333333333333333 * x57
x59 = x7 * boys(3, x28)
x60 = x19 * x21 * x29 - x4 * x59
x61 = -2.0 * x2 * x60 + x4 * x41
x62 = -x61
x63 = 1.732050807568877
x64 = x58 * x63
x65 = x64 * (x0 * x62 - x0 * (x0 * x31 + x61) - x4 * x53 + x41 * x48)
x66 = 2.0 * x0
x67 = x58 * (x0 * x41 + x0 * (x23 * x66 + x41) + x53)
x68 = x8 + A[1]
x69 = -x68
x70 = x10 * x18 - x22 * x69
x71 = x2 * x70
x72 = -x71
x73 = -x70
x74 = x10 * x36 - x17 * x21 * x69
x75 = -x74
x76 = x14 * x75
x77 = -x20 * x73 + x5 * x76
x78 = x4 * x77
x79 = x72 + 2.0 * x78
x80 = x2 * (x70 + x76)
x81 = x10 * x51 - x21 * x35 * x69
x82 = -x81
x83 = x14 * x5
x84 = -x34 * x77 - x40 * (x20 * x75 - x82 * x83) + x80
x85 = -x84
x86 = x2 * x77
x87 = 2.0 * x86
x88 = x4 * x85 + x87
x89 = x72 + x78
x90 = x46 * x55 + x89
x91 = x31 * x55
x92 = 2.0 * x9
x93 = x70 * x9
x94 = x30 + 2.0 * x93
x95 = x2 * x94
x96 = -x43
x97 = x77 * x9
x98 = x96 + 2.0 * x97
x99 = x39 * x98 - x95
x100 = x91 * x92 + x99
x101 = 0.5 * x0
x102 = -x2 * x42
x103 = x85 * x9
x104 = x2 * x98
x105 = -x104
x106 = x105 - x54 * (x102 + 2.0 * x103)
x107 = x79 + x91
x108 = -x19 * x70 + x52 * x74
x109 = -2.0 * x108 * x2 + x4 * x84
x110 = x12 * x57
x111 = x23 * x55
x112 = x111 * x9
x113 = x96 + x97
x114 = x112 + x113
x115 = x41 * x55
x116 = x115 * x9
x117 = x2 * x42
x118 = -x103 + x117
x119 = x64 * x9
x120 = 2.0 * x112 + x98
x121 = -0.5 * x2 * x41 + x84 * x9
x122 = x111 + x77
x123 = x27 * x64
x124 = x11 + A[2]
x125 = -x124
x126 = -x125 * x22 + x13 * x18
x127 = x126 * x2
x128 = -x127
x129 = -x126
x130 = -x125 * x17 * x21 + x13 * x36
x131 = -x130
x132 = x131 * x14
x133 = -x129 * x20 + x132 * x5
x134 = x133 * x4
x135 = x128 + 2.0 * x134
x136 = x2 * (x126 + x132)
x137 = -x125 * x21 * x35 + x13 * x51
x138 = -x137
x139 = -x133 * x34 + x136 - x40 * (x131 * x20 - x138 * x83)
x140 = -x139
x141 = x133 * x2
x142 = 2.0 * x141
x143 = x140 * x4 + x142
x144 = x128 + x134
x145 = x144 + x46 * x56
x146 = x31 * x56
x147 = x135 + x146
x148 = -x126 * x19 + x130 * x52
x149 = x139 * x4 - 2.0 * x148 * x2
x150 = x57 * x9
x151 = 2.0 * x12
x152 = x12 * x126
x153 = 2.0 * x152 + x30
x154 = x153 * x2
x155 = -x154
x156 = x12 * x133
x157 = 2.0 * x156 + x96
x158 = x155 + x157 * x39
x159 = x146 * x151 + x158
x160 = x12 * x140
x161 = x157 * x2
x162 = -x161
x163 = x162 - x54 * (x102 + 2.0 * x160)
x164 = x41 * x56
x165 = x23 * x56
x166 = x133 + x165
x167 = x26 * x64
x168 = x12 * x165
x169 = x157 + 2.0 * x168
x170 = 0.5 * x117
x171 = -x160
x172 = x12 * x164 + x171
x173 = x156 + x96
x174 = x168 + x173
x175 = x12 * x64
x176 = 2.0 * x55
x177 = 2.0 * x70
x178 = x14 * x92
x179 = -x177 * x68 + x178 * x74 + x33
x180 = -x179
x181 = x180 * x2
x182 = -x2 * x32
x183 = 2.0 * x69
x184 = -x2 * x49
x185 = x10 * x14
x186 = -x20 * (-2.0 * x10 * x76 + x182 + x183 * x73) + x83 * (
x183 * x75 + x184 - 2.0 * x185 * x82
)
x187 = x186 * x4
x188 = x176 * x89 + x181 + x187
x189 = x4 * x58
x190 = 0.5 * x55
x191 = x186 * x9
x192 = x191 - x87
x193 = x180 * x9 + 2.0 * x71
x194 = 0.5 * x2
x195 = x190 * x99 + x192 * x4 + x193 * x194
x196 = 0.5 * x181
x197 = x187 + x196 + x55 * x79
x198 = x192 * x9
x199 = x176 * x9
x200 = x113 * x199
x201 = x55 * x98
x202 = x176 * x77 + x186
x203 = x27 * x58
x204 = x10 * x132 - x129 * x69
x205 = -x131 * x69 + x138 * x185
x206 = x20 * x204 - x205 * x83
x207 = x2 * x204
x208 = x206 * x4 - x207
x209 = x208 + x56 * x89
x210 = x4 * x57
x211 = 0.6666666666666667 * x63
x212 = x210 * x211
x213 = x55 * x9
x214 = 0.5 * x56
x215 = -x141
x216 = x206 * x9
x217 = x204 * x9
x218 = x128 + 2.0 * x217
x219 = x2 * x218
x220 = -0.5 * x219 + x4 * (x215 + 2.0 * x216)
x221 = x214 * x99 + x220
x222 = x12 * x56
x223 = -x86
x224 = x12 * x206
x225 = x223 + 2.0 * x224
x226 = x12 * x204
x227 = 2.0 * x226 + x72
x228 = x2 * x227
x229 = x225 * x4 - 0.5 * x228
x230 = x222 * x79 + x229
x231 = x215 + x216
x232 = x113 * x56 + x231
x233 = x150 * x211
x234 = -0.5 * x161 + x225 * x9
x235 = x222 * x98 + x234
x236 = x223 + x224
x237 = x108 * x222 + x236
x238 = x110 * x211
x239 = 2.0 * x56
x240 = 2.0 * x126
x241 = x14 * x151
x242 = -x124 * x240 + x130 * x241 + x33
x243 = -x242
x244 = x2 * x243
x245 = 2.0 * x125
x246 = 2.0 * x13
x247 = x129 * x245 - x132 * x246 + x182
x248 = x131 * x245 - x138 * x14 * x246 + x184
x249 = -x20 * x247 + x248 * x83
x250 = x249 * x4
x251 = x144 * x239 + x244 + x250
x252 = 0.5 * x244
x253 = x135 * x56 + x250 + x252
x254 = x12 * x249 - x142
x255 = x12 * x243 + 2.0 * x127
x256 = x194 * x255
x257 = x158 * x214 + x254 * x4 + x256
x258 = x133 * x239 + x249
x259 = x26 * x58
x260 = x12 * x254
x261 = 2.0 * x222
x262 = x173 * x261
x263 = x0 * x70
x264 = x0 * x94
x265 = x30 + x93
x266 = x58 * x9
x267 = x177 * x55 + x179
x268 = x0 * x4
x269 = x267 * x268
x270 = x4 * x64
x271 = x55 * x94
x272 = x193 - x271
x273 = x193 * x9 + x95
x274 = -x199 * x265 + x273
x275 = x179 * x9 - 2.0 * x2 * (x21 * x29 * x68 - x59 * x9)
x276 = -x271 - x275
x277 = x56 * x70
x278 = x204 + x277
x279 = x56 * x94
x280 = x218 + x279
x281 = x12 * x277
x282 = x227 + 2.0 * x281
x283 = x128 + x217
x284 = x265 * x56 + x283
x285 = x155 + x227 * x92
x286 = x151 * x279 + x285
x287 = x226 + x72
x288 = x281 + x287
x289 = x14 * x9
x290 = x180 * x68 + x289 * (x178 * x81 + x50 - 2.0 * x68 * x74) + 2.0 * x80
x291 = x179 * x55 + x267 * x55 + x290
x292 = x25 * x58
x293 = -x290 * x9
x294 = 0.5 * x9
x295 = -x275
x296 = x179 * x56
x297 = x136 + x178 * x205 - 2.0 * x204 * x68
x298 = x25 * x64
x299 = -x297
x300 = x299 * x9
x301 = 2.0 * x207
x302 = x300 + x301
x303 = x12 * x299
x304 = -x303
x305 = x12 * x296 + x304
x306 = -x228
x307 = x294 * (x180 * x2 - 2.0 * x303) + x306
x308 = x185 * x248 - x247 * x69
x309 = x204 * x239 + x308
x310 = x308 * x9
x311 = x218 * x56 + x252 + x310
x312 = -x301
x313 = x12 * x308 + x312
x314 = x239 * x283 + x244 + x310
x315 = x214 * x285 + x256 + x313 * x9
x316 = x12 * x313
x317 = x261 * x287
x318 = x0 * x126
x319 = x0 * x153
x320 = x152 + x30
x321 = x12 * x58
x322 = x126 * x55
x323 = x204 + x322
x324 = x218 + x322 * x92
x325 = x153 * x55
x326 = x227 + x325
x327 = x283 + x322 * x9
x328 = x285 + x325 * x92
x329 = x287 + x320 * x55
x330 = x240 * x56 + x242
x331 = x268 * x330
x332 = -x153 * x56 + x255
x333 = -x332
x334 = -x330
x335 = x12 * x255 + x154
x336 = -x261 * x320 + x335
x337 = x334 * x55
x338 = x12 * x14 * (-2.0 * x124 * x130 + x137 * x241 + x50) + x124 * x243 + 2.0 * x136
x339 = x242 * x56 + x330 * x56 + x338
x340 = -x12 * x338
x341 = 1.5 * x2 * x243 - x255 * x56 - x332 * x56 - x340
# 108 item(s)
result[0, 0, 0] = numpy.sum(
x58
* (
x0 * x45
+ x0 * (x45 - x46 * x47)
- x44 * x48
- x54 * (3.0 * x2 * x42 + x39 * x53)
)
)
result[0, 0, 1] = numpy.sum(x65 * x9)
result[0, 0, 2] = numpy.sum(x12 * x65)
result[0, 0, 3] = numpy.sum(-x26 * x67)
result[0, 0, 4] = numpy.sum(-x12 * x63 * x67 * x9)
result[0, 0, 5] = numpy.sum(-x27 * x67)
result[0, 1, 0] = numpy.sum(x64 * (x2 * x79 + x4 * x88 + x45 * x55 - x47 * x90))
result[0, 1, 1] = numpy.sum(x57 * (-x100 * x101 - x106 + x55 * x62 * x9))
result[0, 1, 2] = numpy.sum(x110 * (-x0 * x107 - x109 + x55 * x62))
result[0, 1, 3] = numpy.sum(-x119 * (x114 * x66 + x116 + x118))
result[0, 1, 4] = numpy.sum(-x110 * (x0 * x120 + x116 + x121))
result[0, 1, 5] = numpy.sum(-x123 * (x115 + x122 * x66 + x84))
result[0, 2, 0] = numpy.sum(x64 * (x135 * x2 + x143 * x4 - x145 * x47 + x45 * x56))
result[0, 2, 1] = numpy.sum(x150 * (-x0 * x147 - x149 + x56 * x62))
result[0, 2, 2] = numpy.sum(x57 * (-x101 * x159 + x12 * x56 * x62 - x163))
result[0, 2, 3] = numpy.sum(-x167 * (x139 + x164 + x166 * x66))
result[0, 2, 4] = numpy.sum(-x150 * (x0 * x169 + x170 + x172))
result[0, 2, 5] = numpy.sum(-x175 * (x117 + x172 + x174 * x66))
result[0, 3, 0] = numpy.sum(-x189 * (x176 * x90 + x188))
result[0, 3, 1] = numpy.sum(-x64 * (x100 * x190 + x195))
result[0, 3, 2] = numpy.sum(-x175 * (x107 * x55 + x197))
result[0, 3, 3] = numpy.sum(-x58 * (x105 + x114 * x199 + x198 + x200))
result[0, 3, 4] = numpy.sum(-x175 * (x120 * x55 + x192 + x201))
result[0, 3, 5] = numpy.sum(-x203 * (x122 * x176 + x202))
result[0, 4, 0] = numpy.sum(-x212 * (x145 * x55 + x209))
result[0, 4, 1] = numpy.sum(-x57 * (x147 * x213 + x221))
result[0, 4, 2] = numpy.sum(-x57 * (x159 * x190 + x230))
result[0, 4, 3] = numpy.sum(-x233 * (x166 * x213 + x232))
result[0, 4, 4] = numpy.sum(-x57 * (x169 * x213 + x235))
result[0, 4, 5] = numpy.sum(-x238 * (x174 * x55 + x237))
result[0, 5, 0] = numpy.sum(-x189 * (x145 * x239 + x251))
result[0, 5, 1] = numpy.sum(-x119 * (x147 * x56 + x253))
result[0, 5, 2] = numpy.sum(-x64 * (x159 * x214 + x257))
result[0, 5, 3] = numpy.sum(-x259 * (x166 * x239 + x258))
result[0, 5, 4] = numpy.sum(-x119 * (x157 * x56 + x169 * x56 + x254))
result[0, 5, 5] = numpy.sum(-x58 * (x162 + x174 * x261 + x260 + x262))
result[1, 0, 0] = numpy.sum(
x58 * (x2 * x79 + x4 * x88 - x47 * x89 - x47 * (x263 * x4 + x89))
)
result[1, 0, 1] = numpy.sum(-x64 * (x101 * x99 + x101 * (x264 * x39 + x99) + x106))
result[1, 0, 2] = numpy.sum(-x175 * (x0 * x79 + x0 * (x263 * x39 + x79) + x109))
result[1, 0, 3] = numpy.sum(-x266 * (x113 * x66 + x118 + x66 * (x0 * x265 + x113)))
result[1, 0, 4] = numpy.sum(-x175 * (x0 * x98 + x0 * (x264 + x98) + x121))
result[1, 0, 5] = numpy.sum(-x203 * (x108 * x66 + x66 * (x263 + x77) + x84))
result[1, 1, 0] = numpy.sum(-x270 * (x188 + x269))
result[1, 1, 1] = numpy.sum(x57 * (-x195 + x268 * x272))
result[1, 1, 2] = numpy.sum(-x110 * (x197 + x269))
result[1, 1, 3] = numpy.sum(x64 * (x0 * x274 + x104 - x198 - x200))
result[1, 1, 4] = numpy.sum(x110 * (x0 * x276 - x191 - x201 + x87))
result[1, 1, 5] = numpy.sum(-x123 * (x0 * x267 + x202))
result[1, 2, 0] = numpy.sum(-x212 * (x209 + x268 * x278))
result[1, 2, 1] = numpy.sum(-x57 * (x221 + x268 * x280))
result[1, 2, 2] = numpy.sum(-x57 * (x230 + x268 * x282))
result[1, 2, 3] = numpy.sum(-x233 * (x0 * x284 + x232))
result[1, 2, 4] = numpy.sum(-x57 * (x101 * x286 + x235))
result[1, 2, 5] = numpy.sum(-x238 * (x0 * x288 + x237))
result[1, 3, 0] = numpy.sum(-x291 * x292)
result[1, 3, 1] = numpy.sum(
0.5 * x270 * (-3.0 * x180 * x2 + 2.0 * x193 * x55 + 2.0 * x272 * x55 + 2.0 * x293)
)
result[1, 3, 2] = numpy.sum(-x175 * x291 * x4)
result[1, 3, 3] = numpy.sum(
-x58
* (x193 * x48 - x273 * x55 - x274 * x55 + x294 * (3.0 * x180 * x2 - 2.0 * x293))
)
result[1, 3, 4] = numpy.sum(x175 * (x179 * x48 + x276 * x55 - x290 * x9 + x295 * x55))
result[1, 3, 5] = numpy.sum(-x203 * x291)
result[1, 4, 0] = numpy.sum(-x298 * (x176 * x278 + x296 + x297))
result[1, 4, 1] = numpy.sum(x210 * (x193 * x56 - x280 * x55 + x302))
result[1, 4, 2] = numpy.sum(-x210 * (x196 + x282 * x55 + x305))
result[1, 4, 3] = numpy.sum(x64 * (-x199 * x284 + x219 + x273 * x56 + x302 * x9))
result[1, 4, 4] = numpy.sum(x57 * (x12 * x295 * x56 - x190 * x286 - x307))
result[1, 4, 5] = numpy.sum(-x175 * (x176 * x288 + x181 + x305))
result[1, 5, 0] = numpy.sum(-x292 * (x239 * x278 + x309))
result[1, 5, 1] = numpy.sum(-x270 * (x280 * x56 + x311))
result[1, 5, 2] = numpy.sum(-x270 * (x227 * x56 + x282 * x56 + x313))
result[1, 5, 3] = numpy.sum(-x266 * (x239 * x284 + x314))
result[1, 5, 4] = numpy.sum(-x64 * (x214 * x286 + x315))
result[1, 5, 5] = numpy.sum(-x58 * (x261 * x288 + x306 + x316 + x317))
result[2, 0, 0] = numpy.sum(
x58 * (x135 * x2 + x143 * x4 - x144 * x47 - x47 * (x144 + x318 * x4))
)
result[2, 0, 1] = numpy.sum(-x119 * (x0 * x135 + x0 * (x135 + x318 * x39) + x149))
result[2, 0, 2] = numpy.sum(-x64 * (x101 * x158 + x101 * (x158 + x319 * x39) + x163))
result[2, 0, 3] = numpy.sum(-x259 * (x139 + x148 * x66 + x66 * (x133 + x318)))
result[2, 0, 4] = numpy.sum(-x119 * (x0 * x157 + x0 * (x157 + x319) + x170 + x171))
result[2, 0, 5] = numpy.sum(
-x321 * (x117 + x171 + x173 * x66 + x66 * (x0 * x320 + x173))
)
result[2, 1, 0] = numpy.sum(-x212 * (x144 * x55 + x208 + x268 * x323))
result[2, 1, 1] = numpy.sum(-x57 * (x135 * x213 + x220 + x268 * x324))
result[2, 1, 2] = numpy.sum(-x57 * (x158 * x190 + x229 + x268 * x326))
result[2, 1, 3] = numpy.sum(-x233 * (x0 * x327 + x148 * x213 + x231))
result[2, 1, 4] = numpy.sum(
-x57 * (x101 * x328 + x213 * (x148 * x151 - x2 * x60) + x234)
)
result[2, 1, 5] = numpy.sum(-x238 * (x0 * x329 + x173 * x55 + x236))
result[2, 2, 0] = numpy.sum(-x270 * (x251 + x331))
result[2, 2, 1] = numpy.sum(-x150 * (x253 + x331))
result[2, 2, 2] = numpy.sum(-x57 * (x257 + x268 * x333))
result[2, 2, 3] = numpy.sum(x167 * (x0 * x334 - x258))
result[2, 2, 4] = numpy.sum(x150 * (x0 * x332 - x12 * x249 + x142 - x157 * x56))
result[2, 2, 5] = numpy.sum(x64 * (x0 * x336 + x161 - x260 - x262))
result[2, 3, 0] = numpy.sum(
-x292 * (x176 * x323 - x176 * (x126 * x68 - x130 * x289) + x297)
)
result[2, 3, 1] = numpy.sum(x270 * (-x218 * x55 + x300 - x312 - x324 * x55))
result[2, 3, 2] = numpy.sum(-x270 * (x196 + x227 * x55 + x304 + x326 * x55))
result[2, 3, 3] = numpy.sum(
x58 * (-x199 * x283 - x199 * x327 + x2 * x218 + x302 * x9)
)
result[2, 3, 4] = numpy.sum(-x64 * (x190 * x285 + x190 * x328 + x307))
result[2, 3, 5] = numpy.sum(-x321 * (x176 * x287 + x176 * x329 + x181 + x304))
result[2, 4, 0] = numpy.sum(x298 * (-x309 + x337))
result[2, 4, 1] = numpy.sum(x210 * (-x311 + x337 * x9))
result[2, 4, 2] = numpy.sum(x210 * (-x12 * x308 - x227 * x56 + x301 + x332 * x55))
result[2, 4, 3] = numpy.sum(-x119 * (x213 * x330 + x314))
result[2, 4, 4] = numpy.sum(-x57 * (x213 * x333 + x315))
result[2, 4, 5] = numpy.sum(x64 * (x228 - x316 - x317 + x336 * x55))
result[2, 5, 0] = numpy.sum(-x292 * x339)
result[2, 5, 1] = numpy.sum(-x119 * x339 * x4)
result[2, 5, 2] = numpy.sum(-x270 * x341)
result[2, 5, 3] = numpy.sum(-x259 * x339)
result[2, 5, 4] = numpy.sum(-x119 * x341)
result[2, 5, 5] = numpy.sum(
-0.5
* x58
* (
x12 * (3.0 * x2 * x243 - 2.0 * x340)
+ 2.0 * x255 * x48
- 2.0 * x335 * x56
- 2.0 * x336 * x56
)
)
return result
[docs]
def int3c2e3d_sph_123(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pd|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 6, 10), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = 0.5 / (ax + bx)
x6 = x4**2
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = x8**2
x10 = -x2 * (ax * A[2] + bx * B[2])
x11 = -x10 - C[2]
x12 = x11**2
x13 = cx + x1
x14 = x13 ** (-1.0)
x15 = x1 * x14
x16 = cx * x15 * (x12 + x6 + x9)
x17 = boys(4, x16)
x18 = x13 ** (-1.5)
x19 = 17.49341832762486
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2))
x23 = x19 * x22
x24 = x2 * x23
x25 = 2.0 * x18 * x24
x26 = x17 * x25
x27 = cx ** (-1.0)
x28 = x13 ** (-0.5)
x29 = boys(3, x16)
x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26)
x31 = -x3 - A[0]
x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4
x33 = -x32
x34 = boys(5, x16)
x35 = x25 * x34
x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4
x37 = cx * x14
x38 = x36 * x37
x39 = x30 + x31 * x33 - x38 * x4
x40 = x39 * x4
x41 = x33 * x5
x42 = 2.0 * x41
x43 = x40 + x42
x44 = x15 * x4
x45 = x33 * x4
x46 = 2.0 * x5
x47 = x27 * x29 * x46
x48 = x24 * x28 * x47
x49 = x45 + x48
x50 = x15 * x46
x51 = x43 * x44 + x49 * x50
x52 = x23 * x47
x53 = x18 * x52
x54 = x4 * x53 + x44 * x49
x55 = x15 * (x44 * x51 + x50 * x54)
x56 = x1 * x13 ** (-2.5) * x52
x57 = x44 * x54 + x56 * x6
x58 = x0 * x15
x59 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35)
x60 = x25 * boys(6, x16)
x61 = x37 * x4
x62 = (
x31 * x39
- x46 * (x32 + x38)
- x61
* (
x31 * x36
+ x59
- x61 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x60)
)
)
x63 = x4 * x62
x64 = x39 * x5
x65 = 3.0 * x64
x66 = x15 * x5
x67 = 3.0 * x66
x68 = da * db * dc
x69 = 0.06666666666666667 * x68
x70 = 2.23606797749979 * x69
x71 = x15 * x8
x72 = x71 * (x40 + x42)
x73 = x53 * x8
x74 = x45 * x71 + x73
x75 = x15 * (x44 * x72 + x50 * x74)
x76 = x4 * x8
x77 = x44 * x74 + x56 * x76
x78 = 0.3333333333333333 * x68
x79 = x11 * x15
x80 = x79 * (x40 + x42)
x81 = x11 * x53
x82 = x45 * x79 + x81
x83 = x15 * (x44 * x80 + x50 * x82)
x84 = x11 * x56
x85 = x4 * x84 + x44 * x82
x86 = x1**2 / x13**2
x87 = x86 * x9
x88 = x15 * x87 * (x40 + x42)
x89 = x56 * x9
x90 = x45 * x87 + x89
x91 = x8 * x86
x92 = x11 * x91
x93 = x15 * x92 * (x40 + x42)
x94 = x8 * x84
x95 = x45 * x92 + x94
x96 = 1.732050807568877 * x78
x97 = x12 * x86
x98 = x15 * x97 * (x40 + x42)
x99 = x12 * x56
x100 = x45 * x97 + x99
x101 = x1**3 / x13**3
x102 = x101 * x8**3
x103 = x102 * x39
x104 = x0 * x33
x105 = x101 * x9
x106 = x105 * x11
x107 = x106 * x39
x108 = x101 * x12
x109 = x108 * x8
x110 = x109 * x39
x111 = x101 * x11**3
x112 = x111 * x39
x113 = -x7 - A[1]
x114 = -2.0 * x113 * x19 * x2 * x22 * x27 * x28 * x29 + x26 * x8
x115 = -x114
x116 = x115 * x5
x117 = 2.0 * x113 * x17 * x19 * x2 * x22 * x27 * x28 - x35 * x8
x118 = x117 * x37
x119 = x115 * x31 - x118 * x4
x120 = x119 * x4
x121 = x116 + x120
x122 = x44 * (x116 + x121)
x123 = x6 * x86
x124 = x15 * (x116 * x123 + x122 * x44)
x125 = x15 * x20
x126 = x124 + x125 * x57
x127 = -x5 * (x114 + x118)
x128 = 2.0 * x113 * x19 * x2 * x22 * x27 * x28 * x34 - x60 * x8
x129 = x119 * x31 + x127 - x61 * (x117 * x31 - x128 * x61)
x130 = x129 * x4
x131 = x119 * x5
x132 = 2.0 * x131
x133 = x15 * (x122 * x50 + x44 * (x121 * x50 + x44 * (x130 + x132)))
x134 = 3.872983346207417 * x69
x135 = x115 * x8
x136 = x135 + x48
x137 = x136 * x15
x138 = x119 * x8
x139 = x138 + x41
x140 = x137 * x5 + x139 * x44
x141 = x4 * x86
x142 = x141 * x5
x143 = x15 * (x136 * x142 + x140 * x44)
x144 = x125 * x77 + x143
x145 = x129 * x8
x146 = x145 + x64
x147 = x139 * x50
x148 = x15 * (x140 * x50 + x44 * (x146 * x44 + x147))
x149 = x116 * x79
x150 = x120 * x79 + x149
x151 = x11 * x141
x152 = x15 * (x116 * x151 + x150 * x44)
x153 = x125 * x85 + x152
x154 = x132 * x79
x155 = x15 * (x150 * x50 + x44 * (x130 * x79 + x154))
x156 = x137 * x8 + x73
x157 = x71 * (x139 + x41)
x158 = x15 * (x156 * x66 + x157 * x44)
x159 = x125 * x90 + x158
x160 = x71 * (x146 + x64)
x161 = x157 * x50
x162 = x15 * (x160 * x44 + x161)
x163 = x135 * x79 + x81
x164 = x41 * x79
x165 = x138 * x79 + x164
x166 = x15 * (x163 * x66 + x165 * x44)
x167 = x125 * x95 + x166
x168 = x64 * x79
x169 = x145 * x79 + x168
x170 = x165 * x50
x171 = x15 * (x169 * x44 + x170)
x172 = x116 * x97
x173 = x15 * (x120 * x97 + x172)
x174 = x100 * x125 + x173
x175 = x132 * x97
x176 = x15 * (x130 * x97 + x175)
x177 = x15 * (x157 * x71 + x41 * x87)
x178 = x20 * x33
x179 = x102 * x178 + x177
x180 = x15 * (x160 * x71 + x64 * x87)
x181 = x15 * (x165 * x71 + x41 * x92)
x182 = x106 * x178 + x181
x183 = x15 * (x169 * x71 + x64 * x92)
x184 = x41 * x97
x185 = x15 * (x138 * x97 + x184)
x186 = x109 * x178 + x185
x187 = x64 * x97
x188 = x15 * (x145 * x97 + x187)
x189 = x111 * x119
x190 = x111 * x178 + x189
x191 = x111 * x129
x192 = -x10 - A[2]
x193 = x11 * x26 - 2.0 * x19 * x192 * x2 * x22 * x27 * x28 * x29
x194 = -x193
x195 = x194 * x5
x196 = -x11 * x35 + 2.0 * x17 * x19 * x192 * x2 * x22 * x27 * x28
x197 = x196 * x37
x198 = x194 * x31 - x197 * x4
x199 = x198 * x4
x200 = x195 + x199
x201 = x44 * (x195 + x200)
x202 = x15 * (x123 * x195 + x201 * x44)
x203 = x15 * x21
x204 = x202 + x203 * x57
x205 = -x5 * (x193 + x197)
x206 = -x11 * x60 + 2.0 * x19 * x192 * x2 * x22 * x27 * x28 * x34
x207 = x198 * x31 + x205 - x61 * (x196 * x31 - x206 * x61)
x208 = x207 * x4
x209 = x198 * x5
x210 = 2.0 * x209
x211 = x15 * (x201 * x50 + x44 * (x200 * x50 + x44 * (x208 + x210)))
x212 = x195 * x71
x213 = x199 * x71 + x212
x214 = x4 * x91
x215 = x15 * (x195 * x214 + x213 * x44)
x216 = x203 * x77 + x215
x217 = x15 * (x213 * x50 + x44 * x71 * (x208 + x210))
x218 = x11 * x194 + x48
x219 = x218 * x66
x220 = x11 * x198 + x41
x221 = x219 + x220 * x44
x222 = x15 * (x142 * x218 + x221 * x44)
x223 = x203 * x85 + x222
x224 = x11 * x207 + x64
x225 = x220 * x50
x226 = x15 * (x221 * x50 + x44 * (x224 * x44 + x225))
x227 = x195 * x87
x228 = x15 * (x199 * x87 + x227)
x229 = x203 * x90 + x228
x230 = x15 * x87 * (x208 + x210)
x231 = x5 * x91
x232 = x218 * x231
x233 = x15 * (x214 * x220 + x232)
x234 = x203 * x95 + x233
x235 = x15 * (x214 * x224 + x220 * x46 * x91)
x236 = x218 * x79 + x81
x237 = x236 * x66
x238 = x164 + x220 * x79
x239 = x15 * (x237 + x238 * x44)
x240 = x100 * x203 + x239
x241 = x168 + x224 * x79
x242 = x238 * x50
x243 = x15 * (x241 * x44 + x242)
x244 = x102 * x198
x245 = x21 * x33
x246 = x102 * x245 + x244
x247 = x102 * x207
x248 = x105 * x220
x249 = x106 * x245 + x248
x250 = x105 * x224
x251 = x238 * x91
x252 = x109 * x245 + x251
x253 = x241 * x91
x254 = x15 * (x184 + x238 * x79)
x255 = x111 * x245 + x254
x256 = x15 * (x187 + x241 * x79)
x257 = x113 * x115 - x118 * x8 + x30
x258 = x257 * x5
x259 = x37 * x8
x260 = x113 * x117 - x128 * x259 + x59
x261 = x257 * x31 - x260 * x61
x262 = x261 * x4
x263 = x124 * x20 + x15 * (x123 * x258 + x44**2 * (2.0 * x258 + x262))
x264 = x257 * x8
x265 = 2.0 * x116
x266 = x264 + x265
x267 = x266 * x66
x268 = x261 * x8
x269 = x132 + x268
x270 = x143 * x20 + x15 * (x142 * x266 + x44 * (x267 + x269 * x44))
x271 = x258 * x79
x272 = x15 * (x151 * x258 + x44 * (x262 * x79 + x271)) + x152 * x20
x273 = x137 * x46 + x266 * x71
x274 = x273 * x66
x275 = x147 + x269 * x71
x276 = x15 * (x274 + x275 * x44) + x158 * x20
x277 = x79 * (x264 + x265)
x278 = x277 * x66
x279 = x154 + x268 * x79
x280 = x15 * (x278 + x279 * x44) + x166 * x20
x281 = x258 * x97
x282 = x15 * (x262 * x97 + x281) + x173 * x20
x283 = x15 * (x161 + x275 * x71) + x177 * x20
x284 = x15 * (x170 + x279 * x71) + x181 * x20
x285 = x15 * (x175 + x268 * x97) + x185 * x20
x286 = x111 * x261 + x189 * x20
x287 = x113 * x194 - x197 * x8
x288 = x287 * x5
x289 = x113 * x196 - x206 * x259
x290 = x287 * x31 - x289 * x61
x291 = x15 * (x123 * x288 + x44**2 * (2.0 * x288 + x290 * x4))
x292 = x124 * x21 + x291
x293 = x195 + x287 * x8
x294 = x209 + x290 * x8
x295 = x15 * (x142 * x293 + x44 * (x293 * x66 + x294 * x44))
x296 = x143 * x21 + x295
x297 = x11 * x287 + x116
x298 = x11 * x290 + x131
x299 = x15 * (x142 * x297 + x44 * (x297 * x66 + x298 * x44))
x300 = x152 * x21 + x299
x301 = x212 + x293 * x71
x302 = x71 * (x209 + x294)
x303 = x15 * (x301 * x66 + x302 * x44)
x304 = x158 * x21 + x303
x305 = x219 + x297 * x71
x306 = x220 * x66 + x298 * x71
x307 = x15 * (x305 * x66 + x306 * x44)
x308 = x166 * x21 + x307
x309 = x149 + x297 * x79
x310 = x79 * (x131 + x298)
x311 = x15 * (x309 * x66 + x310 * x44)
x312 = x173 * x21 + x311
x313 = x15 * (x209 * x87 + x302 * x71)
x314 = x177 * x21 + x313
x315 = x15 * (x220 * x231 + x306 * x71)
x316 = x181 * x21 + x315
x317 = x15 * (x238 * x66 + x310 * x71)
x318 = x185 * x21 + x317
x319 = x15 * (x131 * x97 + x310 * x79)
x320 = x189 * x21 + x319
x321 = -x11 * x197 + x192 * x194 + x30
x322 = x321 * x5
x323 = x11 * x37
x324 = x192 * x196 - x206 * x323 + x59
x325 = x31 * x321 - x324 * x61
x326 = x325 * x4
x327 = x15 * (x123 * x322 + x44**2 * (2.0 * x322 + x326)) + x202 * x21
x328 = x322 * x71
x329 = x15 * (x214 * x322 + x44 * (x326 * x71 + x328)) + x21 * x215
x330 = x11 * x321 + 2.0 * x195
x331 = x330 * x66
x332 = x11 * x325 + x210
x333 = x15 * (x142 * x330 + x44 * (x331 + x332 * x44)) + x21 * x222
x334 = x322 * x87
x335 = x15 * (x326 * x87 + x334) + x21 * x228
x336 = x231 * x330
x337 = x15 * (x214 * x332 + x336) + x21 * x233
x338 = x218 * x50 + x330 * x79
x339 = x338 * x66
x340 = x225 + x332 * x79
x341 = x15 * (x339 + x340 * x44) + x21 * x239
x342 = x102 * x325 + x21 * x244
x343 = x105 * x332 + x21 * x248
x344 = x21 * x251 + x340 * x91
x345 = x15 * (x242 + x340 * x79) + x21 * x254
x346 = x101 * x4**3
x347 = x0 * x115
x348 = x101 * x6
x349 = x136 * x348
x350 = x11 * x348
x351 = x0 * x141
x352 = x108 * x4
x353 = x156 * x71 + x89
x354 = x163 * x71 + x94
x355 = x135 * x97 + x99
x356 = x257 * x346
x357 = x115 * x20
x358 = x346 * x357 + x356
x359 = x266 * x348
x360 = x20 * x349 + x359
x361 = x257 * x350
x362 = x350 * x357 + x361
x363 = x141 * x273
x364 = x141 * x20
x365 = x156 * x364 + x363
x366 = x141 * x277
x367 = x163 * x364 + x366
x368 = x257 * x352
x369 = x352 * x357 + x368
x370 = x15 * (x156 * x50 + x273 * x71)
x371 = x125 * x353 + x370
x372 = x15 * (x163 * x50 + x277 * x71)
x373 = x125 * x354 + x372
x374 = x15 * x97 * (x264 + x265)
x375 = x125 * x355 + x374
x376 = x111 * x257
x377 = x111 * x357 + x376
x378 = x287 * x346
x379 = x115 * x21
x380 = x346 * x379 + x378
x381 = x293 * x348
x382 = x21 * x349 + x381
x383 = x297 * x348
x384 = x350 * x379 + x383
x385 = x141 * x301
x386 = x141 * x21
x387 = x156 * x386 + x385
x388 = x141 * x305
x389 = x163 * x386 + x388
x390 = x141 * x309
x391 = x352 * x379 + x390
x392 = x15 * (x227 + x301 * x71)
x393 = x203 * x353 + x392
x394 = x15 * (x232 + x305 * x71)
x395 = x203 * x354 + x394
x396 = x15 * (x237 + x309 * x71)
x397 = x203 * x355 + x396
x398 = x15 * (x172 + x309 * x79)
x399 = x111 * x379 + x398
x400 = x113 * x257 + 2.0 * x127 - x259 * x260
x401 = x400 * x8
x402 = 3.0 * x258
x403 = x401 + x402
x404 = 3.0 * x267 + x403 * x71
x405 = x79 * (x401 + x402)
x406 = x113 * x287 + x205 - x259 * x289
x407 = x346 * x406
x408 = 2.0 * x288
x409 = x406 * x8 + x408
x410 = x348 * x409
x411 = x11 * x406 + x258
x412 = x348 * x411
x413 = x293 * x50 + x409 * x71
x414 = x141 * x413
x415 = x297 * x50
x416 = x411 * x71 + x415
x417 = x141 * x416
x418 = x271 + x411 * x79
x419 = x141 * x418
x420 = x15 * (x301 * x50 + x413 * x71)
x421 = x15 * (x305 * x50 + x416 * x71)
x422 = x309 * x50
x423 = x15 * (x418 * x71 + x422)
x424 = x15 * (x281 + x418 * x79)
x425 = x113 * x321 - x259 * x324
x426 = x21 * x378 + x346 * x425
x427 = x322 + x425 * x8
x428 = x21 * x381 + x348 * x427
x429 = x11 * x425 + x408
x430 = x21 * x383 + x348 * x429
x431 = x328 + x427 * x71
x432 = x141 * x431 + x21 * x385
x433 = x331 + x429 * x71
x434 = x141 * x433 + x21 * x388
x435 = x415 + x429 * x79
x436 = x141 * x435 + x21 * x390
x437 = x15 * (x334 + x431 * x71) + x21 * x392
x438 = x15 * (x336 + x433 * x71) + x21 * x394
x439 = x15 * (x339 + x435 * x71) + x21 * x396
x440 = x15 * (x422 + x435 * x79) + x21 * x398
x441 = x0 * x194
x442 = x348 * x8
x443 = x0 * x218
x444 = x105 * x4
x445 = x101 * x76
x446 = x236 * x91
x447 = x236 * x79 + x99
x448 = x194 * x20
x449 = x346 * x448 + x378
x450 = x381 + x442 * x448
x451 = x20 * x218
x452 = x348 * x451 + x383
x453 = x385 + x444 * x448
x454 = x388 + x445 * x451
x455 = x236 * x364 + x390
x456 = x102 * x448 + x392
x457 = x105 * x451 + x394
x458 = x20 * x446 + x396
x459 = x125 * x447 + x398
x460 = x321 * x346
x461 = x194 * x21
x462 = x346 * x461 + x460
x463 = x321 * x442
x464 = x442 * x461 + x463
x465 = x330 * x348
x466 = x21 * x218
x467 = x348 * x466 + x465
x468 = x321 * x444
x469 = x444 * x461 + x468
x470 = x330 * x445
x471 = x445 * x466 + x470
x472 = x141 * x338
x473 = x236 * x386 + x472
x474 = x102 * x321
x475 = x102 * x461 + x474
x476 = x105 * x330
x477 = x105 * x466 + x476
x478 = x338 * x91
x479 = x21 * x446 + x478
x480 = x15 * (x236 * x50 + x338 * x79)
x481 = x203 * x447 + x480
x482 = x192 * x321 + 2.0 * x205 - x323 * x324
x483 = x11 * x482 + 3.0 * x322
x484 = 3.0 * x331 + x483 * x79
# 180 item(s)
result[0, 0, 0] = numpy.sum(
x70
* (
x0 * x55
+ x0 * (x55 + x57 * x58)
+ x15 * (x44 * (x43 * x67 + x44 * (x63 + x65)) + x51 * x67)
)
)
result[0, 0, 1] = numpy.sum(
x78
* (
x0 * x75
+ x0 * (x58 * x77 + x75)
+ x15 * (x44 * x71 * (x63 + x65) + x67 * x72)
)
)
result[0, 0, 2] = numpy.sum(
x78
* (
x0 * x83
+ x0 * (x58 * x85 + x83)
+ x15 * (x44 * x79 * (x63 + x65) + x67 * x80)
)
)
result[0, 0, 3] = numpy.sum(
x78 * (x0 * x88 + x0 * (x58 * x90 + x88) + x15 * x87 * (x63 + x65))
)
result[0, 0, 4] = numpy.sum(
x96 * (x0 * x93 + x0 * (x58 * x95 + x93) + x15 * x92 * (x63 + x65))
)
result[0, 0, 5] = numpy.sum(
x78 * (x0 * x98 + x0 * (x100 * x58 + x98) + x15 * x97 * (x63 + x65))
)
result[0, 0, 6] = numpy.sum(
x70 * (x0 * x103 + x0 * (x102 * x104 + x103) + x102 * x62)
)
result[0, 0, 7] = numpy.sum(
x78 * (x0 * x107 + x0 * (x104 * x106 + x107) + x106 * x62)
)
result[0, 0, 8] = numpy.sum(
x78 * (x0 * x110 + x0 * (x104 * x109 + x110) + x109 * x62)
)
result[0, 0, 9] = numpy.sum(
x70 * (x0 * x112 + x0 * (x104 * x111 + x112) + x111 * x62)
)
result[0, 1, 0] = numpy.sum(x134 * (x0 * x126 + x133 + x20 * x55))
result[0, 1, 1] = numpy.sum(x96 * (x0 * x144 + x148 + x20 * x75))
result[0, 1, 2] = numpy.sum(x96 * (x0 * x153 + x155 + x20 * x83))
result[0, 1, 3] = numpy.sum(x96 * (x0 * x159 + x162 + x20 * x88))
result[0, 1, 4] = numpy.sum(x68 * (x0 * x167 + x171 + x20 * x93))
result[0, 1, 5] = numpy.sum(x96 * (x0 * x174 + x176 + x20 * x98))
result[0, 1, 6] = numpy.sum(x134 * (x0 * x179 + x103 * x20 + x180))
result[0, 1, 7] = numpy.sum(x96 * (x0 * x182 + x107 * x20 + x183))
result[0, 1, 8] = numpy.sum(x96 * (x0 * x186 + x110 * x20 + x188))
result[0, 1, 9] = numpy.sum(x134 * (x0 * x190 + x112 * x20 + x191))
result[0, 2, 0] = numpy.sum(x134 * (x0 * x204 + x21 * x55 + x211))
result[0, 2, 1] = numpy.sum(x96 * (x0 * x216 + x21 * x75 + x217))
result[0, 2, 2] = numpy.sum(x96 * (x0 * x223 + x21 * x83 + x226))
result[0, 2, 3] = numpy.sum(x96 * (x0 * x229 + x21 * x88 + x230))
result[0, 2, 4] = numpy.sum(x68 * (x0 * x234 + x21 * x93 + x235))
result[0, 2, 5] = numpy.sum(x96 * (x0 * x240 + x21 * x98 + x243))
result[0, 2, 6] = numpy.sum(x134 * (x0 * x246 + x103 * x21 + x247))
result[0, 2, 7] = numpy.sum(x96 * (x0 * x249 + x107 * x21 + x250))
result[0, 2, 8] = numpy.sum(x96 * (x0 * x252 + x110 * x21 + x253))
result[0, 2, 9] = numpy.sum(x134 * (x0 * x255 + x112 * x21 + x256))
result[0, 3, 0] = numpy.sum(x70 * (x126 * x20 + x263))
result[0, 3, 1] = numpy.sum(x78 * (x144 * x20 + x270))
result[0, 3, 2] = numpy.sum(x78 * (x153 * x20 + x272))
result[0, 3, 3] = numpy.sum(x78 * (x159 * x20 + x276))
result[0, 3, 4] = numpy.sum(x96 * (x167 * x20 + x280))
result[0, 3, 5] = numpy.sum(x78 * (x174 * x20 + x282))
result[0, 3, 6] = numpy.sum(x70 * (x179 * x20 + x283))
result[0, 3, 7] = numpy.sum(x78 * (x182 * x20 + x284))
result[0, 3, 8] = numpy.sum(x78 * (x186 * x20 + x285))
result[0, 3, 9] = numpy.sum(x70 * (x190 * x20 + x286))
result[0, 4, 0] = numpy.sum(x134 * (x20 * x204 + x292))
result[0, 4, 1] = numpy.sum(x96 * (x20 * x216 + x296))
result[0, 4, 2] = numpy.sum(x96 * (x20 * x223 + x300))
result[0, 4, 3] = numpy.sum(x96 * (x20 * x229 + x304))
result[0, 4, 4] = numpy.sum(x68 * (x20 * x234 + x308))
result[0, 4, 5] = numpy.sum(x96 * (x20 * x240 + x312))
result[0, 4, 6] = numpy.sum(x134 * (x20 * x246 + x314))
result[0, 4, 7] = numpy.sum(x96 * (x20 * x249 + x316))
result[0, 4, 8] = numpy.sum(x96 * (x20 * x252 + x318))
result[0, 4, 9] = numpy.sum(x134 * (x20 * x255 + x320))
result[0, 5, 0] = numpy.sum(x70 * (x204 * x21 + x327))
result[0, 5, 1] = numpy.sum(x78 * (x21 * x216 + x329))
result[0, 5, 2] = numpy.sum(x78 * (x21 * x223 + x333))
result[0, 5, 3] = numpy.sum(x78 * (x21 * x229 + x335))
result[0, 5, 4] = numpy.sum(x96 * (x21 * x234 + x337))
result[0, 5, 5] = numpy.sum(x78 * (x21 * x240 + x341))
result[0, 5, 6] = numpy.sum(x70 * (x21 * x246 + x342))
result[0, 5, 7] = numpy.sum(x78 * (x21 * x249 + x343))
result[0, 5, 8] = numpy.sum(x78 * (x21 * x252 + x344))
result[0, 5, 9] = numpy.sum(x70 * (x21 * x255 + x345))
result[1, 0, 0] = numpy.sum(x70 * (x0 * x124 + x0 * (x124 + x346 * x347) + x133))
result[1, 0, 1] = numpy.sum(x78 * (x0 * x143 + x0 * (x0 * x349 + x143) + x148))
result[1, 0, 2] = numpy.sum(x78 * (x0 * x152 + x0 * (x152 + x347 * x350) + x155))
result[1, 0, 3] = numpy.sum(x78 * (x0 * x158 + x0 * (x156 * x351 + x158) + x162))
result[1, 0, 4] = numpy.sum(x96 * (x0 * x166 + x0 * (x163 * x351 + x166) + x171))
result[1, 0, 5] = numpy.sum(x78 * (x0 * x173 + x0 * (x173 + x347 * x352) + x176))
result[1, 0, 6] = numpy.sum(x70 * (x0 * x177 + x0 * (x177 + x353 * x58) + x180))
result[1, 0, 7] = numpy.sum(x78 * (x0 * x181 + x0 * (x181 + x354 * x58) + x183))
result[1, 0, 8] = numpy.sum(x78 * (x0 * x185 + x0 * (x185 + x355 * x58) + x188))
result[1, 0, 9] = numpy.sum(x70 * (x0 * x189 + x0 * (x111 * x347 + x189) + x191))
result[1, 1, 0] = numpy.sum(x134 * (x0 * x358 + x263))
result[1, 1, 1] = numpy.sum(x96 * (x0 * x360 + x270))
result[1, 1, 2] = numpy.sum(x96 * (x0 * x362 + x272))
result[1, 1, 3] = numpy.sum(x96 * (x0 * x365 + x276))
result[1, 1, 4] = numpy.sum(x68 * (x0 * x367 + x280))
result[1, 1, 5] = numpy.sum(x96 * (x0 * x369 + x282))
result[1, 1, 6] = numpy.sum(x134 * (x0 * x371 + x283))
result[1, 1, 7] = numpy.sum(x96 * (x0 * x373 + x284))
result[1, 1, 8] = numpy.sum(x96 * (x0 * x375 + x285))
result[1, 1, 9] = numpy.sum(x134 * (x0 * x377 + x286))
result[1, 2, 0] = numpy.sum(x134 * (x0 * x380 + x292))
result[1, 2, 1] = numpy.sum(x96 * (x0 * x382 + x296))
result[1, 2, 2] = numpy.sum(x96 * (x0 * x384 + x300))
result[1, 2, 3] = numpy.sum(x96 * (x0 * x387 + x304))
result[1, 2, 4] = numpy.sum(x68 * (x0 * x389 + x308))
result[1, 2, 5] = numpy.sum(x96 * (x0 * x391 + x312))
result[1, 2, 6] = numpy.sum(x134 * (x0 * x393 + x314))
result[1, 2, 7] = numpy.sum(x96 * (x0 * x395 + x316))
result[1, 2, 8] = numpy.sum(x96 * (x0 * x397 + x318))
result[1, 2, 9] = numpy.sum(x134 * (x0 * x399 + x320))
result[1, 3, 0] = numpy.sum(x70 * (x20 * x356 + x20 * x358 + x346 * x400))
result[1, 3, 1] = numpy.sum(x78 * (x20 * x359 + x20 * x360 + x348 * x403))
result[1, 3, 2] = numpy.sum(x78 * (x20 * x361 + x20 * x362 + x350 * x400))
result[1, 3, 3] = numpy.sum(x78 * (x141 * x404 + x20 * x363 + x20 * x365))
result[1, 3, 4] = numpy.sum(x96 * (x141 * x405 + x20 * x366 + x20 * x367))
result[1, 3, 5] = numpy.sum(x78 * (x20 * x368 + x20 * x369 + x352 * x400))
result[1, 3, 6] = numpy.sum(
x70 * (x15 * (3.0 * x274 + x404 * x71) + x20 * x370 + x20 * x371)
)
result[1, 3, 7] = numpy.sum(
x78 * (x15 * (3.0 * x278 + x405 * x71) + x20 * x372 + x20 * x373)
)
result[1, 3, 8] = numpy.sum(
x78 * (x15 * x97 * (x401 + x402) + x20 * x374 + x20 * x375)
)
result[1, 3, 9] = numpy.sum(x70 * (x111 * x400 + x20 * x376 + x20 * x377))
result[1, 4, 0] = numpy.sum(x134 * (x20 * x380 + x21 * x356 + x407))
result[1, 4, 1] = numpy.sum(x96 * (x20 * x382 + x21 * x359 + x410))
result[1, 4, 2] = numpy.sum(x96 * (x20 * x384 + x21 * x361 + x412))
result[1, 4, 3] = numpy.sum(x96 * (x20 * x387 + x21 * x363 + x414))
result[1, 4, 4] = numpy.sum(x68 * (x20 * x389 + x21 * x366 + x417))
result[1, 4, 5] = numpy.sum(x96 * (x20 * x391 + x21 * x368 + x419))
result[1, 4, 6] = numpy.sum(x134 * (x20 * x393 + x21 * x370 + x420))
result[1, 4, 7] = numpy.sum(x96 * (x20 * x395 + x21 * x372 + x421))
result[1, 4, 8] = numpy.sum(x96 * (x20 * x397 + x21 * x374 + x423))
result[1, 4, 9] = numpy.sum(x134 * (x20 * x399 + x21 * x376 + x424))
result[1, 5, 0] = numpy.sum(x70 * (x21 * x380 + x426))
result[1, 5, 1] = numpy.sum(x78 * (x21 * x382 + x428))
result[1, 5, 2] = numpy.sum(x78 * (x21 * x384 + x430))
result[1, 5, 3] = numpy.sum(x78 * (x21 * x387 + x432))
result[1, 5, 4] = numpy.sum(x96 * (x21 * x389 + x434))
result[1, 5, 5] = numpy.sum(x78 * (x21 * x391 + x436))
result[1, 5, 6] = numpy.sum(x70 * (x21 * x393 + x437))
result[1, 5, 7] = numpy.sum(x78 * (x21 * x395 + x438))
result[1, 5, 8] = numpy.sum(x78 * (x21 * x397 + x439))
result[1, 5, 9] = numpy.sum(x70 * (x21 * x399 + x440))
result[2, 0, 0] = numpy.sum(x70 * (x0 * x202 + x0 * (x202 + x346 * x441) + x211))
result[2, 0, 1] = numpy.sum(x78 * (x0 * x215 + x0 * (x215 + x441 * x442) + x217))
result[2, 0, 2] = numpy.sum(x78 * (x0 * x222 + x0 * (x222 + x348 * x443) + x226))
result[2, 0, 3] = numpy.sum(x78 * (x0 * x228 + x0 * (x228 + x441 * x444) + x230))
result[2, 0, 4] = numpy.sum(x96 * (x0 * x233 + x0 * (x233 + x443 * x445) + x235))
result[2, 0, 5] = numpy.sum(x78 * (x0 * x239 + x0 * (x236 * x351 + x239) + x243))
result[2, 0, 6] = numpy.sum(x70 * (x0 * x244 + x0 * (x102 * x441 + x244) + x247))
result[2, 0, 7] = numpy.sum(x78 * (x0 * x248 + x0 * (x105 * x443 + x248) + x250))
result[2, 0, 8] = numpy.sum(x78 * (x0 * x251 + x0 * (x0 * x446 + x251) + x253))
result[2, 0, 9] = numpy.sum(x70 * (x0 * x254 + x0 * (x254 + x447 * x58) + x256))
result[2, 1, 0] = numpy.sum(x134 * (x0 * x449 + x20 * x202 + x291))
result[2, 1, 1] = numpy.sum(x96 * (x0 * x450 + x20 * x215 + x295))
result[2, 1, 2] = numpy.sum(x96 * (x0 * x452 + x20 * x222 + x299))
result[2, 1, 3] = numpy.sum(x96 * (x0 * x453 + x20 * x228 + x303))
result[2, 1, 4] = numpy.sum(x68 * (x0 * x454 + x20 * x233 + x307))
result[2, 1, 5] = numpy.sum(x96 * (x0 * x455 + x20 * x239 + x311))
result[2, 1, 6] = numpy.sum(x134 * (x0 * x456 + x20 * x244 + x313))
result[2, 1, 7] = numpy.sum(x96 * (x0 * x457 + x20 * x248 + x315))
result[2, 1, 8] = numpy.sum(x96 * (x0 * x458 + x20 * x251 + x317))
result[2, 1, 9] = numpy.sum(x134 * (x0 * x459 + x20 * x254 + x319))
result[2, 2, 0] = numpy.sum(x134 * (x0 * x462 + x327))
result[2, 2, 1] = numpy.sum(x96 * (x0 * x464 + x329))
result[2, 2, 2] = numpy.sum(x96 * (x0 * x467 + x333))
result[2, 2, 3] = numpy.sum(x96 * (x0 * x469 + x335))
result[2, 2, 4] = numpy.sum(x68 * (x0 * x471 + x337))
result[2, 2, 5] = numpy.sum(x96 * (x0 * x473 + x341))
result[2, 2, 6] = numpy.sum(x134 * (x0 * x475 + x342))
result[2, 2, 7] = numpy.sum(x96 * (x0 * x477 + x343))
result[2, 2, 8] = numpy.sum(x96 * (x0 * x479 + x344))
result[2, 2, 9] = numpy.sum(x134 * (x0 * x481 + x345))
result[2, 3, 0] = numpy.sum(x70 * (x20 * x378 + x20 * x449 + x407))
result[2, 3, 1] = numpy.sum(x78 * (x20 * x381 + x20 * x450 + x410))
result[2, 3, 2] = numpy.sum(x78 * (x20 * x383 + x20 * x452 + x412))
result[2, 3, 3] = numpy.sum(x78 * (x20 * x385 + x20 * x453 + x414))
result[2, 3, 4] = numpy.sum(x96 * (x20 * x388 + x20 * x454 + x417))
result[2, 3, 5] = numpy.sum(x78 * (x20 * x390 + x20 * x455 + x419))
result[2, 3, 6] = numpy.sum(x70 * (x20 * x392 + x20 * x456 + x420))
result[2, 3, 7] = numpy.sum(x78 * (x20 * x394 + x20 * x457 + x421))
result[2, 3, 8] = numpy.sum(x78 * (x20 * x396 + x20 * x458 + x423))
result[2, 3, 9] = numpy.sum(x70 * (x20 * x398 + x20 * x459 + x424))
result[2, 4, 0] = numpy.sum(x134 * (x20 * x462 + x426))
result[2, 4, 1] = numpy.sum(x96 * (x20 * x464 + x428))
result[2, 4, 2] = numpy.sum(x96 * (x20 * x467 + x430))
result[2, 4, 3] = numpy.sum(x96 * (x20 * x469 + x432))
result[2, 4, 4] = numpy.sum(x68 * (x20 * x471 + x434))
result[2, 4, 5] = numpy.sum(x96 * (x20 * x473 + x436))
result[2, 4, 6] = numpy.sum(x134 * (x20 * x475 + x437))
result[2, 4, 7] = numpy.sum(x96 * (x20 * x477 + x438))
result[2, 4, 8] = numpy.sum(x96 * (x20 * x479 + x439))
result[2, 4, 9] = numpy.sum(x134 * (x20 * x481 + x440))
result[2, 5, 0] = numpy.sum(x70 * (x21 * x460 + x21 * x462 + x346 * x482))
result[2, 5, 1] = numpy.sum(x78 * (x21 * x463 + x21 * x464 + x442 * x482))
result[2, 5, 2] = numpy.sum(x78 * (x21 * x465 + x21 * x467 + x348 * x483))
result[2, 5, 3] = numpy.sum(x78 * (x21 * x468 + x21 * x469 + x444 * x482))
result[2, 5, 4] = numpy.sum(x96 * (x21 * x470 + x21 * x471 + x445 * x483))
result[2, 5, 5] = numpy.sum(x78 * (x141 * x484 + x21 * x472 + x21 * x473))
result[2, 5, 6] = numpy.sum(x70 * (x102 * x482 + x21 * x474 + x21 * x475))
result[2, 5, 7] = numpy.sum(x78 * (x105 * x483 + x21 * x476 + x21 * x477))
result[2, 5, 8] = numpy.sum(x78 * (x21 * x478 + x21 * x479 + x484 * x91))
result[2, 5, 9] = numpy.sum(
x70 * (x15 * (3.0 * x339 + x484 * x79) + x21 * x480 + x21 * x481)
)
return result
[docs]
def int3c2e3d_sph_124(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pd|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 6, 15), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = 0.5 / (ax + bx)
x6 = x4**2
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = x8**2
x10 = -x2 * (ax * A[2] + bx * B[2])
x11 = -x10 - C[2]
x12 = x11**2
x13 = cx + x1
x14 = x13 ** (-1.0)
x15 = x1 * x14
x16 = cx * x15 * (x12 + x6 + x9)
x17 = boys(5, x16)
x18 = x13 ** (-1.5)
x19 = 17.49341832762486
x20 = A[1] - B[1]
x21 = A[2] - B[2]
x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2))
x23 = x19 * x22
x24 = x2 * x23
x25 = 2.0 * x18 * x24
x26 = x17 * x25
x27 = cx ** (-1.0)
x28 = x13 ** (-0.5)
x29 = boys(4, x16)
x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26)
x31 = -x3 - A[0]
x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4
x33 = -x32
x34 = boys(6, x16)
x35 = x25 * x34
x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4
x37 = cx * x14
x38 = x36 * x37
x39 = x30 + x31 * x33 - x38 * x4
x40 = x39 * x4
x41 = x33 * x5
x42 = 2.0 * x41
x43 = x40 + x42
x44 = x15 * x4
x45 = x33 * x4
x46 = 2.0 * x5
x47 = x27 * x29 * x46
x48 = x24 * x28 * x47
x49 = x45 + x48
x50 = x15 * x46
x51 = x43 * x44 + x49 * x50
x52 = x23 * x47
x53 = x18 * x52
x54 = x4 * x53 + x44 * x49
x55 = x44 * x51 + x50 * x54
x56 = x52 * x6
x57 = x1 * x13 ** (-2.5)
x58 = x44 * x54 + x56 * x57
x59 = x15 * (x44 * x55 + x50 * x58)
x60 = x4**3
x61 = x1**2
x62 = x13 ** (-3.5) * x61
x63 = x52 * x62
x64 = x44 * x58 + x60 * x63
x65 = x0 * x15
x66 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35)
x67 = x25 * boys(7, x16)
x68 = x37 * x4
x69 = (
x31 * x39
- x46 * (x32 + x38)
- x68
* (
x31 * x36
+ x66
- x68 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x67)
)
)
x70 = x4 * x69
x71 = x39 * x5
x72 = 3.0 * x71
x73 = x15 * x5
x74 = 3.0 * x73
x75 = da * db * dc
x76 = 0.009523809523809524 * x75
x77 = 5.916079783099616 * x76
x78 = x15 * x8
x79 = x78 * (x40 + x42)
x80 = x53 * x8
x81 = x45 * x78 + x80
x82 = x44 * x79 + x50 * x81
x83 = x52 * x57
x84 = x4 * x83
x85 = x44 * x81 + x8 * x84
x86 = x15 * (x44 * x82 + x50 * x85)
x87 = x56 * x62
x88 = x44 * x85 + x8 * x87
x89 = 0.06666666666666667 * x75
x90 = 2.23606797749979 * x89
x91 = x11 * x15
x92 = x91 * (x40 + x42)
x93 = x11 * x53
x94 = x45 * x91 + x93
x95 = x44 * x92 + x50 * x94
x96 = x11 * x84 + x44 * x94
x97 = x15 * (x44 * x95 + x50 * x96)
x98 = x11 * x87 + x44 * x96
x99 = x61 / x13**2
x100 = x9 * x99
x101 = x100 * (x40 + x42)
x102 = x83 * x9
x103 = x100 * x45 + x102
x104 = x15 * (x101 * x44 + x103 * x50)
x105 = x63 * x9
x106 = x103 * x44 + x105 * x4
x107 = 1.732050807568877
x108 = 0.1111111111111111 * x107 * x75
x109 = x8 * x99
x110 = x109 * x11
x111 = x110 * (x40 + x42)
x112 = x11 * x8
x113 = x112 * x83
x114 = x110 * x45 + x113
x115 = x15 * (x111 * x44 + x114 * x50)
x116 = x112 * x4 * x63 + x114 * x44
x117 = 0.3333333333333333 * x75
x118 = x12 * x99
x119 = x118 * (x40 + x42)
x120 = x12 * x83
x121 = x118 * x45 + x120
x122 = x15 * (x119 * x44 + x121 * x50)
x123 = x12 * x4
x124 = x121 * x44 + x123 * x63
x125 = x8**3
x126 = x1**3 / x13**3
x127 = x125 * x126
x128 = x127 * x15 * (x40 + x42)
x129 = x125 * x63
x130 = x127 * x45 + x129
x131 = x126 * x9
x132 = x11 * x131
x133 = x132 * x15 * (x40 + x42)
x134 = x105 * x11
x135 = x132 * x45 + x134
x136 = x126 * x8
x137 = x12 * x136
x138 = x137 * x15 * (x40 + x42)
x139 = x12 * x63 * x8
x140 = x137 * x45 + x139
x141 = x11**3
x142 = x126 * x141
x143 = x142 * x15 * (x40 + x42)
x144 = x141 * x63
x145 = x142 * x45 + x144
x146 = x1**4 / x13**4
x147 = x146 * x8**4
x148 = x147 * x39
x149 = x0 * x33
x150 = x125 * x146
x151 = x11 * x150
x152 = x151 * x39
x153 = x146 * x39
x154 = x12 * x9
x155 = x153 * x154
x156 = x146 * x149
x157 = x146 * x69
x158 = x141 * x8
x159 = x153 * x158
x160 = x11**4 * x146
x161 = x160 * x39
x162 = -x7 - A[1]
x163 = -2.0 * x162 * x19 * x2 * x22 * x27 * x28 * x29 + x26 * x8
x164 = -x163
x165 = x164 * x5
x166 = 2.0 * x162 * x17 * x19 * x2 * x22 * x27 * x28 - x35 * x8
x167 = x166 * x37
x168 = x164 * x31 - x167 * x4
x169 = x168 * x4
x170 = x165 + x169
x171 = x44 * (x165 + x170)
x172 = x6 * x99
x173 = x165 * x172 + x171 * x44
x174 = x126 * x60
x175 = x15 * (x165 * x174 + x173 * x44)
x176 = x15 * x20
x177 = x175 + x176 * x64
x178 = -x5 * (x163 + x167)
x179 = 2.0 * x162 * x19 * x2 * x22 * x27 * x28 * x34 - x67 * x8
x180 = x168 * x31 + x178 - x68 * (x166 * x31 - x179 * x68)
x181 = x180 * x4
x182 = x168 * x5
x183 = 2.0 * x182
x184 = x15 * (
x173 * x50 + x44 * (x171 * x50 + x44 * (x170 * x50 + x44 * (x181 + x183)))
)
x185 = 10.2469507659596 * x76
x186 = x164 * x8
x187 = x186 + x48
x188 = x15 * x187
x189 = x168 * x8
x190 = x189 + x41
x191 = x188 * x5 + x190 * x44
x192 = x4 * x99
x193 = x187 * x5
x194 = x191 * x44 + x192 * x193
x195 = x126 * x6
x196 = x15 * (x193 * x195 + x194 * x44)
x197 = x176 * x88 + x196
x198 = x180 * x8
x199 = x198 + x71
x200 = x190 * x50
x201 = x15 * (x194 * x50 + x44 * (x191 * x50 + x44 * (x199 * x44 + x200)))
x202 = 3.872983346207417 * x89
x203 = x165 * x91
x204 = x169 * x91 + x203
x205 = x11 * x165
x206 = x192 * x205 + x204 * x44
x207 = x15 * (x195 * x205 + x206 * x44)
x208 = x176 * x98 + x207
x209 = x183 * x91
x210 = x15 * (x206 * x50 + x44 * (x204 * x50 + x44 * (x181 * x91 + x209)))
x211 = x188 * x8 + x80
x212 = x78 * (x190 + x41)
x213 = x211 * x73 + x212 * x44
x214 = x192 * x5
x215 = x15 * (x211 * x214 + x213 * x44)
x216 = x106 * x176 + x215
x217 = x78 * (x199 + x71)
x218 = x212 * x50
x219 = x15 * (x213 * x50 + x44 * (x217 * x44 + x218))
x220 = x186 * x91 + x93
x221 = x41 * x91
x222 = x189 * x91 + x221
x223 = x220 * x73 + x222 * x44
x224 = x15 * (x214 * x220 + x223 * x44)
x225 = x116 * x176 + x224
x226 = x71 * x91
x227 = x198 * x91 + x226
x228 = x222 * x50
x229 = x15 * (x223 * x50 + x44 * (x227 * x44 + x228))
x230 = x107 * x117
x231 = x118 * x165
x232 = x118 * x169 + x231
x233 = x123 * x126
x234 = x15 * (x165 * x233 + x232 * x44)
x235 = x124 * x176 + x234
x236 = x118 * x183
x237 = x15 * (x232 * x50 + x44 * (x118 * x181 + x236))
x238 = x102 + x211 * x78
x239 = x100 * x41 + x212 * x78
x240 = x15 * (x238 * x73 + x239 * x44)
x241 = x130 * x176 + x240
x242 = x100 * x71 + x217 * x78
x243 = x239 * x50
x244 = x15 * (x242 * x44 + x243)
x245 = x113 + x220 * x78
x246 = x110 * x41 + x222 * x78
x247 = x15 * (x245 * x73 + x246 * x44)
x248 = x135 * x176 + x247
x249 = x110 * x71 + x227 * x78
x250 = x246 * x50
x251 = x15 * (x249 * x44 + x250)
x252 = x118 * x186 + x120
x253 = x118 * x41
x254 = x118 * x189 + x253
x255 = x15 * (x252 * x73 + x254 * x44)
x256 = x140 * x176 + x255
x257 = x118 * x71
x258 = x118 * x198 + x257
x259 = x254 * x50
x260 = x15 * (x258 * x44 + x259)
x261 = x142 * x165
x262 = x15 * (x142 * x169 + x261)
x263 = x145 * x176 + x262
x264 = x142 * x183
x265 = x15 * (x142 * x181 + x264)
x266 = x15 * (x127 * x41 + x239 * x78)
x267 = x20 * x33
x268 = x147 * x267 + x266
x269 = x15 * (x127 * x71 + x242 * x78)
x270 = x15 * (x132 * x41 + x246 * x78)
x271 = x151 * x267 + x270
x272 = x15 * (x132 * x71 + x249 * x78)
x273 = x15 * (x137 * x41 + x254 * x78)
x274 = x146 * x267
x275 = x154 * x274 + x273
x276 = x15 * (x137 * x71 + x258 * x78)
x277 = x142 * x41
x278 = x15 * (x142 * x189 + x277)
x279 = x158 * x274 + x278
x280 = x142 * x71
x281 = x15 * (x142 * x198 + x280)
x282 = x160 * x168
x283 = x160 * x267 + x282
x284 = x160 * x180
x285 = -x10 - A[2]
x286 = x11 * x26 - 2.0 * x19 * x2 * x22 * x27 * x28 * x285 * x29
x287 = -x286
x288 = x287 * x5
x289 = -x11 * x35 + 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x285
x290 = x289 * x37
x291 = x287 * x31 - x290 * x4
x292 = x291 * x4
x293 = x288 + x292
x294 = x44 * (x288 + x293)
x295 = x172 * x288 + x294 * x44
x296 = x15 * (x174 * x288 + x295 * x44)
x297 = x15 * x21
x298 = x296 + x297 * x64
x299 = -x5 * (x286 + x290)
x300 = -x11 * x67 + 2.0 * x19 * x2 * x22 * x27 * x28 * x285 * x34
x301 = x291 * x31 + x299 - x68 * (x289 * x31 - x300 * x68)
x302 = x301 * x4
x303 = x291 * x5
x304 = 2.0 * x303
x305 = x15 * (
x295 * x50 + x44 * (x294 * x50 + x44 * (x293 * x50 + x44 * (x302 + x304)))
)
x306 = x288 * x78
x307 = x292 * x78 + x306
x308 = x109 * x4
x309 = x288 * x308 + x307 * x44
x310 = x195 * x8
x311 = x15 * (x288 * x310 + x309 * x44)
x312 = x297 * x88 + x311
x313 = x15 * (x309 * x50 + x44 * (x307 * x50 + x44 * x78 * (x302 + x304)))
x314 = x11 * x287 + x48
x315 = x314 * x73
x316 = x11 * x291 + x41
x317 = x315 + x316 * x44
x318 = x214 * x314 + x317 * x44
x319 = x314 * x5
x320 = x15 * (x195 * x319 + x318 * x44)
x321 = x297 * x98 + x320
x322 = x11 * x301 + x71
x323 = x316 * x50
x324 = x15 * (x318 * x50 + x44 * (x317 * x50 + x44 * (x322 * x44 + x323)))
x325 = x100 * x288
x326 = x100 * x292 + x325
x327 = x131 * x4
x328 = x15 * (x288 * x327 + x326 * x44)
x329 = x106 * x297 + x328
x330 = x15 * (x100 * x44 * (x302 + x304) + x326 * x50)
x331 = x109 * x319
x332 = x308 * x316 + x331
x333 = x136 * x4
x334 = x15 * (x319 * x333 + x332 * x44)
x335 = x116 * x297 + x334
x336 = x316 * x46
x337 = x15 * (x332 * x50 + x44 * (x109 * x336 + x308 * x322))
x338 = x314 * x91 + x93
x339 = x338 * x73
x340 = x221 + x316 * x91
x341 = x339 + x340 * x44
x342 = x15 * (x214 * x338 + x341 * x44)
x343 = x124 * x297 + x342
x344 = x226 + x322 * x91
x345 = x340 * x50
x346 = x15 * (x341 * x50 + x44 * (x344 * x44 + x345))
x347 = x127 * x288
x348 = x15 * (x127 * x292 + x347)
x349 = x130 * x297 + x348
x350 = x127 * x15 * (x302 + x304)
x351 = x131 * x319
x352 = x15 * (x316 * x327 + x351)
x353 = x135 * x297 + x352
x354 = x15 * (x131 * x336 + x322 * x327)
x355 = x109 * x5
x356 = x338 * x355
x357 = x15 * (x308 * x340 + x356)
x358 = x140 * x297 + x357
x359 = x15 * (x109 * x340 * x46 + x308 * x344)
x360 = x120 + x338 * x91
x361 = x360 * x73
x362 = x253 + x340 * x91
x363 = x15 * (x361 + x362 * x44)
x364 = x145 * x297 + x363
x365 = x257 + x344 * x91
x366 = x362 * x50
x367 = x15 * (x365 * x44 + x366)
x368 = x147 * x291
x369 = x21 * x33
x370 = x147 * x369 + x368
x371 = x147 * x301
x372 = x150 * x316
x373 = x151 * x369 + x372
x374 = x150 * x322
x375 = x131 * x340
x376 = x146 * x369
x377 = x154 * x376 + x375
x378 = x131 * x344
x379 = x109 * x362
x380 = x158 * x376 + x379
x381 = x109 * x365
x382 = x15 * (x277 + x362 * x91)
x383 = x160 * x369 + x382
x384 = x15 * (x280 + x365 * x91)
x385 = x162 * x164 - x167 * x8 + x30
x386 = x385 * x5
x387 = x37 * x8
x388 = x162 * x166 - x179 * x387 + x66
x389 = x31 * x385 - x388 * x68
x390 = x389 * x4
x391 = (
x15 * (x174 * x386 + x44 * (x172 * x386 + x44**2 * (2.0 * x386 + x390)))
+ x175 * x20
)
x392 = x385 * x8
x393 = 2.0 * x165
x394 = x392 + x393
x395 = x394 * x73
x396 = x389 * x8
x397 = x183 + x396
x398 = x195 * x5
x399 = (
x15 * (x394 * x398 + x44 * (x214 * x394 + x44 * (x395 + x397 * x44))) + x196 * x20
)
x400 = x386 * x91
x401 = x11 * x386
x402 = (
x15 * (x195 * x401 + x44 * (x192 * x401 + x44 * (x390 * x91 + x400))) + x20 * x207
)
x403 = x188 * x46 + x394 * x78
x404 = x403 * x73
x405 = x200 + x397 * x78
x406 = x15 * (x214 * x403 + x44 * (x404 + x405 * x44)) + x20 * x215
x407 = x91 * (x392 + x393)
x408 = x407 * x73
x409 = x209 + x396 * x91
x410 = x15 * (x214 * x407 + x44 * (x408 + x409 * x44)) + x20 * x224
x411 = x118 * x386
x412 = x15 * (x233 * x386 + x44 * (x118 * x390 + x411)) + x20 * x234
x413 = x211 * x50 + x403 * x78
x414 = x413 * x73
x415 = x218 + x405 * x78
x416 = x15 * (x414 + x415 * x44) + x20 * x240
x417 = x220 * x50 + x407 * x78
x418 = x417 * x73
x419 = x228 + x409 * x78
x420 = x15 * (x418 + x419 * x44) + x20 * x247
x421 = x118 * (x392 + x393)
x422 = x421 * x73
x423 = x118 * x396 + x236
x424 = x15 * (x422 + x423 * x44) + x20 * x255
x425 = x142 * x386
x426 = x15 * (x142 * x390 + x425) + x20 * x262
x427 = x15 * (x243 + x415 * x78) + x20 * x266
x428 = x15 * (x250 + x419 * x78) + x20 * x270
x429 = x15 * (x259 + x423 * x78) + x20 * x273
x430 = x15 * (x142 * x396 + x264) + x20 * x278
x431 = x160 * x389 + x20 * x282
x432 = x162 * x287 - x290 * x8
x433 = x432 * x5
x434 = x162 * x289 - x300 * x387
x435 = x31 * x432 - x434 * x68
x436 = x15 * (x174 * x433 + x44 * (x172 * x433 + x44**2 * (x4 * x435 + 2.0 * x433)))
x437 = x175 * x21 + x436
x438 = x288 + x432 * x8
x439 = x303 + x435 * x8
x440 = x15 * (x398 * x438 + x44 * (x214 * x438 + x44 * (x438 * x73 + x439 * x44)))
x441 = x196 * x21 + x440
x442 = x11 * x432 + x165
x443 = x11 * x435 + x182
x444 = x15 * (x398 * x442 + x44 * (x214 * x442 + x44 * (x44 * x443 + x442 * x73)))
x445 = x207 * x21 + x444
x446 = x306 + x438 * x78
x447 = x78 * (x303 + x439)
x448 = x15 * (x214 * x446 + x44 * (x44 * x447 + x446 * x73))
x449 = x21 * x215 + x448
x450 = x315 + x442 * x78
x451 = x316 * x73 + x443 * x78
x452 = x15 * (x214 * x450 + x44 * (x44 * x451 + x450 * x73))
x453 = x21 * x224 + x452
x454 = x203 + x442 * x91
x455 = x91 * (x182 + x443)
x456 = x15 * (x214 * x454 + x44 * (x44 * x455 + x454 * x73))
x457 = x21 * x234 + x456
x458 = x325 + x446 * x78
x459 = x100 * x303 + x447 * x78
x460 = x15 * (x44 * x459 + x458 * x73)
x461 = x21 * x240 + x460
x462 = x331 + x450 * x78
x463 = x316 * x355 + x451 * x78
x464 = x15 * (x44 * x463 + x462 * x73)
x465 = x21 * x247 + x464
x466 = x339 + x454 * x78
x467 = x340 * x73 + x455 * x78
x468 = x15 * (x44 * x467 + x466 * x73)
x469 = x21 * x255 + x468
x470 = x231 + x454 * x91
x471 = x118 * x182 + x455 * x91
x472 = x15 * (x44 * x471 + x470 * x73)
x473 = x21 * x262 + x472
x474 = x15 * (x127 * x303 + x459 * x78)
x475 = x21 * x266 + x474
x476 = x131 * x5
x477 = x15 * (x316 * x476 + x463 * x78)
x478 = x21 * x270 + x477
x479 = x15 * (x340 * x355 + x467 * x78)
x480 = x21 * x273 + x479
x481 = x15 * (x362 * x73 + x471 * x78)
x482 = x21 * x278 + x481
x483 = x15 * (x142 * x182 + x471 * x91)
x484 = x21 * x282 + x483
x485 = -x11 * x290 + x285 * x287 + x30
x486 = x485 * x5
x487 = x11 * x37
x488 = x285 * x289 - x300 * x487 + x66
x489 = x31 * x485 - x488 * x68
x490 = x4 * x489
x491 = (
x15 * (x174 * x486 + x44 * (x172 * x486 + x44**2 * (2.0 * x486 + x490)))
+ x21 * x296
)
x492 = x486 * x78
x493 = (
x15 * (x310 * x486 + x44 * (x308 * x486 + x44 * (x490 * x78 + x492))) + x21 * x311
)
x494 = x11 * x485 + 2.0 * x288
x495 = x494 * x73
x496 = x11 * x489 + x304
x497 = (
x15 * (x398 * x494 + x44 * (x214 * x494 + x44 * (x44 * x496 + x495))) + x21 * x320
)
x498 = x100 * x486
x499 = x15 * (x327 * x486 + x44 * (x100 * x490 + x498)) + x21 * x328
x500 = x355 * x494
x501 = x4 * x494
x502 = x15 * (x136 * x5 * x501 + x44 * (x308 * x496 + x500)) + x21 * x334
x503 = x314 * x50 + x494 * x91
x504 = x503 * x73
x505 = x323 + x496 * x91
x506 = x15 * (x214 * x503 + x44 * (x44 * x505 + x504)) + x21 * x342
x507 = x127 * x486
x508 = x15 * (x127 * x490 + x507) + x21 * x348
x509 = x476 * x494
x510 = x15 * (x327 * x496 + x509) + x21 * x352
x511 = x355 * x503
x512 = x15 * (x308 * x505 + x511) + x21 * x357
x513 = x338 * x50 + x503 * x91
x514 = x513 * x73
x515 = x345 + x505 * x91
x516 = x15 * (x44 * x515 + x514) + x21 * x363
x517 = x147 * x489 + x21 * x368
x518 = x150 * x496 + x21 * x372
x519 = x131 * x505 + x21 * x375
x520 = x109 * x515 + x21 * x379
x521 = x15 * (x366 + x515 * x91) + x21 * x382
x522 = x146 * x4**4
x523 = x0 * x164
x524 = x146 * x60
x525 = x187 * x524
x526 = x11 * x524
x527 = x0 * x195
x528 = x12 * x6
x529 = x146 * x523
x530 = x0 * x192
x531 = x141 * x4
x532 = x129 + x238 * x78
x533 = x134 + x245 * x78
x534 = x139 + x252 * x78
x535 = x142 * x186 + x144
x536 = x385 * x522
x537 = x164 * x20
x538 = x522 * x537 + x536
x539 = x394 * x524
x540 = x20 * x525 + x539
x541 = x385 * x526
x542 = x526 * x537 + x541
x543 = x195 * x403
x544 = x195 * x20
x545 = x211 * x544 + x543
x546 = x195 * x407
x547 = x220 * x544 + x546
x548 = x146 * x385
x549 = x528 * x548
x550 = x146 * x537
x551 = x528 * x550 + x549
x552 = x192 * x413
x553 = x192 * x20
x554 = x238 * x553 + x552
x555 = x192 * x417
x556 = x245 * x553 + x555
x557 = x192 * x421
x558 = x252 * x553 + x557
x559 = x531 * x548
x560 = x531 * x550 + x559
x561 = x15 * (x238 * x50 + x413 * x78)
x562 = x176 * x532 + x561
x563 = x15 * (x245 * x50 + x417 * x78)
x564 = x176 * x533 + x563
x565 = x15 * (x252 * x50 + x421 * x78)
x566 = x176 * x534 + x565
x567 = x142 * x15 * (x392 + x393)
x568 = x176 * x535 + x567
x569 = x160 * x385
x570 = x160 * x537 + x569
x571 = x432 * x522
x572 = x164 * x21
x573 = x522 * x572 + x571
x574 = x438 * x524
x575 = x21 * x525 + x574
x576 = x442 * x524
x577 = x526 * x572 + x576
x578 = x195 * x446
x579 = x195 * x21
x580 = x211 * x579 + x578
x581 = x195 * x450
x582 = x220 * x579 + x581
x583 = x195 * x454
x584 = x146 * x572
x585 = x528 * x584 + x583
x586 = x192 * x458
x587 = x192 * x21
x588 = x238 * x587 + x586
x589 = x192 * x462
x590 = x245 * x587 + x589
x591 = x192 * x466
x592 = x252 * x587 + x591
x593 = x192 * x470
x594 = x531 * x584 + x593
x595 = x15 * (x347 + x458 * x78)
x596 = x297 * x532 + x595
x597 = x15 * (x351 + x462 * x78)
x598 = x297 * x533 + x597
x599 = x15 * (x356 + x466 * x78)
x600 = x297 * x534 + x599
x601 = x15 * (x361 + x470 * x78)
x602 = x297 * x535 + x601
x603 = x15 * (x261 + x470 * x91)
x604 = x160 * x572 + x603
x605 = x162 * x385 + 2.0 * x178 - x387 * x388
x606 = x605 * x8
x607 = 3.0 * x386
x608 = x606 + x607
x609 = 3.0 * x395 + x608 * x78
x610 = x91 * (x606 + x607)
x611 = x146 * x605
x612 = 3.0 * x404 + x609 * x78
x613 = 3.0 * x408 + x610 * x78
x614 = x118 * (x606 + x607)
x615 = x162 * x432 + x299 - x387 * x434
x616 = x522 * x615
x617 = 2.0 * x433
x618 = x615 * x8 + x617
x619 = x524 * x618
x620 = x11 * x615 + x386
x621 = x524 * x620
x622 = x438 * x50 + x618 * x78
x623 = x195 * x622
x624 = x442 * x50
x625 = x620 * x78 + x624
x626 = x195 * x625
x627 = x400 + x620 * x91
x628 = x195 * x627
x629 = x446 * x50 + x622 * x78
x630 = x192 * x629
x631 = x450 * x50 + x625 * x78
x632 = x192 * x631
x633 = x454 * x50
x634 = x627 * x78 + x633
x635 = x192 * x634
x636 = x411 + x627 * x91
x637 = x192 * x636
x638 = x15 * (x458 * x50 + x629 * x78)
x639 = x15 * (x462 * x50 + x631 * x78)
x640 = x15 * (x466 * x50 + x634 * x78)
x641 = x470 * x50
x642 = x15 * (x636 * x78 + x641)
x643 = x15 * (x425 + x636 * x91)
x644 = x162 * x485 - x387 * x488
x645 = x21 * x571 + x522 * x644
x646 = x486 + x644 * x8
x647 = x21 * x574 + x524 * x646
x648 = x11 * x644 + x617
x649 = x21 * x576 + x524 * x648
x650 = x492 + x646 * x78
x651 = x195 * x650 + x21 * x578
x652 = x495 + x648 * x78
x653 = x195 * x652 + x21 * x581
x654 = x624 + x648 * x91
x655 = x195 * x654 + x21 * x583
x656 = x498 + x650 * x78
x657 = x192 * x656 + x21 * x586
x658 = x500 + x652 * x78
x659 = x192 * x658 + x21 * x589
x660 = x504 + x654 * x78
x661 = x192 * x660 + x21 * x591
x662 = x633 + x654 * x91
x663 = x192 * x662 + x21 * x593
x664 = x15 * (x507 + x656 * x78) + x21 * x595
x665 = x15 * (x509 + x658 * x78) + x21 * x597
x666 = x15 * (x511 + x660 * x78) + x21 * x599
x667 = x15 * (x514 + x662 * x78) + x21 * x601
x668 = x15 * (x641 + x662 * x91) + x21 * x603
x669 = x0 * x287
x670 = x524 * x8
x671 = x0 * x314
x672 = x146 * x6
x673 = x672 * x9
x674 = x672 * x8
x675 = x150 * x4
x676 = x146 * x9
x677 = x4 * x676
x678 = x333 * x338
x679 = x131 * x338
x680 = x109 * x360
x681 = x144 + x360 * x91
x682 = x20 * x287
x683 = x522 * x682 + x571
x684 = x574 + x670 * x682
x685 = x20 * x314
x686 = x524 * x685 + x576
x687 = x578 + x673 * x682
x688 = x581 + x674 * x685
x689 = x338 * x544 + x583
x690 = x586 + x675 * x682
x691 = x589 + x677 * x685
x692 = x20 * x678 + x591
x693 = x360 * x553 + x593
x694 = x147 * x682 + x595
x695 = x150 * x685 + x597
x696 = x20 * x679 + x599
x697 = x20 * x680 + x601
x698 = x176 * x681 + x603
x699 = x485 * x522
x700 = x21 * x287
x701 = x522 * x700 + x699
x702 = x485 * x670
x703 = x670 * x700 + x702
x704 = x494 * x524
x705 = x21 * x314
x706 = x524 * x705 + x704
x707 = x485 * x673
x708 = x673 * x700 + x707
x709 = x494 * x674
x710 = x674 * x705 + x709
x711 = x195 * x503
x712 = x338 * x579 + x711
x713 = x485 * x675
x714 = x675 * x700 + x713
x715 = x501 * x676
x716 = x677 * x705 + x715
x717 = x333 * x503
x718 = x21 * x678 + x717
x719 = x192 * x513
x720 = x360 * x587 + x719
x721 = x147 * x485
x722 = x147 * x700 + x721
x723 = x150 * x494
x724 = x150 * x705 + x723
x725 = x131 * x503
x726 = x21 * x679 + x725
x727 = x109 * x513
x728 = x21 * x680 + x727
x729 = x15 * (x360 * x50 + x513 * x91)
x730 = x297 * x681 + x729
x731 = x285 * x485 + 2.0 * x299 - x487 * x488
x732 = x11 * x731 + 3.0 * x486
x733 = 3.0 * x495 + x732 * x91
x734 = 3.0 * x504 + x733 * x91
# 270 item(s)
result[0, 0, 0] = numpy.sum(
x77
* (
x0 * x59
+ x0 * (x59 + x64 * x65)
+ x15
* (x44 * (x44 * (x43 * x74 + x44 * (x70 + x72)) + x51 * x74) + x55 * x74)
)
)
result[0, 0, 1] = numpy.sum(
x90
* (
x0 * x86
+ x0 * (x65 * x88 + x86)
+ x15 * (x44 * (x44 * x78 * (x70 + x72) + x74 * x79) + x74 * x82)
)
)
result[0, 0, 2] = numpy.sum(
x90
* (
x0 * x97
+ x0 * (x65 * x98 + x97)
+ x15 * (x44 * (x44 * x91 * (x70 + x72) + x74 * x92) + x74 * x95)
)
)
result[0, 0, 3] = numpy.sum(
x108
* (
x0 * x104
+ x0 * (x104 + x106 * x65)
+ x15 * (x100 * x44 * (x70 + x72) + x101 * x74)
)
)
result[0, 0, 4] = numpy.sum(
x117
* (
x0 * x115
+ x0 * (x115 + x116 * x65)
+ x15 * (x110 * x44 * (x70 + x72) + x111 * x74)
)
)
result[0, 0, 5] = numpy.sum(
x108
* (
x0 * x122
+ x0 * (x122 + x124 * x65)
+ x15 * (x118 * x44 * (x70 + x72) + x119 * x74)
)
)
result[0, 0, 6] = numpy.sum(
x90 * (x0 * x128 + x0 * (x128 + x130 * x65) + x127 * x15 * (x70 + x72))
)
result[0, 0, 7] = numpy.sum(
x117 * (x0 * x133 + x0 * (x133 + x135 * x65) + x132 * x15 * (x70 + x72))
)
result[0, 0, 8] = numpy.sum(
x117 * (x0 * x138 + x0 * (x138 + x140 * x65) + x137 * x15 * (x70 + x72))
)
result[0, 0, 9] = numpy.sum(
x90 * (x0 * x143 + x0 * (x143 + x145 * x65) + x142 * x15 * (x70 + x72))
)
result[0, 0, 10] = numpy.sum(
x77 * (x0 * x148 + x0 * (x147 * x149 + x148) + x147 * x69)
)
result[0, 0, 11] = numpy.sum(
x90 * (x0 * x152 + x0 * (x149 * x151 + x152) + x151 * x69)
)
result[0, 0, 12] = numpy.sum(
x108 * (x0 * x155 + x0 * (x154 * x156 + x155) + x154 * x157)
)
result[0, 0, 13] = numpy.sum(
x90 * (x0 * x159 + x0 * (x156 * x158 + x159) + x157 * x158)
)
result[0, 0, 14] = numpy.sum(
x77 * (x0 * x161 + x0 * (x149 * x160 + x161) + x160 * x69)
)
result[0, 1, 0] = numpy.sum(x185 * (x0 * x177 + x184 + x20 * x59))
result[0, 1, 1] = numpy.sum(x202 * (x0 * x197 + x20 * x86 + x201))
result[0, 1, 2] = numpy.sum(x202 * (x0 * x208 + x20 * x97 + x210))
result[0, 1, 3] = numpy.sum(x117 * (x0 * x216 + x104 * x20 + x219))
result[0, 1, 4] = numpy.sum(x230 * (x0 * x225 + x115 * x20 + x229))
result[0, 1, 5] = numpy.sum(x117 * (x0 * x235 + x122 * x20 + x237))
result[0, 1, 6] = numpy.sum(x202 * (x0 * x241 + x128 * x20 + x244))
result[0, 1, 7] = numpy.sum(x230 * (x0 * x248 + x133 * x20 + x251))
result[0, 1, 8] = numpy.sum(x230 * (x0 * x256 + x138 * x20 + x260))
result[0, 1, 9] = numpy.sum(x202 * (x0 * x263 + x143 * x20 + x265))
result[0, 1, 10] = numpy.sum(x185 * (x0 * x268 + x148 * x20 + x269))
result[0, 1, 11] = numpy.sum(x202 * (x0 * x271 + x152 * x20 + x272))
result[0, 1, 12] = numpy.sum(x117 * (x0 * x275 + x155 * x20 + x276))
result[0, 1, 13] = numpy.sum(x202 * (x0 * x279 + x159 * x20 + x281))
result[0, 1, 14] = numpy.sum(x185 * (x0 * x283 + x161 * x20 + x284))
result[0, 2, 0] = numpy.sum(x185 * (x0 * x298 + x21 * x59 + x305))
result[0, 2, 1] = numpy.sum(x202 * (x0 * x312 + x21 * x86 + x313))
result[0, 2, 2] = numpy.sum(x202 * (x0 * x321 + x21 * x97 + x324))
result[0, 2, 3] = numpy.sum(x117 * (x0 * x329 + x104 * x21 + x330))
result[0, 2, 4] = numpy.sum(x230 * (x0 * x335 + x115 * x21 + x337))
result[0, 2, 5] = numpy.sum(x117 * (x0 * x343 + x122 * x21 + x346))
result[0, 2, 6] = numpy.sum(x202 * (x0 * x349 + x128 * x21 + x350))
result[0, 2, 7] = numpy.sum(x230 * (x0 * x353 + x133 * x21 + x354))
result[0, 2, 8] = numpy.sum(x230 * (x0 * x358 + x138 * x21 + x359))
result[0, 2, 9] = numpy.sum(x202 * (x0 * x364 + x143 * x21 + x367))
result[0, 2, 10] = numpy.sum(x185 * (x0 * x370 + x148 * x21 + x371))
result[0, 2, 11] = numpy.sum(x202 * (x0 * x373 + x152 * x21 + x374))
result[0, 2, 12] = numpy.sum(x117 * (x0 * x377 + x155 * x21 + x378))
result[0, 2, 13] = numpy.sum(x202 * (x0 * x380 + x159 * x21 + x381))
result[0, 2, 14] = numpy.sum(x185 * (x0 * x383 + x161 * x21 + x384))
result[0, 3, 0] = numpy.sum(x77 * (x177 * x20 + x391))
result[0, 3, 1] = numpy.sum(x90 * (x197 * x20 + x399))
result[0, 3, 2] = numpy.sum(x90 * (x20 * x208 + x402))
result[0, 3, 3] = numpy.sum(x108 * (x20 * x216 + x406))
result[0, 3, 4] = numpy.sum(x117 * (x20 * x225 + x410))
result[0, 3, 5] = numpy.sum(x108 * (x20 * x235 + x412))
result[0, 3, 6] = numpy.sum(x90 * (x20 * x241 + x416))
result[0, 3, 7] = numpy.sum(x117 * (x20 * x248 + x420))
result[0, 3, 8] = numpy.sum(x117 * (x20 * x256 + x424))
result[0, 3, 9] = numpy.sum(x90 * (x20 * x263 + x426))
result[0, 3, 10] = numpy.sum(x77 * (x20 * x268 + x427))
result[0, 3, 11] = numpy.sum(x90 * (x20 * x271 + x428))
result[0, 3, 12] = numpy.sum(x108 * (x20 * x275 + x429))
result[0, 3, 13] = numpy.sum(x90 * (x20 * x279 + x430))
result[0, 3, 14] = numpy.sum(x77 * (x20 * x283 + x431))
result[0, 4, 0] = numpy.sum(x185 * (x20 * x298 + x437))
result[0, 4, 1] = numpy.sum(x202 * (x20 * x312 + x441))
result[0, 4, 2] = numpy.sum(x202 * (x20 * x321 + x445))
result[0, 4, 3] = numpy.sum(x117 * (x20 * x329 + x449))
result[0, 4, 4] = numpy.sum(x230 * (x20 * x335 + x453))
result[0, 4, 5] = numpy.sum(x117 * (x20 * x343 + x457))
result[0, 4, 6] = numpy.sum(x202 * (x20 * x349 + x461))
result[0, 4, 7] = numpy.sum(x230 * (x20 * x353 + x465))
result[0, 4, 8] = numpy.sum(x230 * (x20 * x358 + x469))
result[0, 4, 9] = numpy.sum(x202 * (x20 * x364 + x473))
result[0, 4, 10] = numpy.sum(x185 * (x20 * x370 + x475))
result[0, 4, 11] = numpy.sum(x202 * (x20 * x373 + x478))
result[0, 4, 12] = numpy.sum(x117 * (x20 * x377 + x480))
result[0, 4, 13] = numpy.sum(x202 * (x20 * x380 + x482))
result[0, 4, 14] = numpy.sum(x185 * (x20 * x383 + x484))
result[0, 5, 0] = numpy.sum(x77 * (x21 * x298 + x491))
result[0, 5, 1] = numpy.sum(x90 * (x21 * x312 + x493))
result[0, 5, 2] = numpy.sum(x90 * (x21 * x321 + x497))
result[0, 5, 3] = numpy.sum(x108 * (x21 * x329 + x499))
result[0, 5, 4] = numpy.sum(x117 * (x21 * x335 + x502))
result[0, 5, 5] = numpy.sum(x108 * (x21 * x343 + x506))
result[0, 5, 6] = numpy.sum(x90 * (x21 * x349 + x508))
result[0, 5, 7] = numpy.sum(x117 * (x21 * x353 + x510))
result[0, 5, 8] = numpy.sum(x117 * (x21 * x358 + x512))
result[0, 5, 9] = numpy.sum(x90 * (x21 * x364 + x516))
result[0, 5, 10] = numpy.sum(x77 * (x21 * x370 + x517))
result[0, 5, 11] = numpy.sum(x90 * (x21 * x373 + x518))
result[0, 5, 12] = numpy.sum(x108 * (x21 * x377 + x519))
result[0, 5, 13] = numpy.sum(x90 * (x21 * x380 + x520))
result[0, 5, 14] = numpy.sum(x77 * (x21 * x383 + x521))
result[1, 0, 0] = numpy.sum(x77 * (x0 * x175 + x0 * (x175 + x522 * x523) + x184))
result[1, 0, 1] = numpy.sum(x90 * (x0 * x196 + x0 * (x0 * x525 + x196) + x201))
result[1, 0, 2] = numpy.sum(x90 * (x0 * x207 + x0 * (x207 + x523 * x526) + x210))
result[1, 0, 3] = numpy.sum(x108 * (x0 * x215 + x0 * (x211 * x527 + x215) + x219))
result[1, 0, 4] = numpy.sum(x117 * (x0 * x224 + x0 * (x220 * x527 + x224) + x229))
result[1, 0, 5] = numpy.sum(x108 * (x0 * x234 + x0 * (x234 + x528 * x529) + x237))
result[1, 0, 6] = numpy.sum(x90 * (x0 * x240 + x0 * (x238 * x530 + x240) + x244))
result[1, 0, 7] = numpy.sum(x117 * (x0 * x247 + x0 * (x245 * x530 + x247) + x251))
result[1, 0, 8] = numpy.sum(x117 * (x0 * x255 + x0 * (x252 * x530 + x255) + x260))
result[1, 0, 9] = numpy.sum(x90 * (x0 * x262 + x0 * (x262 + x529 * x531) + x265))
result[1, 0, 10] = numpy.sum(x77 * (x0 * x266 + x0 * (x266 + x532 * x65) + x269))
result[1, 0, 11] = numpy.sum(x90 * (x0 * x270 + x0 * (x270 + x533 * x65) + x272))
result[1, 0, 12] = numpy.sum(x108 * (x0 * x273 + x0 * (x273 + x534 * x65) + x276))
result[1, 0, 13] = numpy.sum(x90 * (x0 * x278 + x0 * (x278 + x535 * x65) + x281))
result[1, 0, 14] = numpy.sum(x77 * (x0 * x282 + x0 * (x160 * x523 + x282) + x284))
result[1, 1, 0] = numpy.sum(x185 * (x0 * x538 + x391))
result[1, 1, 1] = numpy.sum(x202 * (x0 * x540 + x399))
result[1, 1, 2] = numpy.sum(x202 * (x0 * x542 + x402))
result[1, 1, 3] = numpy.sum(x117 * (x0 * x545 + x406))
result[1, 1, 4] = numpy.sum(x230 * (x0 * x547 + x410))
result[1, 1, 5] = numpy.sum(x117 * (x0 * x551 + x412))
result[1, 1, 6] = numpy.sum(x202 * (x0 * x554 + x416))
result[1, 1, 7] = numpy.sum(x230 * (x0 * x556 + x420))
result[1, 1, 8] = numpy.sum(x230 * (x0 * x558 + x424))
result[1, 1, 9] = numpy.sum(x202 * (x0 * x560 + x426))
result[1, 1, 10] = numpy.sum(x185 * (x0 * x562 + x427))
result[1, 1, 11] = numpy.sum(x202 * (x0 * x564 + x428))
result[1, 1, 12] = numpy.sum(x117 * (x0 * x566 + x429))
result[1, 1, 13] = numpy.sum(x202 * (x0 * x568 + x430))
result[1, 1, 14] = numpy.sum(x185 * (x0 * x570 + x431))
result[1, 2, 0] = numpy.sum(x185 * (x0 * x573 + x437))
result[1, 2, 1] = numpy.sum(x202 * (x0 * x575 + x441))
result[1, 2, 2] = numpy.sum(x202 * (x0 * x577 + x445))
result[1, 2, 3] = numpy.sum(x117 * (x0 * x580 + x449))
result[1, 2, 4] = numpy.sum(x230 * (x0 * x582 + x453))
result[1, 2, 5] = numpy.sum(x117 * (x0 * x585 + x457))
result[1, 2, 6] = numpy.sum(x202 * (x0 * x588 + x461))
result[1, 2, 7] = numpy.sum(x230 * (x0 * x590 + x465))
result[1, 2, 8] = numpy.sum(x230 * (x0 * x592 + x469))
result[1, 2, 9] = numpy.sum(x202 * (x0 * x594 + x473))
result[1, 2, 10] = numpy.sum(x185 * (x0 * x596 + x475))
result[1, 2, 11] = numpy.sum(x202 * (x0 * x598 + x478))
result[1, 2, 12] = numpy.sum(x117 * (x0 * x600 + x480))
result[1, 2, 13] = numpy.sum(x202 * (x0 * x602 + x482))
result[1, 2, 14] = numpy.sum(x185 * (x0 * x604 + x484))
result[1, 3, 0] = numpy.sum(x77 * (x20 * x536 + x20 * x538 + x522 * x605))
result[1, 3, 1] = numpy.sum(x90 * (x20 * x539 + x20 * x540 + x524 * x608))
result[1, 3, 2] = numpy.sum(x90 * (x20 * x541 + x20 * x542 + x526 * x605))
result[1, 3, 3] = numpy.sum(x108 * (x195 * x609 + x20 * x543 + x20 * x545))
result[1, 3, 4] = numpy.sum(x117 * (x195 * x610 + x20 * x546 + x20 * x547))
result[1, 3, 5] = numpy.sum(x108 * (x20 * x549 + x20 * x551 + x528 * x611))
result[1, 3, 6] = numpy.sum(x90 * (x192 * x612 + x20 * x552 + x20 * x554))
result[1, 3, 7] = numpy.sum(x117 * (x192 * x613 + x20 * x555 + x20 * x556))
result[1, 3, 8] = numpy.sum(x117 * (x192 * x614 + x20 * x557 + x20 * x558))
result[1, 3, 9] = numpy.sum(x90 * (x20 * x559 + x20 * x560 + x531 * x611))
result[1, 3, 10] = numpy.sum(
x77 * (x15 * (3.0 * x414 + x612 * x78) + x20 * x561 + x20 * x562)
)
result[1, 3, 11] = numpy.sum(
x90 * (x15 * (3.0 * x418 + x613 * x78) + x20 * x563 + x20 * x564)
)
result[1, 3, 12] = numpy.sum(
x108 * (x15 * (3.0 * x422 + x614 * x78) + x20 * x565 + x20 * x566)
)
result[1, 3, 13] = numpy.sum(
x90 * (x142 * x15 * (x606 + x607) + x20 * x567 + x20 * x568)
)
result[1, 3, 14] = numpy.sum(x77 * (x160 * x605 + x20 * x569 + x20 * x570))
result[1, 4, 0] = numpy.sum(x185 * (x20 * x573 + x21 * x536 + x616))
result[1, 4, 1] = numpy.sum(x202 * (x20 * x575 + x21 * x539 + x619))
result[1, 4, 2] = numpy.sum(x202 * (x20 * x577 + x21 * x541 + x621))
result[1, 4, 3] = numpy.sum(x117 * (x20 * x580 + x21 * x543 + x623))
result[1, 4, 4] = numpy.sum(x230 * (x20 * x582 + x21 * x546 + x626))
result[1, 4, 5] = numpy.sum(x117 * (x20 * x585 + x21 * x549 + x628))
result[1, 4, 6] = numpy.sum(x202 * (x20 * x588 + x21 * x552 + x630))
result[1, 4, 7] = numpy.sum(x230 * (x20 * x590 + x21 * x555 + x632))
result[1, 4, 8] = numpy.sum(x230 * (x20 * x592 + x21 * x557 + x635))
result[1, 4, 9] = numpy.sum(x202 * (x20 * x594 + x21 * x559 + x637))
result[1, 4, 10] = numpy.sum(x185 * (x20 * x596 + x21 * x561 + x638))
result[1, 4, 11] = numpy.sum(x202 * (x20 * x598 + x21 * x563 + x639))
result[1, 4, 12] = numpy.sum(x117 * (x20 * x600 + x21 * x565 + x640))
result[1, 4, 13] = numpy.sum(x202 * (x20 * x602 + x21 * x567 + x642))
result[1, 4, 14] = numpy.sum(x185 * (x20 * x604 + x21 * x569 + x643))
result[1, 5, 0] = numpy.sum(x77 * (x21 * x573 + x645))
result[1, 5, 1] = numpy.sum(x90 * (x21 * x575 + x647))
result[1, 5, 2] = numpy.sum(x90 * (x21 * x577 + x649))
result[1, 5, 3] = numpy.sum(x108 * (x21 * x580 + x651))
result[1, 5, 4] = numpy.sum(x117 * (x21 * x582 + x653))
result[1, 5, 5] = numpy.sum(x108 * (x21 * x585 + x655))
result[1, 5, 6] = numpy.sum(x90 * (x21 * x588 + x657))
result[1, 5, 7] = numpy.sum(x117 * (x21 * x590 + x659))
result[1, 5, 8] = numpy.sum(x117 * (x21 * x592 + x661))
result[1, 5, 9] = numpy.sum(x90 * (x21 * x594 + x663))
result[1, 5, 10] = numpy.sum(x77 * (x21 * x596 + x664))
result[1, 5, 11] = numpy.sum(x90 * (x21 * x598 + x665))
result[1, 5, 12] = numpy.sum(x108 * (x21 * x600 + x666))
result[1, 5, 13] = numpy.sum(x90 * (x21 * x602 + x667))
result[1, 5, 14] = numpy.sum(x77 * (x21 * x604 + x668))
result[2, 0, 0] = numpy.sum(x77 * (x0 * x296 + x0 * (x296 + x522 * x669) + x305))
result[2, 0, 1] = numpy.sum(x90 * (x0 * x311 + x0 * (x311 + x669 * x670) + x313))
result[2, 0, 2] = numpy.sum(x90 * (x0 * x320 + x0 * (x320 + x524 * x671) + x324))
result[2, 0, 3] = numpy.sum(x108 * (x0 * x328 + x0 * (x328 + x669 * x673) + x330))
result[2, 0, 4] = numpy.sum(x117 * (x0 * x334 + x0 * (x334 + x671 * x674) + x337))
result[2, 0, 5] = numpy.sum(x108 * (x0 * x342 + x0 * (x338 * x527 + x342) + x346))
result[2, 0, 6] = numpy.sum(x90 * (x0 * x348 + x0 * (x348 + x669 * x675) + x350))
result[2, 0, 7] = numpy.sum(x117 * (x0 * x352 + x0 * (x352 + x671 * x677) + x354))
result[2, 0, 8] = numpy.sum(x117 * (x0 * x357 + x0 * (x0 * x678 + x357) + x359))
result[2, 0, 9] = numpy.sum(x90 * (x0 * x363 + x0 * (x360 * x530 + x363) + x367))
result[2, 0, 10] = numpy.sum(x77 * (x0 * x368 + x0 * (x147 * x669 + x368) + x371))
result[2, 0, 11] = numpy.sum(x90 * (x0 * x372 + x0 * (x150 * x671 + x372) + x374))
result[2, 0, 12] = numpy.sum(x108 * (x0 * x375 + x0 * (x0 * x679 + x375) + x378))
result[2, 0, 13] = numpy.sum(x90 * (x0 * x379 + x0 * (x0 * x680 + x379) + x381))
result[2, 0, 14] = numpy.sum(x77 * (x0 * x382 + x0 * (x382 + x65 * x681) + x384))
result[2, 1, 0] = numpy.sum(x185 * (x0 * x683 + x20 * x296 + x436))
result[2, 1, 1] = numpy.sum(x202 * (x0 * x684 + x20 * x311 + x440))
result[2, 1, 2] = numpy.sum(x202 * (x0 * x686 + x20 * x320 + x444))
result[2, 1, 3] = numpy.sum(x117 * (x0 * x687 + x20 * x328 + x448))
result[2, 1, 4] = numpy.sum(x230 * (x0 * x688 + x20 * x334 + x452))
result[2, 1, 5] = numpy.sum(x117 * (x0 * x689 + x20 * x342 + x456))
result[2, 1, 6] = numpy.sum(x202 * (x0 * x690 + x20 * x348 + x460))
result[2, 1, 7] = numpy.sum(x230 * (x0 * x691 + x20 * x352 + x464))
result[2, 1, 8] = numpy.sum(x230 * (x0 * x692 + x20 * x357 + x468))
result[2, 1, 9] = numpy.sum(x202 * (x0 * x693 + x20 * x363 + x472))
result[2, 1, 10] = numpy.sum(x185 * (x0 * x694 + x20 * x368 + x474))
result[2, 1, 11] = numpy.sum(x202 * (x0 * x695 + x20 * x372 + x477))
result[2, 1, 12] = numpy.sum(x117 * (x0 * x696 + x20 * x375 + x479))
result[2, 1, 13] = numpy.sum(x202 * (x0 * x697 + x20 * x379 + x481))
result[2, 1, 14] = numpy.sum(x185 * (x0 * x698 + x20 * x382 + x483))
result[2, 2, 0] = numpy.sum(x185 * (x0 * x701 + x491))
result[2, 2, 1] = numpy.sum(x202 * (x0 * x703 + x493))
result[2, 2, 2] = numpy.sum(x202 * (x0 * x706 + x497))
result[2, 2, 3] = numpy.sum(x117 * (x0 * x708 + x499))
result[2, 2, 4] = numpy.sum(x230 * (x0 * x710 + x502))
result[2, 2, 5] = numpy.sum(x117 * (x0 * x712 + x506))
result[2, 2, 6] = numpy.sum(x202 * (x0 * x714 + x508))
result[2, 2, 7] = numpy.sum(x230 * (x0 * x716 + x510))
result[2, 2, 8] = numpy.sum(x230 * (x0 * x718 + x512))
result[2, 2, 9] = numpy.sum(x202 * (x0 * x720 + x516))
result[2, 2, 10] = numpy.sum(x185 * (x0 * x722 + x517))
result[2, 2, 11] = numpy.sum(x202 * (x0 * x724 + x518))
result[2, 2, 12] = numpy.sum(x117 * (x0 * x726 + x519))
result[2, 2, 13] = numpy.sum(x202 * (x0 * x728 + x520))
result[2, 2, 14] = numpy.sum(x185 * (x0 * x730 + x521))
result[2, 3, 0] = numpy.sum(x77 * (x20 * x571 + x20 * x683 + x616))
result[2, 3, 1] = numpy.sum(x90 * (x20 * x574 + x20 * x684 + x619))
result[2, 3, 2] = numpy.sum(x90 * (x20 * x576 + x20 * x686 + x621))
result[2, 3, 3] = numpy.sum(x108 * (x20 * x578 + x20 * x687 + x623))
result[2, 3, 4] = numpy.sum(x117 * (x20 * x581 + x20 * x688 + x626))
result[2, 3, 5] = numpy.sum(x108 * (x20 * x583 + x20 * x689 + x628))
result[2, 3, 6] = numpy.sum(x90 * (x20 * x586 + x20 * x690 + x630))
result[2, 3, 7] = numpy.sum(x117 * (x20 * x589 + x20 * x691 + x632))
result[2, 3, 8] = numpy.sum(x117 * (x20 * x591 + x20 * x692 + x635))
result[2, 3, 9] = numpy.sum(x90 * (x20 * x593 + x20 * x693 + x637))
result[2, 3, 10] = numpy.sum(x77 * (x20 * x595 + x20 * x694 + x638))
result[2, 3, 11] = numpy.sum(x90 * (x20 * x597 + x20 * x695 + x639))
result[2, 3, 12] = numpy.sum(x108 * (x20 * x599 + x20 * x696 + x640))
result[2, 3, 13] = numpy.sum(x90 * (x20 * x601 + x20 * x697 + x642))
result[2, 3, 14] = numpy.sum(x77 * (x20 * x603 + x20 * x698 + x643))
result[2, 4, 0] = numpy.sum(x185 * (x20 * x701 + x645))
result[2, 4, 1] = numpy.sum(x202 * (x20 * x703 + x647))
result[2, 4, 2] = numpy.sum(x202 * (x20 * x706 + x649))
result[2, 4, 3] = numpy.sum(x117 * (x20 * x708 + x651))
result[2, 4, 4] = numpy.sum(x230 * (x20 * x710 + x653))
result[2, 4, 5] = numpy.sum(x117 * (x20 * x712 + x655))
result[2, 4, 6] = numpy.sum(x202 * (x20 * x714 + x657))
result[2, 4, 7] = numpy.sum(x230 * (x20 * x716 + x659))
result[2, 4, 8] = numpy.sum(x230 * (x20 * x718 + x661))
result[2, 4, 9] = numpy.sum(x202 * (x20 * x720 + x663))
result[2, 4, 10] = numpy.sum(x185 * (x20 * x722 + x664))
result[2, 4, 11] = numpy.sum(x202 * (x20 * x724 + x665))
result[2, 4, 12] = numpy.sum(x117 * (x20 * x726 + x666))
result[2, 4, 13] = numpy.sum(x202 * (x20 * x728 + x667))
result[2, 4, 14] = numpy.sum(x185 * (x20 * x730 + x668))
result[2, 5, 0] = numpy.sum(x77 * (x21 * x699 + x21 * x701 + x522 * x731))
result[2, 5, 1] = numpy.sum(x90 * (x21 * x702 + x21 * x703 + x670 * x731))
result[2, 5, 2] = numpy.sum(x90 * (x21 * x704 + x21 * x706 + x524 * x732))
result[2, 5, 3] = numpy.sum(x108 * (x21 * x707 + x21 * x708 + x673 * x731))
result[2, 5, 4] = numpy.sum(x117 * (x21 * x709 + x21 * x710 + x674 * x732))
result[2, 5, 5] = numpy.sum(x108 * (x195 * x733 + x21 * x711 + x21 * x712))
result[2, 5, 6] = numpy.sum(x90 * (x21 * x713 + x21 * x714 + x675 * x731))
result[2, 5, 7] = numpy.sum(x117 * (x21 * x715 + x21 * x716 + x677 * x732))
result[2, 5, 8] = numpy.sum(x117 * (x21 * x717 + x21 * x718 + x333 * x733))
result[2, 5, 9] = numpy.sum(x90 * (x192 * x734 + x21 * x719 + x21 * x720))
result[2, 5, 10] = numpy.sum(x77 * (x147 * x731 + x21 * x721 + x21 * x722))
result[2, 5, 11] = numpy.sum(x90 * (x150 * x732 + x21 * x723 + x21 * x724))
result[2, 5, 12] = numpy.sum(x108 * (x131 * x733 + x21 * x725 + x21 * x726))
result[2, 5, 13] = numpy.sum(x90 * (x109 * x734 + x21 * x727 + x21 * x728))
result[2, 5, 14] = numpy.sum(
x77 * (x15 * (3.0 * x514 + x734 * x91) + x21 * x729 + x21 * x730)
)
return result
[docs]
def int3c2e3d_sph_130(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pf|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 10, 1), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - A[0]
x5 = 0.5 / (ax + bx)
x6 = -x3 - C[0]
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = -x2 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = cx + x1
x12 = cx / x11
x13 = x1 * x12 * (x10**2 + x6**2 + x8**2)
x14 = boys(1, x13)
x15 = 17.49341832762486
x16 = A[1] - B[1]
x17 = A[2] - B[2]
x18 = numpy.exp(-ax * bx * x2 * (x0**2 + x16**2 + x17**2))
x19 = 2.0 * x11 ** (-1.5) * x15 * x18 * x2
x20 = x14 * x19
x21 = cx ** (-1.0)
x22 = x11 ** (-0.5)
x23 = boys(0, x13)
x24 = 2.0 * x15 * x18 * x2 * x21 * x22 * x23 - x20
x25 = x24 * x5
x26 = -2.0 * x15 * x18 * x2 * x21 * x22 * x23 * x4 + x20 * x6
x27 = -x26
x28 = boys(2, x13)
x29 = x19 * x28
x30 = -2.0 * x14 * x15 * x18 * x2 * x21 * x22 * x4 + x29 * x6
x31 = -x30
x32 = x12 * x31
x33 = x32 * x6
x34 = x25 + x27 * x4 - x33
x35 = 2.0 * x5
x36 = x5 * (2.0 * x14 * x15 * x18 * x2 * x21 * x22 - x29)
x37 = boys(3, x13)
x38 = x19 * x37
x39 = 2.0 * x15 * x18 * x2 * x21 * x22 * x28 * x4 - x38 * x6
x40 = x12 * x39
x41 = x31 * x4 + x36 - x40 * x6
x42 = x12 * x41
x43 = x34 * x4 - x35 * (x26 + x32) - x42 * x6
x44 = x0 * x34 + x43
x45 = -x24 * x5
x46 = x5 * (2.0 * x15 * x18 * x2 * x21 * x22 * x28 - x38)
x47 = x19 * boys(4, x13)
x48 = x12 * x6
x49 = da * db * dc
x50 = 0.2581988897471611 * x49
x51 = -x7 - A[1]
x52 = -2.0 * x14 * x15 * x18 * x2 * x21 * x22 * x51 + x29 * x8
x53 = -x52
x54 = x12 * x53
x55 = -2.0 * x15 * x18 * x2 * x21 * x22 * x23 * x51 + x20 * x8
x56 = -x5 * (x54 + x55)
x57 = -x55
x58 = x54 * x6
x59 = -x4 * x57 + x58
x60 = -x59
x61 = 2.0 * x15 * x18 * x2 * x21 * x22 * x28 * x51 - x38 * x8
x62 = x12 * x61
x63 = x4 * x53 - x6 * x62
x64 = x12 * x63
x65 = x4 * x60 + x56 - x6 * x64
x66 = x16 * x34 + x65
x67 = x4 * x57 - x58
x68 = x16 * x27 + x67
x69 = -x5 * (x52 + x62)
x70 = 2.0 * x15 * x18 * x2 * x21 * x22 * x37 * x51 - x47 * x8
x71 = (
-x35 * (x59 + x64)
+ x4 * x65
- x48 * (x4 * x63 - x48 * (x4 * x61 - x48 * x70) + x69)
)
x72 = 0.5773502691896258 * x49
x73 = -x9 - A[2]
x74 = x10 * x29 - 2.0 * x14 * x15 * x18 * x2 * x21 * x22 * x73
x75 = -x74
x76 = x12 * x75
x77 = x10 * x20 - 2.0 * x15 * x18 * x2 * x21 * x22 * x23 * x73
x78 = -x5 * (x76 + x77)
x79 = -x77
x80 = x6 * x76
x81 = -x4 * x79 + x80
x82 = -x81
x83 = -x10 * x38 + 2.0 * x15 * x18 * x2 * x21 * x22 * x28 * x73
x84 = x12 * x83
x85 = x4 * x75 - x6 * x84
x86 = x12 * x85
x87 = x4 * x82 - x6 * x86 + x78
x88 = x17 * x34 + x87
x89 = x4 * x79 - x80
x90 = x17 * x27 + x89
x91 = -x5 * (x74 + x84)
x92 = -x10 * x47 + 2.0 * x15 * x18 * x2 * x21 * x22 * x37 * x73
x93 = (
-x35 * (x81 + x86)
+ x4 * x87
- x48 * (x4 * x85 - x48 * (x4 * x83 - x48 * x92) + x91)
)
x94 = x54 * x8
x95 = x25 + x51 * x57 - x94
x96 = x36 + x51 * x53 - x62 * x8
x97 = x12 * x96
x98 = x6 * x97
x99 = x16 * x60 + x4 * x95 - x98
x100 = x16 * x68 + x99
x101 = x5 * (-x45 + x51 * x57 - x94 - x97)
x102 = x4 * x95 - x98
x103 = x12 * x8
x104 = -x103 * x70 + x46 + x51 * x61
x105 = x101 + x102 * x4 + x16 * x65 + x48 * (x104 * x48 - x4 * x96)
x106 = x76 * x8
x107 = x106 - x51 * x79
x108 = -x107
x109 = x51 * x75 - x8 * x84
x110 = x109 * x12
x111 = x110 * x6
x112 = x108 * x4 - x111
x113 = x112 + x17 * x60
x114 = x113 + x16 * x90
x115 = -x5 * (x107 + x110)
x116 = x108 * x4 - x111
x117 = -x103 * x92 + x51 * x83
x118 = x115 + x116 * x4 - x48 * (x109 * x4 - x117 * x48)
x119 = x118 + x17 * x65
x120 = x10 * x76
x121 = -x120 + x25 + x73 * x79
x122 = -x10 * x84 + x36 + x73 * x75
x123 = x12 * x122
x124 = x123 * x6
x125 = x121 * x4 - x124 + x17 * x82
x126 = x125 + x17 * x90
x127 = x5 * (-x120 - x123 - x45 + x73 * x79)
x128 = x121 * x4 - x124
x129 = x10 * x12
x130 = -x129 * x92 + x46 + x73 * x83
x131 = x127 + x128 * x4 + x17 * x87 - x48 * (x122 * x4 - x130 * x48)
x132 = x51 * x95 + 2.0 * x56 - x8 * x97
x133 = -x103 * x104 + x51 * x96 + 2.0 * x69
x134 = x102 * x16 + x132 * x4 - x133 * x48 + x16 * x99
x135 = x108 * x51 - x110 * x8 + x78
x136 = -x103 * x117 + x109 * x51 + x91
x137 = x135 * x4 - x136 * x48
x138 = x102 * x17 + x113 * x16 + x137
x139 = x123 * x8
x140 = x121 * x51 - x139
x141 = -x103 * x130 + x122 * x51
x142 = x116 * x17 + x140 * x4 - x141 * x48
x143 = x113 * x17 + x142
x144 = -x10 * x123 + x121 * x73 + 2.0 * x78
x145 = x122 * x73 - x129 * x130 + 2.0 * x91
x146 = x125 * x17 + x128 * x17 + x144 * x4 - x145 * x48
x147 = x0 * x60 + x65
x148 = x16 * x57 + x95
x149 = -x106 + x51 * x79
x150 = x149 + x17 * x57
x151 = x132 + x16 * x95
x152 = x148 * x16 + x151
x153 = x135 + x17 * x95
x154 = x150 * x16 + x153
x155 = x108 * x17 + x121 * x51 - x139
x156 = x150 * x17 + x155
x157 = -x103 * x136 + 2.0 * x115 + x135 * x51
x158 = -x103 * x141 + x127 + x135 * x17 + x140 * x51
x159 = -x103 * x145 + x140 * x17 + x144 * x51 + x155 * x17
x160 = x0 * x82 + x87
x161 = x112 + x16 * x82
x162 = x149 + x16 * x79
x163 = x121 + x17 * x79
x164 = x108 * x16 + x135
x165 = x16 * x162 + x164
x166 = x155 + x16 * x163
x167 = x121 * x17 + x144
x168 = x163 * x17 + x167
# 30 item(s)
result[0, 0, 0] = numpy.sum(
x50
* (
x0 * x43
+ x0 * x44
+ x0 * (x0 * (x0 * x27 + x34) + x44)
+ x4 * x43
+ x48
* (
x35 * (x30 + x40)
- x4 * x41
+ x48
* (
x39 * x4
+ x46
- x48 * (2.0 * x15 * x18 * x2 * x21 * x22 * x37 * x4 - x47 * x6)
)
)
- 3.0 * x5 * (-x27 * x4 + x33 + x42 + x45)
)
)
result[0, 1, 0] = numpy.sum(
x72 * (x0 * x66 + x0 * (x0 * x68 + x66) + x16 * x43 + x71)
)
result[0, 2, 0] = numpy.sum(
x72 * (x0 * x88 + x0 * (x0 * x90 + x88) + x17 * x43 + x93)
)
result[0, 3, 0] = numpy.sum(x72 * (x0 * x100 + x105 + x16 * x66))
result[0, 4, 0] = numpy.sum(x49 * (x0 * x114 + x119 + x16 * x88))
result[0, 5, 0] = numpy.sum(x72 * (x0 * x126 + x131 + x17 * x88))
result[0, 6, 0] = numpy.sum(x50 * (x100 * x16 + x134))
result[0, 7, 0] = numpy.sum(x72 * (x114 * x16 + x138))
result[0, 8, 0] = numpy.sum(x72 * (x126 * x16 + x143))
result[0, 9, 0] = numpy.sum(x50 * (x126 * x17 + x146))
result[1, 0, 0] = numpy.sum(
x50 * (x0 * x147 + x0 * x65 + x0 * (x0 * (x0 * x57 + x67) + x147) + x71)
)
result[1, 1, 0] = numpy.sum(x72 * (x0 * x99 + x0 * (x0 * x148 + x99) + x105))
result[1, 2, 0] = numpy.sum(x72 * (x0 * x113 + x0 * (x0 * x150 + x113) + x119))
result[1, 3, 0] = numpy.sum(x72 * (x0 * x152 + x134))
result[1, 4, 0] = numpy.sum(x49 * (x0 * x154 + x138))
result[1, 5, 0] = numpy.sum(x72 * (x0 * x156 + x143))
result[1, 6, 0] = numpy.sum(
x50
* (3.0 * x101 - x103 * x133 + x132 * x16 + x132 * x51 + x151 * x16 + x152 * x16)
)
result[1, 7, 0] = numpy.sum(x72 * (x132 * x17 + x153 * x16 + x154 * x16 + x157))
result[1, 8, 0] = numpy.sum(x72 * (x153 * x17 + x156 * x16 + x158))
result[1, 9, 0] = numpy.sum(x50 * (x156 * x17 + x159))
result[2, 0, 0] = numpy.sum(
x50 * (x0 * x160 + x0 * x87 + x0 * (x0 * (x0 * x79 + x89) + x160) + x93)
)
result[2, 1, 0] = numpy.sum(
x72 * (x0 * x161 + x0 * (x0 * x162 + x161) + x118 + x16 * x87)
)
result[2, 2, 0] = numpy.sum(x72 * (x0 * x125 + x0 * (x0 * x163 + x125) + x131))
result[2, 3, 0] = numpy.sum(x72 * (x0 * x165 + x116 * x16 + x137 + x16 * x161))
result[2, 4, 0] = numpy.sum(x49 * (x0 * x166 + x125 * x16 + x142))
result[2, 5, 0] = numpy.sum(x72 * (x0 * x168 + x146))
result[2, 6, 0] = numpy.sum(x50 * (x135 * x16 + x157 + x16 * x164 + x16 * x165))
result[2, 7, 0] = numpy.sum(x72 * (x155 * x16 + x158 + x16 * x166))
result[2, 8, 0] = numpy.sum(x72 * (x159 + x16 * x168))
result[2, 9, 0] = numpy.sum(
x50
* (3.0 * x127 - x129 * x145 + x144 * x17 + x144 * x73 + x167 * x17 + x168 * x17)
)
return result
[docs]
def int3c2e3d_sph_131(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pf|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 10, 3), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = -x3 - A[0]
x6 = 0.5 / (ax + bx)
x7 = -x2 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = -x2 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = cx + x1
x12 = x11 ** (-1.0)
x13 = cx * x12
x14 = x1 * x13 * (x10**2 + x4**2 + x8**2)
x15 = boys(2, x14)
x16 = 17.49341832762486
x17 = A[1] - B[1]
x18 = A[2] - B[2]
x19 = numpy.exp(-ax * bx * x2 * (x0**2 + x17**2 + x18**2))
x20 = x16 * x19 * x2
x21 = 2.0 * x11 ** (-1.5) * x20
x22 = x15 * x21
x23 = cx ** (-1.0)
x24 = x11 ** (-0.5)
x25 = boys(1, x14)
x26 = 2.0 * x16 * x19 * x2 * x23 * x24 * x25 - x22
x27 = x26 * x6
x28 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x5 + x22 * x4
x29 = -x28
x30 = boys(3, x14)
x31 = x21 * x30
x32 = -2.0 * x15 * x16 * x19 * x2 * x23 * x24 * x5 + x31 * x4
x33 = -x32
x34 = x13 * x33
x35 = x34 * x4
x36 = x27 + x29 * x5 - x35
x37 = 2.0 * x6
x38 = x6 * (2.0 * x15 * x16 * x19 * x2 * x23 * x24 - x31)
x39 = boys(4, x14)
x40 = x21 * x39
x41 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x5 - x4 * x40
x42 = x13 * x41
x43 = x33 * x5 + x38 - x4 * x42
x44 = x13 * x43
x45 = x36 * x5 - x37 * (x28 + x34) - x4 * x44
x46 = x36 * x6
x47 = x1 * x12
x48 = x47 * (x4 * x45 + 3.0 * x46)
x49 = x29 * x6
x50 = x47 * (x36 * x4 + 2.0 * x49)
x51 = x0 * x50 + x48
x52 = x20 * x23 * x24 * x25 * x37
x53 = x47 * (x29 * x4 + x52)
x54 = -x26 * x6
x55 = x6 * (2.0 * x16 * x19 * x2 * x23 * x24 * x30 - x40)
x56 = x21 * boys(5, x14)
x57 = x13 * x4
x58 = (
x45 * x5
+ x57
* (
x37 * (x32 + x42)
- x43 * x5
+ x57
* (
x41 * x5
+ x55
- x57 * (2.0 * x16 * x19 * x2 * x23 * x24 * x39 * x5 - x4 * x56)
)
)
- 3.0 * x6 * (-x29 * x5 + x35 + x44 + x54)
)
x59 = x45 * x6
x60 = da * db * dc
x61 = 0.2581988897471611 * x60
x62 = x47 * x8
x63 = x45 * x62
x64 = x36 * x62
x65 = x0 * x64 + x63
x66 = x0 * x29
x67 = x10 * x47
x68 = x45 * x67
x69 = x36 * x67
x70 = x0 * x69 + x68
x71 = -x7 - A[1]
x72 = -2.0 * x15 * x16 * x19 * x2 * x23 * x24 * x71 + x31 * x8
x73 = -x72
x74 = x13 * x73
x75 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x71 + x22 * x8
x76 = -x6 * (x74 + x75)
x77 = -x75
x78 = x4 * x74 - x5 * x77
x79 = -x78
x80 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x71 - x40 * x8
x81 = x13 * x80
x82 = -x4 * x81 + x5 * x73
x83 = x13 * x82
x84 = -x4 * x83 + x5 * x79 + x76
x85 = x6 * x79
x86 = 2.0 * x85
x87 = x47 * (x4 * x84 + x86)
x88 = x17 * x50 + x87
x89 = x6 * x77
x90 = x47 * (x4 * x79 + x89)
x91 = x17 * x53 + x90
x92 = -x6 * (x72 + x81)
x93 = 2.0 * x16 * x19 * x2 * x23 * x24 * x39 * x71 - x56 * x8
x94 = (
-x37 * (x78 + x83)
+ x5 * x84
- x57 * (x5 * x82 - x57 * (x5 * x80 - x57 * x93) + x92)
)
x95 = x6 * x84
x96 = x47 * (x4 * x94 + 3.0 * x95)
x97 = 0.5773502691896258 * x60
x98 = x47 * (x46 + x8 * x84)
x99 = x17 * x64 + x98
x100 = x47 * (x49 + x79 * x8)
x101 = x17 * x29
x102 = x100 + x101 * x62
x103 = x47 * (x59 + x8 * x94)
x104 = x67 * x84
x105 = x104 + x17 * x69
x106 = x67 * x79
x107 = x101 * x67 + x106
x108 = x67 * x94
x109 = -x9 - A[2]
x110 = x10 * x31 - 2.0 * x109 * x15 * x16 * x19 * x2 * x23 * x24
x111 = -x110
x112 = x111 * x13
x113 = x10 * x22 - 2.0 * x109 * x16 * x19 * x2 * x23 * x24 * x25
x114 = -x6 * (x112 + x113)
x115 = -x113
x116 = x112 * x4 - x115 * x5
x117 = -x116
x118 = -x10 * x40 + 2.0 * x109 * x16 * x19 * x2 * x23 * x24 * x30
x119 = x118 * x13
x120 = x111 * x5 - x119 * x4
x121 = x120 * x13
x122 = x114 + x117 * x5 - x121 * x4
x123 = x117 * x6
x124 = 2.0 * x123
x125 = x47 * (x122 * x4 + x124)
x126 = x125 + x18 * x50
x127 = x115 * x6
x128 = x47 * (x117 * x4 + x127)
x129 = x128 + x18 * x53
x130 = -x6 * (x110 + x119)
x131 = -x10 * x56 + 2.0 * x109 * x16 * x19 * x2 * x23 * x24 * x39
x132 = (
x122 * x5
- x37 * (x116 + x121)
- x57 * (x120 * x5 + x130 - x57 * (x118 * x5 - x131 * x57))
)
x133 = x122 * x6
x134 = x47 * (x132 * x4 + 3.0 * x133)
x135 = x122 * x62
x136 = x135 + x18 * x64
x137 = x117 * x62
x138 = x18 * x29
x139 = x137 + x138 * x62
x140 = x132 * x62
x141 = x47 * (x10 * x122 + x46)
x142 = x141 + x18 * x69
x143 = x47 * (x10 * x117 + x49)
x144 = x138 * x67 + x143
x145 = x47 * (x10 * x132 + x59)
x146 = x74 * x8
x147 = -x146 + x27 + x71 * x77
x148 = x147 * x6
x149 = x38 + x71 * x73 - x8 * x81
x150 = x13 * x149
x151 = x147 * x5 - x150 * x4
x152 = x47 * (x148 + x151 * x4)
x153 = x152 + x17 * x90
x154 = x153 + x17 * x91
x155 = x6 * (-x146 - x150 - x54 + x71 * x77)
x156 = x13 * x8
x157 = -x156 * x93 + x55 + x71 * x80
x158 = x151 * x5 + x155 - x57 * (x149 * x5 - x157 * x57)
x159 = x151 * x6
x160 = x17 * x87 + x47 * (x158 * x4 + 2.0 * x159)
x161 = x47 * (x151 * x8 + x86)
x162 = x100 * x17 + x161
x163 = x102 * x17 + x162
x164 = x17 * x98 + x47 * (x158 * x8 + 2.0 * x95)
x165 = x151 * x67
x166 = x106 * x17 + x165
x167 = x107 * x17 + x166
x168 = x104 * x17 + x158 * x67
x169 = x112 * x8 - x115 * x71
x170 = -x169
x171 = x170 * x6
x172 = x111 * x71 - x119 * x8
x173 = x13 * x172
x174 = x170 * x5 - x173 * x4
x175 = x47 * (x171 + x174 * x4)
x176 = x175 + x18 * x90
x177 = x129 * x17 + x176
x178 = -x6 * (x169 + x173)
x179 = x118 * x71 - x131 * x156
x180 = x174 * x5 + x178 - x57 * (x172 * x5 - x179 * x57)
x181 = x174 * x37
x182 = x47 * (x180 * x4 + x181)
x183 = x18 * x87 + x182
x184 = x47 * (x123 + x174 * x8)
x185 = x100 * x18 + x184
x186 = x139 * x17 + x185
x187 = x47 * (x133 + x180 * x8)
x188 = x18 * x98 + x187
x189 = x47 * (x10 * x174 + x85)
x190 = x106 * x18 + x189
x191 = x144 * x17 + x190
x192 = x47 * (x10 * x180 + x95)
x193 = x104 * x18 + x192
x194 = x10 * x112
x195 = x109 * x115 - x194 + x27
x196 = x195 * x6
x197 = -x10 * x119 + x109 * x111 + x38
x198 = x13 * x197
x199 = x195 * x5 - x198 * x4
x200 = x47 * (x196 + x199 * x4)
x201 = x128 * x18 + x200
x202 = x129 * x18 + x201
x203 = x6 * (x109 * x115 - x194 - x198 - x54)
x204 = x10 * x13
x205 = x109 * x118 - x131 * x204 + x55
x206 = x199 * x5 + x203 - x57 * (x197 * x5 - x205 * x57)
x207 = x199 * x6
x208 = x125 * x18 + x47 * (x206 * x4 + 2.0 * x207)
x209 = x199 * x62
x210 = x137 * x18 + x209
x211 = x139 * x18 + x210
x212 = x135 * x18 + x206 * x62
x213 = x47 * (x10 * x199 + x124)
x214 = x143 * x18 + x213
x215 = x144 * x18 + x214
x216 = x141 * x18 + x47 * (x10 * x206 + 2.0 * x133)
x217 = x147 * x71 - x150 * x8 + 2.0 * x76
x218 = x217 * x6
x219 = x149 * x71 - x156 * x157 + 2.0 * x92
x220 = x217 * x5 - x219 * x57
x221 = x152 * x17 + x153 * x17 + x47 * (x218 + x220 * x4)
x222 = x161 * x17 + x162 * x17 + x47 * (3.0 * x159 + x220 * x8)
x223 = x165 * x17 + x166 * x17 + x220 * x67
x224 = x114 + x170 * x71 - x173 * x8
x225 = x224 * x6
x226 = x130 - x156 * x179 + x172 * x71
x227 = x224 * x5 - x226 * x57
x228 = x47 * (x225 + x227 * x4)
x229 = x152 * x18 + x17 * x176 + x228
x230 = x47 * (x181 + x227 * x8)
x231 = x161 * x18 + x17 * x185 + x230
x232 = x47 * (x10 * x227 + x159)
x233 = x165 * x18 + x17 * x190 + x232
x234 = x195 * x71 - x198 * x8
x235 = x234 * x6
x236 = -x156 * x205 + x197 * x71
x237 = x234 * x5 - x236 * x57
x238 = x175 * x18 + x47 * (x235 + x237 * x4)
x239 = x176 * x18 + x238
x240 = x18 * x184 + x47 * (x207 + x237 * x8)
x241 = x18 * x185 + x240
x242 = x18 * x189 + x47 * (x10 * x237 + x181)
x243 = x18 * x190 + x242
x244 = -x10 * x198 + x109 * x195 + 2.0 * x114
x245 = x244 * x6
x246 = x109 * x197 + 2.0 * x130 - x204 * x205
x247 = x244 * x5 - x246 * x57
x248 = x18 * x200 + x18 * x201 + x47 * (x245 + x247 * x4)
x249 = x18 * x209 + x18 * x210 + x247 * x62
x250 = x18 * x213 + x18 * x214 + x47 * (x10 * x247 + 3.0 * x207)
x251 = x0 * x90 + x87
x252 = x4 * x47
x253 = x0 * x77
x254 = x0 * x100 + x98
x255 = x47 * (x52 + x77 * x8)
x256 = x0 * x106 + x104
x257 = x147 * x252
x258 = x17 * x77
x259 = x252 * x258 + x257
x260 = x47 * (x147 * x8 + 2.0 * x89)
x261 = x17 * x255 + x260
x262 = x147 * x67
x263 = x258 * x67 + x262
x264 = x170 * x252
x265 = x18 * x77
x266 = x252 * x265 + x264
x267 = x47 * (x127 + x170 * x8)
x268 = x18 * x255 + x267
x269 = x47 * (x10 * x170 + x89)
x270 = x265 * x67 + x269
x271 = x217 * x252
x272 = x17 * x257 + x271
x273 = x17 * x259 + x272
x274 = x47 * (3.0 * x148 + x217 * x8)
x275 = x17 * x260 + x274
x276 = x17 * x261 + x275
x277 = x217 * x67
x278 = x17 * x262 + x277
x279 = x17 * x263 + x278
x280 = x224 * x252
x281 = x18 * x257 + x280
x282 = x17 * x266 + x281
x283 = 2.0 * x171
x284 = x47 * (x224 * x8 + x283)
x285 = x18 * x260 + x284
x286 = x17 * x268 + x285
x287 = x47 * (x10 * x224 + x148)
x288 = x18 * x262 + x287
x289 = x17 * x270 + x288
x290 = x234 * x252
x291 = x18 * x264 + x290
x292 = x18 * x266 + x291
x293 = x47 * (x196 + x234 * x8)
x294 = x18 * x267 + x293
x295 = x18 * x268 + x294
x296 = x47 * (x10 * x234 + x283)
x297 = x18 * x269 + x296
x298 = x18 * x270 + x297
x299 = 3.0 * x155 - x156 * x219 + x217 * x71
x300 = -x156 * x226 + 2.0 * x178 + x224 * x71
x301 = x252 * x300
x302 = x47 * (3.0 * x225 + x300 * x8)
x303 = x47 * (x10 * x300 + x218)
x304 = -x156 * x236 + x203 + x234 * x71
x305 = x18 * x280 + x252 * x304
x306 = x18 * x284 + x47 * (2.0 * x235 + x304 * x8)
x307 = x18 * x287 + x47 * (x10 * x304 + 2.0 * x225)
x308 = -x156 * x246 + x244 * x71
x309 = x18 * x290 + x18 * x291 + x252 * x308
x310 = x18 * x293 + x18 * x294 + x47 * (x245 + x308 * x8)
x311 = x18 * x296 + x18 * x297 + x47 * (x10 * x308 + 3.0 * x235)
x312 = x0 * x128 + x125
x313 = x0 * x115
x314 = x0 * x137 + x135
x315 = x0 * x143 + x141
x316 = x47 * (x10 * x115 + x52)
x317 = x128 * x17 + x175
x318 = x115 * x17
x319 = x252 * x318 + x264
x320 = x137 * x17 + x184
x321 = x267 + x318 * x62
x322 = x143 * x17 + x189
x323 = x17 * x316 + x269
x324 = x195 * x252
x325 = x115 * x18
x326 = x252 * x325 + x324
x327 = x195 * x62
x328 = x325 * x62 + x327
x329 = x47 * (x10 * x195 + 2.0 * x127)
x330 = x18 * x316 + x329
x331 = x17 * x264 + x280
x332 = x17 * x319 + x331
x333 = x17 * x267 + x284
x334 = x17 * x321 + x333
x335 = x17 * x269 + x287
x336 = x17 * x323 + x335
x337 = x17 * x326 + x291
x338 = x17 * x328 + x294
x339 = x17 * x330 + x297
x340 = x244 * x252
x341 = x18 * x324 + x340
x342 = x18 * x326 + x341
x343 = x244 * x62
x344 = x18 * x327 + x343
x345 = x18 * x328 + x344
x346 = x47 * (x10 * x244 + 3.0 * x196)
x347 = x18 * x329 + x346
x348 = x18 * x330 + x347
x349 = x109 * x244 + 3.0 * x203 - x204 * x246
# 90 item(s)
result[0, 0, 0] = numpy.sum(
x61
* (
x0 * x48
+ x0 * x51
+ x0 * (x0 * (x0 * x53 + x50) + x51)
+ x47 * (x4 * x58 + 4.0 * x59)
)
)
result[0, 0, 1] = numpy.sum(
x61 * (x0 * x63 + x0 * x65 + x0 * (x0 * (x62 * x66 + x64) + x65) + x58 * x62)
)
result[0, 0, 2] = numpy.sum(
x61 * (x0 * x68 + x0 * x70 + x0 * (x0 * (x66 * x67 + x69) + x70) + x58 * x67)
)
result[0, 1, 0] = numpy.sum(
x97 * (x0 * x88 + x0 * (x0 * x91 + x88) + x17 * x48 + x96)
)
result[0, 1, 1] = numpy.sum(
x97 * (x0 * x99 + x0 * (x0 * x102 + x99) + x103 + x17 * x63)
)
result[0, 1, 2] = numpy.sum(
x97 * (x0 * x105 + x0 * (x0 * x107 + x105) + x108 + x17 * x68)
)
result[0, 2, 0] = numpy.sum(
x97 * (x0 * x126 + x0 * (x0 * x129 + x126) + x134 + x18 * x48)
)
result[0, 2, 1] = numpy.sum(
x97 * (x0 * x136 + x0 * (x0 * x139 + x136) + x140 + x18 * x63)
)
result[0, 2, 2] = numpy.sum(
x97 * (x0 * x142 + x0 * (x0 * x144 + x142) + x145 + x18 * x68)
)
result[0, 3, 0] = numpy.sum(x97 * (x0 * x154 + x160 + x17 * x88))
result[0, 3, 1] = numpy.sum(x97 * (x0 * x163 + x164 + x17 * x99))
result[0, 3, 2] = numpy.sum(x97 * (x0 * x167 + x105 * x17 + x168))
result[0, 4, 0] = numpy.sum(x60 * (x0 * x177 + x126 * x17 + x183))
result[0, 4, 1] = numpy.sum(x60 * (x0 * x186 + x136 * x17 + x188))
result[0, 4, 2] = numpy.sum(x60 * (x0 * x191 + x142 * x17 + x193))
result[0, 5, 0] = numpy.sum(x97 * (x0 * x202 + x126 * x18 + x208))
result[0, 5, 1] = numpy.sum(x97 * (x0 * x211 + x136 * x18 + x212))
result[0, 5, 2] = numpy.sum(x97 * (x0 * x215 + x142 * x18 + x216))
result[0, 6, 0] = numpy.sum(x61 * (x154 * x17 + x221))
result[0, 6, 1] = numpy.sum(x61 * (x163 * x17 + x222))
result[0, 6, 2] = numpy.sum(x61 * (x167 * x17 + x223))
result[0, 7, 0] = numpy.sum(x97 * (x17 * x177 + x229))
result[0, 7, 1] = numpy.sum(x97 * (x17 * x186 + x231))
result[0, 7, 2] = numpy.sum(x97 * (x17 * x191 + x233))
result[0, 8, 0] = numpy.sum(x97 * (x17 * x202 + x239))
result[0, 8, 1] = numpy.sum(x97 * (x17 * x211 + x241))
result[0, 8, 2] = numpy.sum(x97 * (x17 * x215 + x243))
result[0, 9, 0] = numpy.sum(x61 * (x18 * x202 + x248))
result[0, 9, 1] = numpy.sum(x61 * (x18 * x211 + x249))
result[0, 9, 2] = numpy.sum(x61 * (x18 * x215 + x250))
result[1, 0, 0] = numpy.sum(
x61 * (x0 * x251 + x0 * x87 + x0 * (x0 * (x252 * x253 + x90) + x251) + x96)
)
result[1, 0, 1] = numpy.sum(
x61 * (x0 * x254 + x0 * x98 + x0 * (x0 * (x0 * x255 + x100) + x254) + x103)
)
result[1, 0, 2] = numpy.sum(
x61 * (x0 * x104 + x0 * x256 + x0 * (x0 * (x106 + x253 * x67) + x256) + x108)
)
result[1, 1, 0] = numpy.sum(x97 * (x0 * x153 + x0 * (x0 * x259 + x153) + x160))
result[1, 1, 1] = numpy.sum(x97 * (x0 * x162 + x0 * (x0 * x261 + x162) + x164))
result[1, 1, 2] = numpy.sum(x97 * (x0 * x166 + x0 * (x0 * x263 + x166) + x168))
result[1, 2, 0] = numpy.sum(x97 * (x0 * x176 + x0 * (x0 * x266 + x176) + x183))
result[1, 2, 1] = numpy.sum(x97 * (x0 * x185 + x0 * (x0 * x268 + x185) + x188))
result[1, 2, 2] = numpy.sum(x97 * (x0 * x190 + x0 * (x0 * x270 + x190) + x193))
result[1, 3, 0] = numpy.sum(x97 * (x0 * x273 + x221))
result[1, 3, 1] = numpy.sum(x97 * (x0 * x276 + x222))
result[1, 3, 2] = numpy.sum(x97 * (x0 * x279 + x223))
result[1, 4, 0] = numpy.sum(x60 * (x0 * x282 + x229))
result[1, 4, 1] = numpy.sum(x60 * (x0 * x286 + x231))
result[1, 4, 2] = numpy.sum(x60 * (x0 * x289 + x233))
result[1, 5, 0] = numpy.sum(x97 * (x0 * x292 + x239))
result[1, 5, 1] = numpy.sum(x97 * (x0 * x295 + x241))
result[1, 5, 2] = numpy.sum(x97 * (x0 * x298 + x243))
result[1, 6, 0] = numpy.sum(
x61 * (x17 * x271 + x17 * x272 + x17 * x273 + x252 * x299)
)
result[1, 6, 1] = numpy.sum(
x61 * (x17 * x274 + x17 * x275 + x17 * x276 + x47 * (4.0 * x218 + x299 * x8))
)
result[1, 6, 2] = numpy.sum(x61 * (x17 * x277 + x17 * x278 + x17 * x279 + x299 * x67))
result[1, 7, 0] = numpy.sum(x97 * (x17 * x281 + x17 * x282 + x18 * x271 + x301))
result[1, 7, 1] = numpy.sum(x97 * (x17 * x285 + x17 * x286 + x18 * x274 + x302))
result[1, 7, 2] = numpy.sum(x97 * (x17 * x288 + x17 * x289 + x18 * x277 + x303))
result[1, 8, 0] = numpy.sum(x97 * (x17 * x292 + x18 * x281 + x305))
result[1, 8, 1] = numpy.sum(x97 * (x17 * x295 + x18 * x285 + x306))
result[1, 8, 2] = numpy.sum(x97 * (x17 * x298 + x18 * x288 + x307))
result[1, 9, 0] = numpy.sum(x61 * (x18 * x292 + x309))
result[1, 9, 1] = numpy.sum(x61 * (x18 * x295 + x310))
result[1, 9, 2] = numpy.sum(x61 * (x18 * x298 + x311))
result[2, 0, 0] = numpy.sum(
x61 * (x0 * x125 + x0 * x312 + x0 * (x0 * (x128 + x252 * x313) + x312) + x134)
)
result[2, 0, 1] = numpy.sum(
x61 * (x0 * x135 + x0 * x314 + x0 * (x0 * (x137 + x313 * x62) + x314) + x140)
)
result[2, 0, 2] = numpy.sum(
x61 * (x0 * x141 + x0 * x315 + x0 * (x0 * (x0 * x316 + x143) + x315) + x145)
)
result[2, 1, 0] = numpy.sum(
x97 * (x0 * x317 + x0 * (x0 * x319 + x317) + x125 * x17 + x182)
)
result[2, 1, 1] = numpy.sum(
x97 * (x0 * x320 + x0 * (x0 * x321 + x320) + x135 * x17 + x187)
)
result[2, 1, 2] = numpy.sum(
x97 * (x0 * x322 + x0 * (x0 * x323 + x322) + x141 * x17 + x192)
)
result[2, 2, 0] = numpy.sum(x97 * (x0 * x201 + x0 * (x0 * x326 + x201) + x208))
result[2, 2, 1] = numpy.sum(x97 * (x0 * x210 + x0 * (x0 * x328 + x210) + x212))
result[2, 2, 2] = numpy.sum(x97 * (x0 * x214 + x0 * (x0 * x330 + x214) + x216))
result[2, 3, 0] = numpy.sum(x97 * (x0 * x332 + x17 * x175 + x17 * x317 + x228))
result[2, 3, 1] = numpy.sum(x97 * (x0 * x334 + x17 * x184 + x17 * x320 + x230))
result[2, 3, 2] = numpy.sum(x97 * (x0 * x336 + x17 * x189 + x17 * x322 + x232))
result[2, 4, 0] = numpy.sum(x60 * (x0 * x337 + x17 * x201 + x238))
result[2, 4, 1] = numpy.sum(x60 * (x0 * x338 + x17 * x210 + x240))
result[2, 4, 2] = numpy.sum(x60 * (x0 * x339 + x17 * x214 + x242))
result[2, 5, 0] = numpy.sum(x97 * (x0 * x342 + x248))
result[2, 5, 1] = numpy.sum(x97 * (x0 * x345 + x249))
result[2, 5, 2] = numpy.sum(x97 * (x0 * x348 + x250))
result[2, 6, 0] = numpy.sum(x61 * (x17 * x280 + x17 * x331 + x17 * x332 + x301))
result[2, 6, 1] = numpy.sum(x61 * (x17 * x284 + x17 * x333 + x17 * x334 + x302))
result[2, 6, 2] = numpy.sum(x61 * (x17 * x287 + x17 * x335 + x17 * x336 + x303))
result[2, 7, 0] = numpy.sum(x97 * (x17 * x291 + x17 * x337 + x305))
result[2, 7, 1] = numpy.sum(x97 * (x17 * x294 + x17 * x338 + x306))
result[2, 7, 2] = numpy.sum(x97 * (x17 * x297 + x17 * x339 + x307))
result[2, 8, 0] = numpy.sum(x97 * (x17 * x342 + x309))
result[2, 8, 1] = numpy.sum(x97 * (x17 * x345 + x310))
result[2, 8, 2] = numpy.sum(x97 * (x17 * x348 + x311))
result[2, 9, 0] = numpy.sum(
x61 * (x18 * x340 + x18 * x341 + x18 * x342 + x252 * x349)
)
result[2, 9, 1] = numpy.sum(x61 * (x18 * x343 + x18 * x344 + x18 * x345 + x349 * x62))
result[2, 9, 2] = numpy.sum(
x61 * (x18 * x346 + x18 * x347 + x18 * x348 + x47 * (x10 * x349 + 4.0 * x245))
)
return result
[docs]
def int3c2e3d_sph_132(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pf|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 10, 6), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = -x3 - A[0]
x6 = 0.5 / (ax + bx)
x7 = x4**2
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = -x8 - C[1]
x10 = x9**2
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = -x11 - C[2]
x13 = x12**2
x14 = cx + x1
x15 = x14 ** (-1.0)
x16 = cx * x15
x17 = x1 * x16 * (x10 + x13 + x7)
x18 = boys(3, x17)
x19 = x14 ** (-1.5)
x20 = 17.49341832762486
x21 = A[1] - B[1]
x22 = A[2] - B[2]
x23 = numpy.exp(-ax * bx * x2 * (x0**2 + x21**2 + x22**2))
x24 = x2 * x20 * x23
x25 = 2.0 * x19 * x24
x26 = x18 * x25
x27 = cx ** (-1.0)
x28 = x14 ** (-0.5)
x29 = boys(2, x17)
x30 = 2.0 * x2 * x20 * x23 * x27 * x28 * x29 - x26
x31 = x30 * x6
x32 = -2.0 * x2 * x20 * x23 * x27 * x28 * x29 * x5 + x26 * x4
x33 = -x32
x34 = boys(4, x17)
x35 = x25 * x34
x36 = -2.0 * x18 * x2 * x20 * x23 * x27 * x28 * x5 + x35 * x4
x37 = -x36
x38 = x16 * x37
x39 = x38 * x4
x40 = x31 + x33 * x5 - x39
x41 = 2.0 * x6
x42 = x6 * (2.0 * x18 * x2 * x20 * x23 * x27 * x28 - x35)
x43 = boys(5, x17)
x44 = x25 * x43
x45 = 2.0 * x2 * x20 * x23 * x27 * x28 * x34 * x5 - x4 * x44
x46 = x16 * x45
x47 = x37 * x5 - x4 * x46 + x42
x48 = x16 * x47
x49 = -x4 * x48 + x40 * x5 - x41 * (x32 + x38)
x50 = x4 * x49
x51 = x40 * x6
x52 = 3.0 * x51
x53 = x50 + x52
x54 = x1 * x15
x55 = x4 * x54
x56 = x4 * x40
x57 = x33 * x6
x58 = 2.0 * x57
x59 = x56 + x58
x60 = 3.0 * x6
x61 = x54 * x60
x62 = x54 * (x53 * x55 + x59 * x61)
x63 = x33 * x4
x64 = x27 * x29 * x41
x65 = x24 * x28 * x64
x66 = x63 + x65
x67 = x41 * x54
x68 = x54 * (x55 * x59 + x66 * x67)
x69 = x0 * x68 + x62
x70 = x19 * x20 * x23 * x64
x71 = x4 * x70 + x55 * x66
x72 = x0 * x54
x73 = -x30 * x6
x74 = x6 * (2.0 * x2 * x20 * x23 * x27 * x28 * x34 - x44)
x75 = x25 * boys(6, x17)
x76 = x16 * x4
x77 = (
x49 * x5
- x60 * (-x33 * x5 + x39 + x48 + x73)
+ x76
* (
x41 * (x36 + x46)
- x47 * x5
+ x76
* (
x45 * x5
+ x74
- x76 * (2.0 * x2 * x20 * x23 * x27 * x28 * x43 * x5 - x4 * x75)
)
)
)
x78 = x4 * x77
x79 = x49 * x6
x80 = 4.0 * x79
x81 = x54 * x6
x82 = da * db * dc
x83 = 0.06666666666666667 * x82
x84 = 2.23606797749979 * x83
x85 = x54 * x9
x86 = x54 * x85 * (x50 + x52)
x87 = x54 * x85 * (x56 + x58)
x88 = x0 * x87 + x86
x89 = x70 * x9
x90 = x63 * x85 + x89
x91 = 3.872983346207417 * x83
x92 = x12 * x54
x93 = x54 * x92 * (x50 + x52)
x94 = x54 * x92 * (x56 + x58)
x95 = x0 * x94 + x93
x96 = x12 * x70
x97 = x63 * x92 + x96
x98 = x1**2 / x14**2
x99 = x10 * x98
x100 = x49 * x99
x101 = x40 * x99
x102 = x0 * x101 + x100
x103 = x0 * x33
x104 = x9 * x98
x105 = x104 * x12
x106 = x105 * x49
x107 = x105 * x40
x108 = x0 * x107 + x106
x109 = x13 * x98
x110 = x109 * x49
x111 = x109 * x40
x112 = x0 * x111 + x110
x113 = -x8 - A[1]
x114 = -2.0 * x113 * x18 * x2 * x20 * x23 * x27 * x28 + x35 * x9
x115 = -x114
x116 = x115 * x16
x117 = -2.0 * x113 * x2 * x20 * x23 * x27 * x28 * x29 + x26 * x9
x118 = -x6 * (x116 + x117)
x119 = -x117
x120 = x116 * x4 - x119 * x5
x121 = -x120
x122 = 2.0 * x113 * x2 * x20 * x23 * x27 * x28 * x34 - x44 * x9
x123 = x122 * x16
x124 = x115 * x5 - x123 * x4
x125 = x124 * x16
x126 = x118 + x121 * x5 - x125 * x4
x127 = x126 * x4
x128 = x121 * x6
x129 = 2.0 * x128
x130 = x127 + x129
x131 = x119 * x6
x132 = x121 * x4
x133 = x131 + x132
x134 = x54 * (x130 * x55 + x133 * x67)
x135 = x134 + x21 * x68
x136 = x54 * x55 * (x131 + x133)
x137 = x21 * x54
x138 = x136 + x137 * x71
x139 = -x6 * (x114 + x123)
x140 = 2.0 * x113 * x2 * x20 * x23 * x27 * x28 * x43 - x75 * x9
x141 = (
x126 * x5
- x41 * (x120 + x125)
- x76 * (x124 * x5 + x139 - x76 * (x122 * x5 - x140 * x76))
)
x142 = x141 * x4
x143 = x126 * x6
x144 = 3.0 * x143
x145 = x54 * (x130 * x61 + x55 * (x142 + x144))
x146 = 0.3333333333333333 * x82
x147 = x126 * x9
x148 = x147 + x51
x149 = x121 * x9
x150 = x149 + x57
x151 = x150 * x67
x152 = x54 * (x148 * x55 + x151)
x153 = x152 + x21 * x87
x154 = x119 * x9
x155 = x154 + x65
x156 = x54 * (x150 * x55 + x155 * x81)
x157 = x137 * x90 + x156
x158 = x141 * x9
x159 = x158 + x79
x160 = x54 * (x148 * x61 + x159 * x55)
x161 = 1.732050807568877 * x146
x162 = x129 * x92
x163 = x54 * (x127 * x92 + x162)
x164 = x163 + x21 * x94
x165 = x131 * x92
x166 = x54 * (x132 * x92 + x165)
x167 = x137 * x97 + x166
x168 = x54 * x92 * (x142 + x144)
x169 = x54 * x85 * (x148 + x51)
x170 = x101 * x21 + x169
x171 = x54 * x85 * (x150 + x57)
x172 = x21 * x33
x173 = x171 + x172 * x99
x174 = x54 * x85 * (x159 + x79)
x175 = x51 * x92
x176 = x54 * (x147 * x92 + x175)
x177 = x107 * x21 + x176
x178 = x57 * x92
x179 = x54 * (x149 * x92 + x178)
x180 = x105 * x172 + x179
x181 = x79 * x92
x182 = x54 * (x158 * x92 + x181)
x183 = x109 * x126
x184 = x111 * x21 + x183
x185 = x109 * x121
x186 = x109 * x172 + x185
x187 = x109 * x141
x188 = -x11 - A[2]
x189 = x12 * x35 - 2.0 * x18 * x188 * x2 * x20 * x23 * x27 * x28
x190 = -x189
x191 = x16 * x190
x192 = x12 * x26 - 2.0 * x188 * x2 * x20 * x23 * x27 * x28 * x29
x193 = -x6 * (x191 + x192)
x194 = -x192
x195 = x191 * x4 - x194 * x5
x196 = -x195
x197 = -x12 * x44 + 2.0 * x188 * x2 * x20 * x23 * x27 * x28 * x34
x198 = x16 * x197
x199 = x190 * x5 - x198 * x4
x200 = x16 * x199
x201 = x193 + x196 * x5 - x200 * x4
x202 = x201 * x4
x203 = x196 * x6
x204 = 2.0 * x203
x205 = x202 + x204
x206 = x194 * x6
x207 = x196 * x4
x208 = x206 + x207
x209 = x54 * (x205 * x55 + x208 * x67)
x210 = x209 + x22 * x68
x211 = x54 * x55 * (x206 + x208)
x212 = x22 * x54
x213 = x211 + x212 * x71
x214 = -x6 * (x189 + x198)
x215 = -x12 * x75 + 2.0 * x188 * x2 * x20 * x23 * x27 * x28 * x43
x216 = (
x201 * x5
- x41 * (x195 + x200)
- x76 * (x199 * x5 + x214 - x76 * (x197 * x5 - x215 * x76))
)
x217 = x216 * x4
x218 = x201 * x6
x219 = 3.0 * x218
x220 = x54 * (x205 * x61 + x55 * (x217 + x219))
x221 = x54 * x85 * (x202 + x204)
x222 = x22 * x87 + x221
x223 = x206 * x85
x224 = x54 * (x207 * x85 + x223)
x225 = x212 * x90 + x224
x226 = x54 * x85 * (x217 + x219)
x227 = x12 * x201 + x51
x228 = x12 * x196 + x57
x229 = x228 * x67
x230 = x54 * (x227 * x55 + x229)
x231 = x22 * x94 + x230
x232 = x12 * x194 + x65
x233 = x232 * x81
x234 = x54 * (x228 * x55 + x233)
x235 = x212 * x97 + x234
x236 = x12 * x216 + x79
x237 = x54 * (x227 * x61 + x236 * x55)
x238 = x201 * x99
x239 = x101 * x22 + x238
x240 = x196 * x99
x241 = x22 * x33
x242 = x240 + x241 * x99
x243 = x216 * x99
x244 = x104 * x227
x245 = x107 * x22 + x244
x246 = x104 * x228
x247 = x105 * x241 + x246
x248 = x104 * x236
x249 = x54 * (x175 + x227 * x92)
x250 = x111 * x22 + x249
x251 = x54 * (x178 + x228 * x92)
x252 = x109 * x241 + x251
x253 = x54 * (x181 + x236 * x92)
x254 = x116 * x9
x255 = x113 * x119 - x254 + x31
x256 = x255 * x6
x257 = x113 * x115 - x123 * x9 + x42
x258 = x16 * x257
x259 = x255 * x5 - x258 * x4
x260 = x259 * x4
x261 = x256 + x260
x262 = x54 * x55 * (x256 + x261)
x263 = x136 * x21 + x262
x264 = x138 * x21 + x263
x265 = x6 * (x113 * x119 - x254 - x258 - x73)
x266 = x16 * x9
x267 = x113 * x122 - x140 * x266 + x74
x268 = x259 * x5 + x265 - x76 * (x257 * x5 - x267 * x76)
x269 = x268 * x4
x270 = x259 * x6
x271 = 2.0 * x270
x272 = x134 * x21 + x54 * (x261 * x67 + x55 * (x269 + x271))
x273 = x255 * x9
x274 = 2.0 * x131
x275 = x273 + x274
x276 = x259 * x9
x277 = x129 + x276
x278 = x54 * (x275 * x81 + x277 * x55)
x279 = x156 * x21 + x278
x280 = x157 * x21 + x279
x281 = x268 * x9
x282 = 2.0 * x143
x283 = x281 + x282
x284 = x152 * x21 + x54 * (x277 * x67 + x283 * x55)
x285 = x256 * x92
x286 = x54 * (x260 * x92 + x285)
x287 = x166 * x21 + x286
x288 = x167 * x21 + x287
x289 = x163 * x21 + x54 * x92 * (x269 + x271)
x290 = x54 * (x151 + x277 * x85)
x291 = x171 * x21 + x290
x292 = x173 * x21 + x291
x293 = x169 * x21 + x54 * (x148 * x67 + x283 * x85)
x294 = x54 * (x162 + x276 * x92)
x295 = x179 * x21 + x294
x296 = x180 * x21 + x295
x297 = x176 * x21 + x54 * x92 * (x281 + x282)
x298 = x109 * x259
x299 = x185 * x21 + x298
x300 = x186 * x21 + x299
x301 = x109 * x268 + x183 * x21
x302 = -x113 * x194 + x191 * x9
x303 = -x302
x304 = x303 * x6
x305 = x113 * x190 - x198 * x9
x306 = x16 * x305
x307 = x303 * x5 - x306 * x4
x308 = x304 + x307 * x4
x309 = x54 * x55 * (x304 + x308)
x310 = x136 * x22 + x309
x311 = x21 * x213 + x310
x312 = -x6 * (x302 + x306)
x313 = x113 * x197 - x215 * x266
x314 = x307 * x5 + x312 - x76 * (x305 * x5 - x313 * x76)
x315 = x307 * x41
x316 = x54 * (x308 * x67 + x55 * (x314 * x4 + x315))
x317 = x134 * x22 + x316
x318 = x206 + x303 * x9
x319 = x203 + x307 * x9
x320 = x54 * (x318 * x81 + x319 * x55)
x321 = x156 * x22 + x320
x322 = x21 * x225 + x321
x323 = x218 + x314 * x9
x324 = x319 * x67
x325 = x54 * (x323 * x55 + x324)
x326 = x152 * x22 + x325
x327 = x12 * x303 + x131
x328 = x12 * x307 + x128
x329 = x54 * (x327 * x81 + x328 * x55)
x330 = x166 * x22 + x329
x331 = x21 * x235 + x330
x332 = x12 * x314 + x143
x333 = x328 * x67
x334 = x54 * (x332 * x55 + x333)
x335 = x163 * x22 + x334
x336 = x54 * x85 * (x203 + x319)
x337 = x171 * x22 + x336
x338 = x21 * x242 + x337
x339 = x54 * x85 * (x218 + x323)
x340 = x169 * x22 + x339
x341 = x54 * (x228 * x81 + x328 * x85)
x342 = x179 * x22 + x341
x343 = x21 * x247 + x342
x344 = x54 * (x227 * x81 + x332 * x85)
x345 = x176 * x22 + x344
x346 = x54 * x92 * (x128 + x328)
x347 = x185 * x22 + x346
x348 = x21 * x252 + x347
x349 = x54 * x92 * (x143 + x332)
x350 = x183 * x22 + x349
x351 = x12 * x191
x352 = x188 * x194 + x31 - x351
x353 = x352 * x6
x354 = -x12 * x198 + x188 * x190 + x42
x355 = x16 * x354
x356 = x352 * x5 - x355 * x4
x357 = x356 * x4
x358 = x353 + x357
x359 = x54 * x55 * (x353 + x358)
x360 = x211 * x22 + x359
x361 = x213 * x22 + x360
x362 = x6 * (x188 * x194 - x351 - x355 - x73)
x363 = x12 * x16
x364 = x188 * x197 - x215 * x363 + x74
x365 = x356 * x5 + x362 - x76 * (x354 * x5 - x364 * x76)
x366 = x365 * x4
x367 = x356 * x6
x368 = 2.0 * x367
x369 = x209 * x22 + x54 * (x358 * x67 + x55 * (x366 + x368))
x370 = x353 * x85
x371 = x54 * (x357 * x85 + x370)
x372 = x22 * x224 + x371
x373 = x22 * x225 + x372
x374 = x22 * x221 + x54 * x85 * (x366 + x368)
x375 = x12 * x352 + 2.0 * x206
x376 = x375 * x81
x377 = x12 * x356 + x204
x378 = x54 * (x376 + x377 * x55)
x379 = x22 * x234 + x378
x380 = x22 * x235 + x379
x381 = x12 * x365 + 2.0 * x218
x382 = x22 * x230 + x54 * (x377 * x67 + x381 * x55)
x383 = x356 * x99
x384 = x22 * x240 + x383
x385 = x22 * x242 + x384
x386 = x22 * x238 + x365 * x99
x387 = x104 * x377
x388 = x22 * x246 + x387
x389 = x22 * x247 + x388
x390 = x104 * x381 + x22 * x244
x391 = x54 * (x229 + x377 * x92)
x392 = x22 * x251 + x391
x393 = x22 * x252 + x392
x394 = x22 * x249 + x54 * (x227 * x67 + x381 * x92)
x395 = x113 * x255 + 2.0 * x118 - x258 * x9
x396 = x395 * x6
x397 = x113 * x257 + 2.0 * x139 - x266 * x267
x398 = x395 * x5 - x397 * x76
x399 = x398 * x4
x400 = x21 * x262 + x21 * x263 + x54 * x55 * (2.0 * x396 + x399)
x401 = x395 * x9
x402 = 3.0 * x256
x403 = x401 + x402
x404 = x403 * x81
x405 = x398 * x9
x406 = 3.0 * x270
x407 = x405 + x406
x408 = x21 * x278 + x21 * x279 + x54 * (x404 + x407 * x55)
x409 = x396 * x92
x410 = x21 * x286 + x21 * x287 + x54 * (x399 * x92 + x409)
x411 = x21 * x290 + x21 * x291 + x54 * (x277 * x61 + x407 * x85)
x412 = x21 * x294 + x21 * x295 + x54 * x92 * (x405 + x406)
x413 = x109 * x398 + x21 * x298 + x21 * x299
x414 = x113 * x303 + x193 - x306 * x9
x415 = x414 * x6
x416 = x113 * x305 + x214 - x266 * x313
x417 = x414 * x5 - x416 * x76
x418 = x54 * x55 * (x4 * x417 + 2.0 * x415)
x419 = x21 * x310 + x22 * x262 + x418
x420 = 2.0 * x304
x421 = x414 * x9 + x420
x422 = x315 + x417 * x9
x423 = x54 * (x421 * x81 + x422 * x55)
x424 = x21 * x321 + x22 * x278 + x423
x425 = x12 * x414 + x256
x426 = x12 * x417 + x270
x427 = x54 * (x425 * x81 + x426 * x55)
x428 = x21 * x330 + x22 * x286 + x427
x429 = x54 * (x324 + x422 * x85)
x430 = x21 * x337 + x22 * x290 + x429
x431 = x54 * (x333 + x426 * x85)
x432 = x21 * x342 + x22 * x294 + x431
x433 = x54 * x92 * (x270 + x426)
x434 = x21 * x347 + x22 * x298 + x433
x435 = x113 * x352 - x355 * x9
x436 = x435 * x6
x437 = x113 * x354 - x266 * x364
x438 = x435 * x5 - x437 * x76
x439 = x22 * x309 + x54 * x55 * (x4 * x438 + 2.0 * x436)
x440 = x22 * x310 + x439
x441 = x353 + x435 * x9
x442 = x367 + x438 * x9
x443 = x22 * x320 + x54 * (x441 * x81 + x442 * x55)
x444 = x22 * x321 + x443
x445 = x12 * x435 + x420
x446 = x12 * x438 + x315
x447 = x22 * x329 + x54 * (x445 * x81 + x446 * x55)
x448 = x22 * x330 + x447
x449 = x22 * x336 + x54 * x85 * (x367 + x442)
x450 = x22 * x337 + x449
x451 = x22 * x341 + x54 * (x377 * x81 + x446 * x85)
x452 = x22 * x342 + x451
x453 = x22 * x346 + x54 * (x333 + x446 * x92)
x454 = x22 * x347 + x453
x455 = -x12 * x355 + x188 * x352 + 2.0 * x193
x456 = x455 * x6
x457 = x188 * x354 + 2.0 * x214 - x363 * x364
x458 = x455 * x5 - x457 * x76
x459 = x4 * x458
x460 = x22 * x359 + x22 * x360 + x54 * x55 * (2.0 * x456 + x459)
x461 = x456 * x85
x462 = x22 * x371 + x22 * x372 + x54 * (x459 * x85 + x461)
x463 = x12 * x455 + 3.0 * x353
x464 = x463 * x81
x465 = x12 * x458 + 3.0 * x367
x466 = x22 * x378 + x22 * x379 + x54 * (x464 + x465 * x55)
x467 = x22 * x383 + x22 * x384 + x458 * x99
x468 = x104 * x465 + x22 * x387 + x22 * x388
x469 = x22 * x391 + x22 * x392 + x54 * (x377 * x61 + x465 * x92)
x470 = x0 * x136 + x134
x471 = x7 * x98
x472 = x0 * x119
x473 = x0 * x156 + x152
x474 = x4 * x98
x475 = x155 * x474
x476 = x0 * x166 + x163
x477 = x12 * x474
x478 = x0 * x171 + x169
x479 = x155 * x85 + x89
x480 = x0 * x179 + x176
x481 = x154 * x92 + x96
x482 = x0 * x185 + x183
x483 = x255 * x471
x484 = x119 * x21
x485 = x471 * x484 + x483
x486 = x275 * x474
x487 = x21 * x475 + x486
x488 = x255 * x477
x489 = x477 * x484 + x488
x490 = x54 * (x155 * x67 + x275 * x85)
x491 = x137 * x479 + x490
x492 = x54 * x92 * (x273 + x274)
x493 = x137 * x481 + x492
x494 = x109 * x255
x495 = x109 * x484 + x494
x496 = x303 * x471
x497 = x119 * x22
x498 = x471 * x497 + x496
x499 = x318 * x474
x500 = x22 * x475 + x499
x501 = x327 * x474
x502 = x477 * x497 + x501
x503 = x54 * (x223 + x318 * x85)
x504 = x212 * x479 + x503
x505 = x54 * (x233 + x327 * x85)
x506 = x212 * x481 + x505
x507 = x54 * (x165 + x327 * x92)
x508 = x109 * x497 + x507
x509 = x395 * x471
x510 = x21 * x483 + x509
x511 = x21 * x485 + x510
x512 = x403 * x474
x513 = x21 * x486 + x512
x514 = x21 * x487 + x513
x515 = x395 * x477
x516 = x21 * x488 + x515
x517 = x21 * x489 + x516
x518 = x54 * (x275 * x61 + x403 * x85)
x519 = x21 * x490 + x518
x520 = x21 * x491 + x519
x521 = x54 * x92 * (x401 + x402)
x522 = x21 * x492 + x521
x523 = x21 * x493 + x522
x524 = x109 * x395
x525 = x21 * x494 + x524
x526 = x21 * x495 + x525
x527 = x414 * x471
x528 = x22 * x483 + x527
x529 = x21 * x498 + x528
x530 = x421 * x474
x531 = x22 * x486 + x530
x532 = x21 * x500 + x531
x533 = x425 * x474
x534 = x22 * x488 + x533
x535 = x21 * x502 + x534
x536 = x54 * (x318 * x67 + x421 * x85)
x537 = x22 * x490 + x536
x538 = x21 * x504 + x537
x539 = x327 * x67
x540 = x54 * (x425 * x85 + x539)
x541 = x22 * x492 + x540
x542 = x21 * x506 + x541
x543 = x54 * (x285 + x425 * x92)
x544 = x22 * x494 + x543
x545 = x21 * x508 + x544
x546 = x435 * x471
x547 = x22 * x496 + x546
x548 = x22 * x498 + x547
x549 = x441 * x474
x550 = x22 * x499 + x549
x551 = x22 * x500 + x550
x552 = x445 * x474
x553 = x22 * x501 + x552
x554 = x22 * x502 + x553
x555 = x54 * (x370 + x441 * x85)
x556 = x22 * x503 + x555
x557 = x22 * x504 + x556
x558 = x54 * (x376 + x445 * x85)
x559 = x22 * x505 + x558
x560 = x22 * x506 + x559
x561 = x54 * (x445 * x92 + x539)
x562 = x22 * x507 + x561
x563 = x22 * x508 + x562
x564 = x113 * x395 + 3.0 * x265 - x266 * x397
x565 = x564 * x9
x566 = 4.0 * x396
x567 = x565 + x566
x568 = x113 * x414 - x266 * x416 + 2.0 * x312
x569 = x471 * x568
x570 = 3.0 * x415 + x568 * x9
x571 = x474 * x570
x572 = x12 * x568 + x396
x573 = x474 * x572
x574 = x54 * (x421 * x61 + x570 * x85)
x575 = x54 * (x425 * x61 + x572 * x85)
x576 = x54 * (x409 + x572 * x92)
x577 = x113 * x435 - x266 * x437 + x362
x578 = x22 * x527 + x471 * x577
x579 = 2.0 * x436 + x577 * x9
x580 = x22 * x530 + x474 * x579
x581 = x12 * x577 + 2.0 * x415
x582 = x22 * x533 + x474 * x581
x583 = x22 * x536 + x54 * (x441 * x67 + x579 * x85)
x584 = x22 * x540 + x54 * (x445 * x67 + x581 * x85)
x585 = x22 * x543 + x54 * (x425 * x67 + x581 * x92)
x586 = x113 * x455 - x266 * x457
x587 = x22 * x546 + x22 * x547 + x471 * x586
x588 = x456 + x586 * x9
x589 = x22 * x549 + x22 * x550 + x474 * x588
x590 = x12 * x586 + 3.0 * x436
x591 = x22 * x552 + x22 * x553 + x474 * x590
x592 = x22 * x555 + x22 * x556 + x54 * (x461 + x588 * x85)
x593 = x22 * x558 + x22 * x559 + x54 * (x464 + x590 * x85)
x594 = x22 * x561 + x22 * x562 + x54 * (x445 * x61 + x590 * x92)
x595 = x0 * x211 + x209
x596 = x0 * x194
x597 = x0 * x224 + x221
x598 = x104 * x4
x599 = x0 * x234 + x230
x600 = x0 * x232
x601 = x0 * x240 + x238
x602 = x0 * x246 + x244
x603 = x0 * x251 + x249
x604 = x232 * x92 + x96
x605 = x21 * x211 + x309
x606 = x194 * x21
x607 = x471 * x606 + x496
x608 = x21 * x224 + x320
x609 = x499 + x598 * x606
x610 = x21 * x234 + x329
x611 = x21 * x232
x612 = x474 * x611 + x501
x613 = x21 * x240 + x336
x614 = x503 + x606 * x99
x615 = x21 * x246 + x341
x616 = x104 * x611 + x505
x617 = x21 * x251 + x346
x618 = x137 * x604 + x507
x619 = x352 * x471
x620 = x194 * x22
x621 = x471 * x620 + x619
x622 = x352 * x598
x623 = x598 * x620 + x622
x624 = x375 * x474
x625 = x22 * x232
x626 = x474 * x625 + x624
x627 = x352 * x99
x628 = x620 * x99 + x627
x629 = x104 * x375
x630 = x104 * x625 + x629
x631 = x54 * (x232 * x67 + x375 * x92)
x632 = x212 * x604 + x631
x633 = x21 * x496 + x527
x634 = x21 * x607 + x633
x635 = x21 * x499 + x530
x636 = x21 * x609 + x635
x637 = x21 * x501 + x533
x638 = x21 * x612 + x637
x639 = x21 * x503 + x536
x640 = x21 * x614 + x639
x641 = x21 * x505 + x540
x642 = x21 * x616 + x641
x643 = x21 * x507 + x543
x644 = x21 * x618 + x643
x645 = x21 * x621 + x547
x646 = x21 * x623 + x550
x647 = x21 * x626 + x553
x648 = x21 * x628 + x556
x649 = x21 * x630 + x559
x650 = x21 * x632 + x562
x651 = x455 * x471
x652 = x22 * x619 + x651
x653 = x22 * x621 + x652
x654 = x455 * x598
x655 = x22 * x622 + x654
x656 = x22 * x623 + x655
x657 = x463 * x474
x658 = x22 * x624 + x657
x659 = x22 * x626 + x658
x660 = x455 * x99
x661 = x22 * x627 + x660
x662 = x22 * x628 + x661
x663 = x104 * x463
x664 = x22 * x629 + x663
x665 = x22 * x630 + x664
x666 = x54 * (x375 * x61 + x463 * x92)
x667 = x22 * x631 + x666
x668 = x22 * x632 + x667
x669 = x188 * x455 + 3.0 * x362 - x363 * x457
x670 = x12 * x669 + 4.0 * x456
# 180 item(s)
result[0, 0, 0] = numpy.sum(
x84
* (
x0 * x62
+ x0 * x69
+ x0 * (x0 * (x68 + x71 * x72) + x69)
+ x54 * (4.0 * x53 * x81 + x55 * (x78 + x80))
)
)
result[0, 0, 1] = numpy.sum(
x91
* (
x0 * x86
+ x0 * x88
+ x0 * (x0 * (x72 * x90 + x87) + x88)
+ x54 * x85 * (x78 + x80)
)
)
result[0, 0, 2] = numpy.sum(
x91
* (
x0 * x93
+ x0 * x95
+ x0 * (x0 * (x72 * x97 + x94) + x95)
+ x54 * x92 * (x78 + x80)
)
)
result[0, 0, 3] = numpy.sum(
x84 * (x0 * x100 + x0 * x102 + x0 * (x0 * (x101 + x103 * x99) + x102) + x77 * x99)
)
result[0, 0, 4] = numpy.sum(
x91
* (x0 * x106 + x0 * x108 + x0 * (x0 * (x103 * x105 + x107) + x108) + x105 * x77)
)
result[0, 0, 5] = numpy.sum(
x84
* (x0 * x110 + x0 * x112 + x0 * (x0 * (x103 * x109 + x111) + x112) + x109 * x77)
)
result[0, 1, 0] = numpy.sum(
x146 * (x0 * x135 + x0 * (x0 * x138 + x135) + x145 + x21 * x62)
)
result[0, 1, 1] = numpy.sum(
x161 * (x0 * x153 + x0 * (x0 * x157 + x153) + x160 + x21 * x86)
)
result[0, 1, 2] = numpy.sum(
x161 * (x0 * x164 + x0 * (x0 * x167 + x164) + x168 + x21 * x93)
)
result[0, 1, 3] = numpy.sum(
x146 * (x0 * x170 + x0 * (x0 * x173 + x170) + x100 * x21 + x174)
)
result[0, 1, 4] = numpy.sum(
x161 * (x0 * x177 + x0 * (x0 * x180 + x177) + x106 * x21 + x182)
)
result[0, 1, 5] = numpy.sum(
x146 * (x0 * x184 + x0 * (x0 * x186 + x184) + x110 * x21 + x187)
)
result[0, 2, 0] = numpy.sum(
x146 * (x0 * x210 + x0 * (x0 * x213 + x210) + x22 * x62 + x220)
)
result[0, 2, 1] = numpy.sum(
x161 * (x0 * x222 + x0 * (x0 * x225 + x222) + x22 * x86 + x226)
)
result[0, 2, 2] = numpy.sum(
x161 * (x0 * x231 + x0 * (x0 * x235 + x231) + x22 * x93 + x237)
)
result[0, 2, 3] = numpy.sum(
x146 * (x0 * x239 + x0 * (x0 * x242 + x239) + x100 * x22 + x243)
)
result[0, 2, 4] = numpy.sum(
x161 * (x0 * x245 + x0 * (x0 * x247 + x245) + x106 * x22 + x248)
)
result[0, 2, 5] = numpy.sum(
x146 * (x0 * x250 + x0 * (x0 * x252 + x250) + x110 * x22 + x253)
)
result[0, 3, 0] = numpy.sum(x146 * (x0 * x264 + x135 * x21 + x272))
result[0, 3, 1] = numpy.sum(x161 * (x0 * x280 + x153 * x21 + x284))
result[0, 3, 2] = numpy.sum(x161 * (x0 * x288 + x164 * x21 + x289))
result[0, 3, 3] = numpy.sum(x146 * (x0 * x292 + x170 * x21 + x293))
result[0, 3, 4] = numpy.sum(x161 * (x0 * x296 + x177 * x21 + x297))
result[0, 3, 5] = numpy.sum(x146 * (x0 * x300 + x184 * x21 + x301))
result[0, 4, 0] = numpy.sum(x161 * (x0 * x311 + x21 * x210 + x317))
result[0, 4, 1] = numpy.sum(x82 * (x0 * x322 + x21 * x222 + x326))
result[0, 4, 2] = numpy.sum(x82 * (x0 * x331 + x21 * x231 + x335))
result[0, 4, 3] = numpy.sum(x161 * (x0 * x338 + x21 * x239 + x340))
result[0, 4, 4] = numpy.sum(x82 * (x0 * x343 + x21 * x245 + x345))
result[0, 4, 5] = numpy.sum(x161 * (x0 * x348 + x21 * x250 + x350))
result[0, 5, 0] = numpy.sum(x146 * (x0 * x361 + x210 * x22 + x369))
result[0, 5, 1] = numpy.sum(x161 * (x0 * x373 + x22 * x222 + x374))
result[0, 5, 2] = numpy.sum(x161 * (x0 * x380 + x22 * x231 + x382))
result[0, 5, 3] = numpy.sum(x146 * (x0 * x385 + x22 * x239 + x386))
result[0, 5, 4] = numpy.sum(x161 * (x0 * x389 + x22 * x245 + x390))
result[0, 5, 5] = numpy.sum(x146 * (x0 * x393 + x22 * x250 + x394))
result[0, 6, 0] = numpy.sum(x84 * (x21 * x264 + x400))
result[0, 6, 1] = numpy.sum(x91 * (x21 * x280 + x408))
result[0, 6, 2] = numpy.sum(x91 * (x21 * x288 + x410))
result[0, 6, 3] = numpy.sum(x84 * (x21 * x292 + x411))
result[0, 6, 4] = numpy.sum(x91 * (x21 * x296 + x412))
result[0, 6, 5] = numpy.sum(x84 * (x21 * x300 + x413))
result[0, 7, 0] = numpy.sum(x146 * (x21 * x311 + x419))
result[0, 7, 1] = numpy.sum(x161 * (x21 * x322 + x424))
result[0, 7, 2] = numpy.sum(x161 * (x21 * x331 + x428))
result[0, 7, 3] = numpy.sum(x146 * (x21 * x338 + x430))
result[0, 7, 4] = numpy.sum(x161 * (x21 * x343 + x432))
result[0, 7, 5] = numpy.sum(x146 * (x21 * x348 + x434))
result[0, 8, 0] = numpy.sum(x146 * (x21 * x361 + x440))
result[0, 8, 1] = numpy.sum(x161 * (x21 * x373 + x444))
result[0, 8, 2] = numpy.sum(x161 * (x21 * x380 + x448))
result[0, 8, 3] = numpy.sum(x146 * (x21 * x385 + x450))
result[0, 8, 4] = numpy.sum(x161 * (x21 * x389 + x452))
result[0, 8, 5] = numpy.sum(x146 * (x21 * x393 + x454))
result[0, 9, 0] = numpy.sum(x84 * (x22 * x361 + x460))
result[0, 9, 1] = numpy.sum(x91 * (x22 * x373 + x462))
result[0, 9, 2] = numpy.sum(x91 * (x22 * x380 + x466))
result[0, 9, 3] = numpy.sum(x84 * (x22 * x385 + x467))
result[0, 9, 4] = numpy.sum(x91 * (x22 * x389 + x468))
result[0, 9, 5] = numpy.sum(x84 * (x22 * x393 + x469))
result[1, 0, 0] = numpy.sum(
x84 * (x0 * x134 + x0 * x470 + x0 * (x0 * (x136 + x471 * x472) + x470) + x145)
)
result[1, 0, 1] = numpy.sum(
x91 * (x0 * x152 + x0 * x473 + x0 * (x0 * (x0 * x475 + x156) + x473) + x160)
)
result[1, 0, 2] = numpy.sum(
x91 * (x0 * x163 + x0 * x476 + x0 * (x0 * (x166 + x472 * x477) + x476) + x168)
)
result[1, 0, 3] = numpy.sum(
x84 * (x0 * x169 + x0 * x478 + x0 * (x0 * (x171 + x479 * x72) + x478) + x174)
)
result[1, 0, 4] = numpy.sum(
x91 * (x0 * x176 + x0 * x480 + x0 * (x0 * (x179 + x481 * x72) + x480) + x182)
)
result[1, 0, 5] = numpy.sum(
x84 * (x0 * x183 + x0 * x482 + x0 * (x0 * (x109 * x472 + x185) + x482) + x187)
)
result[1, 1, 0] = numpy.sum(x146 * (x0 * x263 + x0 * (x0 * x485 + x263) + x272))
result[1, 1, 1] = numpy.sum(x161 * (x0 * x279 + x0 * (x0 * x487 + x279) + x284))
result[1, 1, 2] = numpy.sum(x161 * (x0 * x287 + x0 * (x0 * x489 + x287) + x289))
result[1, 1, 3] = numpy.sum(x146 * (x0 * x291 + x0 * (x0 * x491 + x291) + x293))
result[1, 1, 4] = numpy.sum(x161 * (x0 * x295 + x0 * (x0 * x493 + x295) + x297))
result[1, 1, 5] = numpy.sum(x146 * (x0 * x299 + x0 * (x0 * x495 + x299) + x301))
result[1, 2, 0] = numpy.sum(x146 * (x0 * x310 + x0 * (x0 * x498 + x310) + x317))
result[1, 2, 1] = numpy.sum(x161 * (x0 * x321 + x0 * (x0 * x500 + x321) + x326))
result[1, 2, 2] = numpy.sum(x161 * (x0 * x330 + x0 * (x0 * x502 + x330) + x335))
result[1, 2, 3] = numpy.sum(x146 * (x0 * x337 + x0 * (x0 * x504 + x337) + x340))
result[1, 2, 4] = numpy.sum(x161 * (x0 * x342 + x0 * (x0 * x506 + x342) + x345))
result[1, 2, 5] = numpy.sum(x146 * (x0 * x347 + x0 * (x0 * x508 + x347) + x350))
result[1, 3, 0] = numpy.sum(x146 * (x0 * x511 + x400))
result[1, 3, 1] = numpy.sum(x161 * (x0 * x514 + x408))
result[1, 3, 2] = numpy.sum(x161 * (x0 * x517 + x410))
result[1, 3, 3] = numpy.sum(x146 * (x0 * x520 + x411))
result[1, 3, 4] = numpy.sum(x161 * (x0 * x523 + x412))
result[1, 3, 5] = numpy.sum(x146 * (x0 * x526 + x413))
result[1, 4, 0] = numpy.sum(x161 * (x0 * x529 + x419))
result[1, 4, 1] = numpy.sum(x82 * (x0 * x532 + x424))
result[1, 4, 2] = numpy.sum(x82 * (x0 * x535 + x428))
result[1, 4, 3] = numpy.sum(x161 * (x0 * x538 + x430))
result[1, 4, 4] = numpy.sum(x82 * (x0 * x542 + x432))
result[1, 4, 5] = numpy.sum(x161 * (x0 * x545 + x434))
result[1, 5, 0] = numpy.sum(x146 * (x0 * x548 + x440))
result[1, 5, 1] = numpy.sum(x161 * (x0 * x551 + x444))
result[1, 5, 2] = numpy.sum(x161 * (x0 * x554 + x448))
result[1, 5, 3] = numpy.sum(x146 * (x0 * x557 + x450))
result[1, 5, 4] = numpy.sum(x161 * (x0 * x560 + x452))
result[1, 5, 5] = numpy.sum(x146 * (x0 * x563 + x454))
result[1, 6, 0] = numpy.sum(
x84 * (x21 * x509 + x21 * x510 + x21 * x511 + x471 * x564)
)
result[1, 6, 1] = numpy.sum(
x91 * (x21 * x512 + x21 * x513 + x21 * x514 + x474 * x567)
)
result[1, 6, 2] = numpy.sum(
x91 * (x21 * x515 + x21 * x516 + x21 * x517 + x477 * x564)
)
result[1, 6, 3] = numpy.sum(
x84 * (x21 * x518 + x21 * x519 + x21 * x520 + x54 * (4.0 * x404 + x567 * x85))
)
result[1, 6, 4] = numpy.sum(
x91 * (x21 * x521 + x21 * x522 + x21 * x523 + x54 * x92 * (x565 + x566))
)
result[1, 6, 5] = numpy.sum(
x84 * (x109 * x564 + x21 * x524 + x21 * x525 + x21 * x526)
)
result[1, 7, 0] = numpy.sum(x146 * (x21 * x528 + x21 * x529 + x22 * x509 + x569))
result[1, 7, 1] = numpy.sum(x161 * (x21 * x531 + x21 * x532 + x22 * x512 + x571))
result[1, 7, 2] = numpy.sum(x161 * (x21 * x534 + x21 * x535 + x22 * x515 + x573))
result[1, 7, 3] = numpy.sum(x146 * (x21 * x537 + x21 * x538 + x22 * x518 + x574))
result[1, 7, 4] = numpy.sum(x161 * (x21 * x541 + x21 * x542 + x22 * x521 + x575))
result[1, 7, 5] = numpy.sum(x146 * (x21 * x544 + x21 * x545 + x22 * x524 + x576))
result[1, 8, 0] = numpy.sum(x146 * (x21 * x548 + x22 * x528 + x578))
result[1, 8, 1] = numpy.sum(x161 * (x21 * x551 + x22 * x531 + x580))
result[1, 8, 2] = numpy.sum(x161 * (x21 * x554 + x22 * x534 + x582))
result[1, 8, 3] = numpy.sum(x146 * (x21 * x557 + x22 * x537 + x583))
result[1, 8, 4] = numpy.sum(x161 * (x21 * x560 + x22 * x541 + x584))
result[1, 8, 5] = numpy.sum(x146 * (x21 * x563 + x22 * x544 + x585))
result[1, 9, 0] = numpy.sum(x84 * (x22 * x548 + x587))
result[1, 9, 1] = numpy.sum(x91 * (x22 * x551 + x589))
result[1, 9, 2] = numpy.sum(x91 * (x22 * x554 + x591))
result[1, 9, 3] = numpy.sum(x84 * (x22 * x557 + x592))
result[1, 9, 4] = numpy.sum(x91 * (x22 * x560 + x593))
result[1, 9, 5] = numpy.sum(x84 * (x22 * x563 + x594))
result[2, 0, 0] = numpy.sum(
x84 * (x0 * x209 + x0 * x595 + x0 * (x0 * (x211 + x471 * x596) + x595) + x220)
)
result[2, 0, 1] = numpy.sum(
x91 * (x0 * x221 + x0 * x597 + x0 * (x0 * (x224 + x596 * x598) + x597) + x226)
)
result[2, 0, 2] = numpy.sum(
x91 * (x0 * x230 + x0 * x599 + x0 * (x0 * (x234 + x474 * x600) + x599) + x237)
)
result[2, 0, 3] = numpy.sum(
x84 * (x0 * x238 + x0 * x601 + x0 * (x0 * (x240 + x596 * x99) + x601) + x243)
)
result[2, 0, 4] = numpy.sum(
x91 * (x0 * x244 + x0 * x602 + x0 * (x0 * (x104 * x600 + x246) + x602) + x248)
)
result[2, 0, 5] = numpy.sum(
x84 * (x0 * x249 + x0 * x603 + x0 * (x0 * (x251 + x604 * x72) + x603) + x253)
)
result[2, 1, 0] = numpy.sum(
x146 * (x0 * x605 + x0 * (x0 * x607 + x605) + x209 * x21 + x316)
)
result[2, 1, 1] = numpy.sum(
x161 * (x0 * x608 + x0 * (x0 * x609 + x608) + x21 * x221 + x325)
)
result[2, 1, 2] = numpy.sum(
x161 * (x0 * x610 + x0 * (x0 * x612 + x610) + x21 * x230 + x334)
)
result[2, 1, 3] = numpy.sum(
x146 * (x0 * x613 + x0 * (x0 * x614 + x613) + x21 * x238 + x339)
)
result[2, 1, 4] = numpy.sum(
x161 * (x0 * x615 + x0 * (x0 * x616 + x615) + x21 * x244 + x344)
)
result[2, 1, 5] = numpy.sum(
x146 * (x0 * x617 + x0 * (x0 * x618 + x617) + x21 * x249 + x349)
)
result[2, 2, 0] = numpy.sum(x146 * (x0 * x360 + x0 * (x0 * x621 + x360) + x369))
result[2, 2, 1] = numpy.sum(x161 * (x0 * x372 + x0 * (x0 * x623 + x372) + x374))
result[2, 2, 2] = numpy.sum(x161 * (x0 * x379 + x0 * (x0 * x626 + x379) + x382))
result[2, 2, 3] = numpy.sum(x146 * (x0 * x384 + x0 * (x0 * x628 + x384) + x386))
result[2, 2, 4] = numpy.sum(x161 * (x0 * x388 + x0 * (x0 * x630 + x388) + x390))
result[2, 2, 5] = numpy.sum(x146 * (x0 * x392 + x0 * (x0 * x632 + x392) + x394))
result[2, 3, 0] = numpy.sum(x146 * (x0 * x634 + x21 * x309 + x21 * x605 + x418))
result[2, 3, 1] = numpy.sum(x161 * (x0 * x636 + x21 * x320 + x21 * x608 + x423))
result[2, 3, 2] = numpy.sum(x161 * (x0 * x638 + x21 * x329 + x21 * x610 + x427))
result[2, 3, 3] = numpy.sum(x146 * (x0 * x640 + x21 * x336 + x21 * x613 + x429))
result[2, 3, 4] = numpy.sum(x161 * (x0 * x642 + x21 * x341 + x21 * x615 + x431))
result[2, 3, 5] = numpy.sum(x146 * (x0 * x644 + x21 * x346 + x21 * x617 + x433))
result[2, 4, 0] = numpy.sum(x161 * (x0 * x645 + x21 * x360 + x439))
result[2, 4, 1] = numpy.sum(x82 * (x0 * x646 + x21 * x372 + x443))
result[2, 4, 2] = numpy.sum(x82 * (x0 * x647 + x21 * x379 + x447))
result[2, 4, 3] = numpy.sum(x161 * (x0 * x648 + x21 * x384 + x449))
result[2, 4, 4] = numpy.sum(x82 * (x0 * x649 + x21 * x388 + x451))
result[2, 4, 5] = numpy.sum(x161 * (x0 * x650 + x21 * x392 + x453))
result[2, 5, 0] = numpy.sum(x146 * (x0 * x653 + x460))
result[2, 5, 1] = numpy.sum(x161 * (x0 * x656 + x462))
result[2, 5, 2] = numpy.sum(x161 * (x0 * x659 + x466))
result[2, 5, 3] = numpy.sum(x146 * (x0 * x662 + x467))
result[2, 5, 4] = numpy.sum(x161 * (x0 * x665 + x468))
result[2, 5, 5] = numpy.sum(x146 * (x0 * x668 + x469))
result[2, 6, 0] = numpy.sum(x84 * (x21 * x527 + x21 * x633 + x21 * x634 + x569))
result[2, 6, 1] = numpy.sum(x91 * (x21 * x530 + x21 * x635 + x21 * x636 + x571))
result[2, 6, 2] = numpy.sum(x91 * (x21 * x533 + x21 * x637 + x21 * x638 + x573))
result[2, 6, 3] = numpy.sum(x84 * (x21 * x536 + x21 * x639 + x21 * x640 + x574))
result[2, 6, 4] = numpy.sum(x91 * (x21 * x540 + x21 * x641 + x21 * x642 + x575))
result[2, 6, 5] = numpy.sum(x84 * (x21 * x543 + x21 * x643 + x21 * x644 + x576))
result[2, 7, 0] = numpy.sum(x146 * (x21 * x547 + x21 * x645 + x578))
result[2, 7, 1] = numpy.sum(x161 * (x21 * x550 + x21 * x646 + x580))
result[2, 7, 2] = numpy.sum(x161 * (x21 * x553 + x21 * x647 + x582))
result[2, 7, 3] = numpy.sum(x146 * (x21 * x556 + x21 * x648 + x583))
result[2, 7, 4] = numpy.sum(x161 * (x21 * x559 + x21 * x649 + x584))
result[2, 7, 5] = numpy.sum(x146 * (x21 * x562 + x21 * x650 + x585))
result[2, 8, 0] = numpy.sum(x146 * (x21 * x653 + x587))
result[2, 8, 1] = numpy.sum(x161 * (x21 * x656 + x589))
result[2, 8, 2] = numpy.sum(x161 * (x21 * x659 + x591))
result[2, 8, 3] = numpy.sum(x146 * (x21 * x662 + x592))
result[2, 8, 4] = numpy.sum(x161 * (x21 * x665 + x593))
result[2, 8, 5] = numpy.sum(x146 * (x21 * x668 + x594))
result[2, 9, 0] = numpy.sum(
x84 * (x22 * x651 + x22 * x652 + x22 * x653 + x471 * x669)
)
result[2, 9, 1] = numpy.sum(
x91 * (x22 * x654 + x22 * x655 + x22 * x656 + x598 * x669)
)
result[2, 9, 2] = numpy.sum(
x91 * (x22 * x657 + x22 * x658 + x22 * x659 + x474 * x670)
)
result[2, 9, 3] = numpy.sum(x84 * (x22 * x660 + x22 * x661 + x22 * x662 + x669 * x99))
result[2, 9, 4] = numpy.sum(
x91 * (x104 * x670 + x22 * x663 + x22 * x664 + x22 * x665)
)
result[2, 9, 5] = numpy.sum(
x84 * (x22 * x666 + x22 * x667 + x22 * x668 + x54 * (4.0 * x464 + x670 * x92))
)
return result
[docs]
def int3c2e3d_sph_133(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pf|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 10, 10), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = -x3 - A[0]
x6 = 0.5 / (ax + bx)
x7 = x4**2
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = -x8 - C[1]
x10 = x9**2
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = -x11 - C[2]
x13 = x12**2
x14 = cx + x1
x15 = x14 ** (-1.0)
x16 = cx * x15
x17 = x1 * x16 * (x10 + x13 + x7)
x18 = boys(4, x17)
x19 = x14 ** (-1.5)
x20 = 17.49341832762486
x21 = A[1] - B[1]
x22 = A[2] - B[2]
x23 = numpy.exp(-ax * bx * x2 * (x0**2 + x21**2 + x22**2))
x24 = x20 * x23
x25 = x2 * x24
x26 = 2.0 * x19 * x25
x27 = x18 * x26
x28 = cx ** (-1.0)
x29 = x14 ** (-0.5)
x30 = boys(3, x17)
x31 = 2.0 * x2 * x20 * x23 * x28 * x29 * x30 - x27
x32 = x31 * x6
x33 = -2.0 * x2 * x20 * x23 * x28 * x29 * x30 * x5 + x27 * x4
x34 = -x33
x35 = boys(5, x17)
x36 = x26 * x35
x37 = -2.0 * x18 * x2 * x20 * x23 * x28 * x29 * x5 + x36 * x4
x38 = -x37
x39 = x16 * x38
x40 = x39 * x4
x41 = x32 + x34 * x5 - x40
x42 = 2.0 * x6
x43 = x6 * (2.0 * x18 * x2 * x20 * x23 * x28 * x29 - x36)
x44 = boys(6, x17)
x45 = x26 * x44
x46 = 2.0 * x2 * x20 * x23 * x28 * x29 * x35 * x5 - x4 * x45
x47 = x16 * x46
x48 = x38 * x5 - x4 * x47 + x43
x49 = x16 * x48
x50 = -x4 * x49 + x41 * x5 - x42 * (x33 + x39)
x51 = x4 * x50
x52 = x41 * x6
x53 = 3.0 * x52
x54 = x51 + x53
x55 = x1 * x15
x56 = x4 * x55
x57 = x4 * x41
x58 = x34 * x6
x59 = 2.0 * x58
x60 = x57 + x59
x61 = 3.0 * x6
x62 = x55 * x61
x63 = x54 * x56 + x60 * x62
x64 = x34 * x4
x65 = x28 * x30 * x42
x66 = x25 * x29 * x65
x67 = x64 + x66
x68 = x42 * x55
x69 = x56 * x60 + x67 * x68
x70 = x55 * (x56 * x63 + x62 * x69)
x71 = x24 * x65
x72 = x19 * x71
x73 = x4 * x72 + x56 * x67
x74 = x55 * (x56 * x69 + x68 * x73)
x75 = x0 * x74 + x70
x76 = x1 * x14 ** (-2.5) * x71
x77 = x56 * x73 + x7 * x76
x78 = x0 * x55
x79 = -x31 * x6
x80 = x6 * (2.0 * x2 * x20 * x23 * x28 * x29 * x35 - x45)
x81 = x26 * boys(7, x17)
x82 = x16 * x4
x83 = (
x5 * x50
- x61 * (-x34 * x5 + x40 + x49 + x79)
+ x82
* (
x42 * (x37 + x47)
- x48 * x5
+ x82
* (
x46 * x5
+ x80
- x82 * (2.0 * x2 * x20 * x23 * x28 * x29 * x44 * x5 - x4 * x81)
)
)
)
x84 = x4 * x83
x85 = x50 * x6
x86 = 4.0 * x85
x87 = x55 * x6
x88 = 4.0 * x87
x89 = da * db * dc
x90 = 0.06666666666666667 * x89
x91 = x55 * x9
x92 = x91 * (x51 + x53)
x93 = x91 * (x57 + x59)
x94 = x55 * (x56 * x92 + x62 * x93)
x95 = x72 * x9
x96 = x64 * x91 + x95
x97 = x55 * (x56 * x93 + x68 * x96)
x98 = x0 * x97 + x94
x99 = x4 * x9
x100 = x56 * x96 + x76 * x99
x101 = 2.23606797749979 * x90
x102 = x12 * x55
x103 = x102 * (x51 + x53)
x104 = x102 * (x57 + x59)
x105 = x55 * (x103 * x56 + x104 * x62)
x106 = x12 * x72
x107 = x102 * x64 + x106
x108 = x55 * (x104 * x56 + x107 * x68)
x109 = x0 * x108 + x105
x110 = x12 * x76
x111 = x107 * x56 + x110 * x4
x112 = x1**2 / x14**2
x113 = x10 * x112
x114 = x113 * x55 * (x51 + x53)
x115 = x113 * x55 * (x57 + x59)
x116 = x0 * x115 + x114
x117 = x10 * x76
x118 = x113 * x64 + x117
x119 = x112 * x9
x120 = x119 * x12
x121 = x120 * x55 * (x51 + x53)
x122 = x120 * x55 * (x57 + x59)
x123 = x0 * x122 + x121
x124 = x110 * x9
x125 = x120 * x64 + x124
x126 = 3.872983346207417 * x90
x127 = x112 * x13
x128 = x127 * x55 * (x51 + x53)
x129 = x127 * x55 * (x57 + x59)
x130 = x0 * x129 + x128
x131 = x13 * x76
x132 = x127 * x64 + x131
x133 = x1**3 / x14**3
x134 = x133 * x9**3
x135 = x134 * x50
x136 = x134 * x41
x137 = x0 * x136 + x135
x138 = x0 * x34
x139 = x10 * x133
x140 = x12 * x139
x141 = x140 * x50
x142 = x140 * x41
x143 = x0 * x142 + x141
x144 = x13 * x133
x145 = x144 * x9
x146 = x145 * x50
x147 = x145 * x41
x148 = x0 * x147 + x146
x149 = x12**3 * x133
x150 = x149 * x50
x151 = x149 * x41
x152 = x0 * x151 + x150
x153 = -x8 - A[1]
x154 = -2.0 * x153 * x18 * x2 * x20 * x23 * x28 * x29 + x36 * x9
x155 = -x154
x156 = x155 * x16
x157 = -2.0 * x153 * x2 * x20 * x23 * x28 * x29 * x30 + x27 * x9
x158 = -x6 * (x156 + x157)
x159 = -x157
x160 = x156 * x4 - x159 * x5
x161 = -x160
x162 = 2.0 * x153 * x2 * x20 * x23 * x28 * x29 * x35 - x45 * x9
x163 = x16 * x162
x164 = x155 * x5 - x163 * x4
x165 = x16 * x164
x166 = x158 + x161 * x5 - x165 * x4
x167 = x166 * x4
x168 = x161 * x6
x169 = 2.0 * x168
x170 = x167 + x169
x171 = x159 * x6
x172 = x161 * x4
x173 = x171 + x172
x174 = x170 * x56 + x173 * x68
x175 = x56 * (x171 + x173)
x176 = x55 * (x174 * x56 + x175 * x68)
x177 = x176 + x21 * x74
x178 = x112 * x7
x179 = x55 * (x171 * x178 + x175 * x56)
x180 = x21 * x55
x181 = x179 + x180 * x77
x182 = -x6 * (x154 + x163)
x183 = 2.0 * x153 * x2 * x20 * x23 * x28 * x29 * x44 - x81 * x9
x184 = (
x166 * x5
- x42 * (x160 + x165)
- x82 * (x164 * x5 + x182 - x82 * (x162 * x5 - x183 * x82))
)
x185 = x184 * x4
x186 = x166 * x6
x187 = 3.0 * x186
x188 = x55 * (x174 * x62 + x56 * (x170 * x62 + x56 * (x185 + x187)))
x189 = x166 * x9
x190 = x189 + x52
x191 = x161 * x9
x192 = x191 + x58
x193 = x192 * x68
x194 = x190 * x56 + x193
x195 = x159 * x9
x196 = x195 + x66
x197 = x196 * x55
x198 = x192 * x56 + x197 * x6
x199 = x55 * (x194 * x56 + x198 * x68)
x200 = x199 + x21 * x97
x201 = x112 * x4
x202 = x201 * x6
x203 = x55 * (x196 * x202 + x198 * x56)
x204 = x100 * x180 + x203
x205 = x184 * x9
x206 = x205 + x85
x207 = x55 * (x194 * x62 + x56 * (x190 * x62 + x206 * x56))
x208 = 0.3333333333333333 * x89
x209 = x102 * x169
x210 = x102 * x167 + x209
x211 = x102 * x171
x212 = x102 * x172 + x211
x213 = x55 * (x210 * x56 + x212 * x68)
x214 = x108 * x21 + x213
x215 = x12 * x201
x216 = x55 * (x171 * x215 + x212 * x56)
x217 = x111 * x180 + x216
x218 = x55 * (x102 * x56 * (x185 + x187) + x210 * x62)
x219 = x91 * (x190 + x52)
x220 = x91 * (x192 + x58)
x221 = x220 * x68
x222 = x55 * (x219 * x56 + x221)
x223 = x115 * x21 + x222
x224 = x197 * x9 + x95
x225 = x55 * (x220 * x56 + x224 * x87)
x226 = x118 * x180 + x225
x227 = x91 * (x206 + x85)
x228 = x55 * (x219 * x62 + x227 * x56)
x229 = x102 * x52
x230 = x102 * x189 + x229
x231 = x102 * x58
x232 = x102 * x191 + x231
x233 = x232 * x68
x234 = x55 * (x230 * x56 + x233)
x235 = x122 * x21 + x234
x236 = x102 * x195 + x106
x237 = x55 * (x232 * x56 + x236 * x87)
x238 = x125 * x180 + x237
x239 = x102 * x85
x240 = x102 * x205 + x239
x241 = x55 * (x230 * x62 + x240 * x56)
x242 = 1.732050807568877 * x208
x243 = x127 * x169
x244 = x55 * (x127 * x167 + x243)
x245 = x129 * x21 + x244
x246 = x127 * x171
x247 = x55 * (x127 * x172 + x246)
x248 = x132 * x180 + x247
x249 = x127 * x55 * (x185 + x187)
x250 = x55 * (x113 * x52 + x219 * x91)
x251 = x136 * x21 + x250
x252 = x55 * (x113 * x58 + x220 * x91)
x253 = x21 * x34
x254 = x134 * x253 + x252
x255 = x55 * (x113 * x85 + x227 * x91)
x256 = x55 * (x120 * x52 + x230 * x91)
x257 = x142 * x21 + x256
x258 = x55 * (x120 * x58 + x232 * x91)
x259 = x140 * x253 + x258
x260 = x55 * (x120 * x85 + x240 * x91)
x261 = x127 * x52
x262 = x55 * (x127 * x189 + x261)
x263 = x147 * x21 + x262
x264 = x127 * x58
x265 = x55 * (x127 * x191 + x264)
x266 = x145 * x253 + x265
x267 = x127 * x85
x268 = x55 * (x127 * x205 + x267)
x269 = x149 * x166
x270 = x151 * x21 + x269
x271 = x149 * x161
x272 = x149 * x253 + x271
x273 = x149 * x184
x274 = -x11 - A[2]
x275 = x12 * x36 - 2.0 * x18 * x2 * x20 * x23 * x274 * x28 * x29
x276 = -x275
x277 = x16 * x276
x278 = x12 * x27 - 2.0 * x2 * x20 * x23 * x274 * x28 * x29 * x30
x279 = -x6 * (x277 + x278)
x280 = -x278
x281 = x277 * x4 - x280 * x5
x282 = -x281
x283 = -x12 * x45 + 2.0 * x2 * x20 * x23 * x274 * x28 * x29 * x35
x284 = x16 * x283
x285 = x276 * x5 - x284 * x4
x286 = x16 * x285
x287 = x279 + x282 * x5 - x286 * x4
x288 = x287 * x4
x289 = x282 * x6
x290 = 2.0 * x289
x291 = x288 + x290
x292 = x280 * x6
x293 = x282 * x4
x294 = x292 + x293
x295 = x291 * x56 + x294 * x68
x296 = x56 * (x292 + x294)
x297 = x55 * (x295 * x56 + x296 * x68)
x298 = x22 * x74 + x297
x299 = x55 * (x178 * x292 + x296 * x56)
x300 = x22 * x55
x301 = x299 + x300 * x77
x302 = -x6 * (x275 + x284)
x303 = -x12 * x81 + 2.0 * x2 * x20 * x23 * x274 * x28 * x29 * x44
x304 = (
x287 * x5
- x42 * (x281 + x286)
- x82 * (x285 * x5 + x302 - x82 * (x283 * x5 - x303 * x82))
)
x305 = x304 * x4
x306 = x287 * x6
x307 = 3.0 * x306
x308 = x55 * (x295 * x62 + x56 * (x291 * x62 + x56 * (x305 + x307)))
x309 = x91 * (x288 + x290)
x310 = x292 * x91
x311 = x293 * x91 + x310
x312 = x55 * (x309 * x56 + x311 * x68)
x313 = x22 * x97 + x312
x314 = x119 * x4
x315 = x55 * (x292 * x314 + x311 * x56)
x316 = x100 * x300 + x315
x317 = x55 * (x309 * x62 + x56 * x91 * (x305 + x307))
x318 = x12 * x287 + x52
x319 = x12 * x282 + x58
x320 = x319 * x68
x321 = x318 * x56 + x320
x322 = x12 * x280 + x66
x323 = x322 * x87
x324 = x319 * x56 + x323
x325 = x55 * (x321 * x56 + x324 * x68)
x326 = x108 * x22 + x325
x327 = x55 * (x202 * x322 + x324 * x56)
x328 = x111 * x300 + x327
x329 = x12 * x304 + x85
x330 = x55 * (x321 * x62 + x56 * (x318 * x62 + x329 * x56))
x331 = x113 * x55 * (x288 + x290)
x332 = x115 * x22 + x331
x333 = x113 * x292
x334 = x55 * (x113 * x293 + x333)
x335 = x118 * x300 + x334
x336 = x113 * x55 * (x305 + x307)
x337 = x119 * x42
x338 = x55 * (x314 * x318 + x319 * x337)
x339 = x122 * x22 + x338
x340 = x119 * x6
x341 = x322 * x340
x342 = x55 * (x314 * x319 + x341)
x343 = x125 * x300 + x342
x344 = x55 * (x119 * x318 * x61 + x314 * x329)
x345 = x102 * x318 + x229
x346 = x102 * x319 + x231
x347 = x346 * x68
x348 = x55 * (x345 * x56 + x347)
x349 = x129 * x22 + x348
x350 = x102 * x322 + x106
x351 = x350 * x87
x352 = x55 * (x346 * x56 + x351)
x353 = x132 * x300 + x352
x354 = x102 * x329 + x239
x355 = x55 * (x345 * x62 + x354 * x56)
x356 = x134 * x287
x357 = x136 * x22 + x356
x358 = x134 * x282
x359 = x22 * x34
x360 = x134 * x359 + x358
x361 = x134 * x304
x362 = x139 * x318
x363 = x142 * x22 + x362
x364 = x139 * x319
x365 = x140 * x359 + x364
x366 = x139 * x329
x367 = x119 * x345
x368 = x147 * x22 + x367
x369 = x119 * x346
x370 = x145 * x359 + x369
x371 = x119 * x354
x372 = x55 * (x102 * x345 + x261)
x373 = x151 * x22 + x372
x374 = x55 * (x102 * x346 + x264)
x375 = x149 * x359 + x374
x376 = x55 * (x102 * x354 + x267)
x377 = x156 * x9
x378 = x153 * x159 + x32 - x377
x379 = x378 * x6
x380 = x153 * x155 - x163 * x9 + x43
x381 = x16 * x380
x382 = x378 * x5 - x381 * x4
x383 = x382 * x4
x384 = x379 + x383
x385 = x56 * (x379 + x384)
x386 = x55 * (x178 * x379 + x385 * x56)
x387 = x179 * x21 + x386
x388 = x181 * x21 + x387
x389 = x6 * (x153 * x159 - x377 - x381 - x79)
x390 = x16 * x9
x391 = x153 * x162 - x183 * x390 + x80
x392 = x382 * x5 + x389 - x82 * (x380 * x5 - x391 * x82)
x393 = x392 * x4
x394 = x382 * x6
x395 = 2.0 * x394
x396 = x176 * x21 + x55 * (x385 * x68 + x56 * (x384 * x68 + x56 * (x393 + x395)))
x397 = x378 * x9
x398 = 2.0 * x171
x399 = x397 + x398
x400 = x382 * x9
x401 = x169 + x400
x402 = x399 * x87 + x401 * x56
x403 = x55 * (x202 * x399 + x402 * x56)
x404 = x203 * x21 + x403
x405 = x204 * x21 + x404
x406 = x392 * x9
x407 = 2.0 * x186
x408 = x406 + x407
x409 = x199 * x21 + x55 * (x402 * x68 + x56 * (x401 * x68 + x408 * x56))
x410 = x102 * x379
x411 = x102 * x383 + x410
x412 = x55 * (x215 * x379 + x411 * x56)
x413 = x21 * x216 + x412
x414 = x21 * x217 + x413
x415 = x21 * x213 + x55 * (x102 * x56 * (x393 + x395) + x411 * x68)
x416 = x197 * x42 + x399 * x91
x417 = x193 + x401 * x91
x418 = x55 * (x416 * x87 + x417 * x56)
x419 = x21 * x225 + x418
x420 = x21 * x226 + x419
x421 = x190 * x68 + x408 * x91
x422 = x21 * x222 + x55 * (x417 * x68 + x421 * x56)
x423 = x102 * (x397 + x398)
x424 = x102 * x400 + x209
x425 = x55 * (x423 * x87 + x424 * x56)
x426 = x21 * x237 + x425
x427 = x21 * x238 + x426
x428 = x102 * (x406 + x407)
x429 = x21 * x234 + x55 * (x424 * x68 + x428 * x56)
x430 = x127 * x379
x431 = x55 * (x127 * x383 + x430)
x432 = x21 * x247 + x431
x433 = x21 * x248 + x432
x434 = x127 * x55 * (x393 + x395) + x21 * x244
x435 = x55 * (x221 + x417 * x91)
x436 = x21 * x252 + x435
x437 = x21 * x254 + x436
x438 = x21 * x250 + x55 * (x219 * x68 + x421 * x91)
x439 = x55 * (x233 + x424 * x91)
x440 = x21 * x258 + x439
x441 = x21 * x259 + x440
x442 = x21 * x256 + x55 * (x230 * x68 + x428 * x91)
x443 = x55 * (x127 * x400 + x243)
x444 = x21 * x265 + x443
x445 = x21 * x266 + x444
x446 = x127 * x55 * (x406 + x407) + x21 * x262
x447 = x149 * x382
x448 = x21 * x271 + x447
x449 = x21 * x272 + x448
x450 = x149 * x392 + x21 * x269
x451 = -x153 * x280 + x277 * x9
x452 = -x451
x453 = x452 * x6
x454 = x153 * x276 - x284 * x9
x455 = x16 * x454
x456 = -x4 * x455 + x452 * x5
x457 = x4 * x456 + x453
x458 = x56 * (x453 + x457)
x459 = x55 * (x178 * x453 + x458 * x56)
x460 = x179 * x22 + x459
x461 = x21 * x301 + x460
x462 = -x6 * (x451 + x455)
x463 = x153 * x283 - x303 * x390
x464 = x456 * x5 + x462 - x82 * (x454 * x5 - x463 * x82)
x465 = x42 * x456
x466 = x55 * (x458 * x68 + x56 * (x457 * x68 + x56 * (x4 * x464 + x465)))
x467 = x176 * x22 + x466
x468 = x292 + x452 * x9
x469 = x289 + x456 * x9
x470 = x468 * x87 + x469 * x56
x471 = x55 * (x202 * x468 + x470 * x56)
x472 = x203 * x22 + x471
x473 = x21 * x316 + x472
x474 = x306 + x464 * x9
x475 = x469 * x68
x476 = x55 * (x470 * x68 + x56 * (x474 * x56 + x475))
x477 = x199 * x22 + x476
x478 = x12 * x452 + x171
x479 = x12 * x456 + x168
x480 = x478 * x87 + x479 * x56
x481 = x55 * (x202 * x478 + x480 * x56)
x482 = x216 * x22 + x481
x483 = x21 * x328 + x482
x484 = x12 * x464 + x186
x485 = x479 * x68
x486 = x55 * (x480 * x68 + x56 * (x484 * x56 + x485))
x487 = x213 * x22 + x486
x488 = x310 + x468 * x91
x489 = x91 * (x289 + x469)
x490 = x55 * (x488 * x87 + x489 * x56)
x491 = x22 * x225 + x490
x492 = x21 * x335 + x491
x493 = x91 * (x306 + x474)
x494 = x489 * x68
x495 = x55 * (x493 * x56 + x494)
x496 = x22 * x222 + x495
x497 = x323 + x478 * x91
x498 = x319 * x87 + x479 * x91
x499 = x55 * (x497 * x87 + x498 * x56)
x500 = x22 * x237 + x499
x501 = x21 * x343 + x500
x502 = x318 * x87 + x484 * x91
x503 = x498 * x68
x504 = x55 * (x502 * x56 + x503)
x505 = x22 * x234 + x504
x506 = x102 * x478 + x211
x507 = x102 * (x168 + x479)
x508 = x55 * (x506 * x87 + x507 * x56)
x509 = x22 * x247 + x508
x510 = x21 * x353 + x509
x511 = x102 * (x186 + x484)
x512 = x507 * x68
x513 = x55 * (x511 * x56 + x512)
x514 = x22 * x244 + x513
x515 = x55 * (x113 * x289 + x489 * x91)
x516 = x22 * x252 + x515
x517 = x21 * x360 + x516
x518 = x55 * (x113 * x306 + x493 * x91)
x519 = x22 * x250 + x518
x520 = x55 * (x319 * x340 + x498 * x91)
x521 = x22 * x258 + x520
x522 = x21 * x365 + x521
x523 = x55 * (x318 * x340 + x502 * x91)
x524 = x22 * x256 + x523
x525 = x55 * (x346 * x87 + x507 * x91)
x526 = x22 * x265 + x525
x527 = x21 * x370 + x526
x528 = x55 * (x345 * x87 + x511 * x91)
x529 = x22 * x262 + x528
x530 = x55 * (x102 * x507 + x127 * x168)
x531 = x22 * x271 + x530
x532 = x21 * x375 + x531
x533 = x55 * (x102 * x511 + x127 * x186)
x534 = x22 * x269 + x533
x535 = x12 * x277
x536 = x274 * x280 + x32 - x535
x537 = x536 * x6
x538 = -x12 * x284 + x274 * x276 + x43
x539 = x16 * x538
x540 = -x4 * x539 + x5 * x536
x541 = x4 * x540
x542 = x537 + x541
x543 = x56 * (x537 + x542)
x544 = x55 * (x178 * x537 + x543 * x56)
x545 = x22 * x299 + x544
x546 = x22 * x301 + x545
x547 = x6 * (x274 * x280 - x535 - x539 - x79)
x548 = x12 * x16
x549 = x274 * x283 - x303 * x548 + x80
x550 = x5 * x540 + x547 - x82 * (x5 * x538 - x549 * x82)
x551 = x4 * x550
x552 = x540 * x6
x553 = 2.0 * x552
x554 = x22 * x297 + x55 * (x543 * x68 + x56 * (x542 * x68 + x56 * (x551 + x553)))
x555 = x537 * x91
x556 = x541 * x91 + x555
x557 = x55 * (x314 * x537 + x556 * x56)
x558 = x22 * x315 + x557
x559 = x22 * x316 + x558
x560 = x22 * x312 + x55 * (x556 * x68 + x56 * x91 * (x551 + x553))
x561 = x12 * x536 + 2.0 * x292
x562 = x561 * x87
x563 = x12 * x540 + x290
x564 = x56 * x563 + x562
x565 = x55 * (x202 * x561 + x56 * x564)
x566 = x22 * x327 + x565
x567 = x22 * x328 + x566
x568 = x12 * x550 + 2.0 * x306
x569 = x22 * x325 + x55 * (x56 * (x56 * x568 + x563 * x68) + x564 * x68)
x570 = x113 * x537
x571 = x55 * (x113 * x541 + x570)
x572 = x22 * x334 + x571
x573 = x22 * x335 + x572
x574 = x113 * x55 * (x551 + x553) + x22 * x331
x575 = x340 * x561
x576 = x55 * (x314 * x563 + x575)
x577 = x22 * x342 + x576
x578 = x22 * x343 + x577
x579 = x22 * x338 + x55 * (x314 * x568 + x337 * x563)
x580 = x102 * x561 + x322 * x68
x581 = x580 * x87
x582 = x102 * x563 + x320
x583 = x55 * (x56 * x582 + x581)
x584 = x22 * x352 + x583
x585 = x22 * x353 + x584
x586 = x102 * x568 + x318 * x68
x587 = x22 * x348 + x55 * (x56 * x586 + x582 * x68)
x588 = x134 * x540
x589 = x22 * x358 + x588
x590 = x22 * x360 + x589
x591 = x134 * x550 + x22 * x356
x592 = x139 * x563
x593 = x22 * x364 + x592
x594 = x22 * x365 + x593
x595 = x139 * x568 + x22 * x362
x596 = x119 * x582
x597 = x22 * x369 + x596
x598 = x22 * x370 + x597
x599 = x119 * x586 + x22 * x367
x600 = x55 * (x102 * x582 + x347)
x601 = x22 * x374 + x600
x602 = x22 * x375 + x601
x603 = x22 * x372 + x55 * (x102 * x586 + x345 * x68)
x604 = x153 * x378 + 2.0 * x158 - x381 * x9
x605 = x6 * x604
x606 = x153 * x380 + 2.0 * x182 - x390 * x391
x607 = x5 * x604 - x606 * x82
x608 = x4 * x607
x609 = x21 * x386 + x21 * x387 + x55 * (x178 * x605 + x56**2 * (2.0 * x605 + x608))
x610 = x604 * x9
x611 = 3.0 * x379
x612 = x610 + x611
x613 = x612 * x87
x614 = x607 * x9
x615 = 3.0 * x394
x616 = x614 + x615
x617 = x21 * x403 + x21 * x404 + x55 * (x202 * x612 + x56 * (x56 * x616 + x613))
x618 = x102 * x605
x619 = x21 * x412 + x21 * x413 + x55 * (x215 * x605 + x56 * (x102 * x608 + x618))
x620 = x399 * x62 + x612 * x91
x621 = x620 * x87
x622 = x401 * x62 + x616 * x91
x623 = x21 * x418 + x21 * x419 + x55 * (x56 * x622 + x621)
x624 = x102 * (x610 + x611)
x625 = x624 * x87
x626 = x102 * (x614 + x615)
x627 = x21 * x425 + x21 * x426 + x55 * (x56 * x626 + x625)
x628 = x127 * x605
x629 = x21 * x431 + x21 * x432 + x55 * (x127 * x608 + x628)
x630 = x21 * x435 + x21 * x436 + x55 * (x417 * x62 + x622 * x91)
x631 = x21 * x439 + x21 * x440 + x55 * (x424 * x62 + x626 * x91)
x632 = x127 * x55 * (x614 + x615) + x21 * x443 + x21 * x444
x633 = x149 * x607 + x21 * x447 + x21 * x448
x634 = x153 * x452 + x279 - x455 * x9
x635 = x6 * x634
x636 = x153 * x454 + x302 - x390 * x463
x637 = x5 * x634 - x636 * x82
x638 = x55 * (x178 * x635 + x56**2 * (x4 * x637 + 2.0 * x635))
x639 = x21 * x460 + x22 * x386 + x638
x640 = 2.0 * x453
x641 = x634 * x9 + x640
x642 = x465 + x637 * x9
x643 = x55 * (x202 * x641 + x56 * (x56 * x642 + x641 * x87))
x644 = x21 * x472 + x22 * x403 + x643
x645 = x12 * x634 + x379
x646 = x12 * x637 + x394
x647 = x55 * (x202 * x645 + x56 * (x56 * x646 + x645 * x87))
x648 = x21 * x482 + x22 * x412 + x647
x649 = x468 * x68 + x641 * x91
x650 = x475 + x642 * x91
x651 = x55 * (x56 * x650 + x649 * x87)
x652 = x21 * x491 + x22 * x418 + x651
x653 = x478 * x68
x654 = x645 * x91 + x653
x655 = x485 + x646 * x91
x656 = x55 * (x56 * x655 + x654 * x87)
x657 = x21 * x500 + x22 * x425 + x656
x658 = x102 * x645 + x410
x659 = x102 * (x394 + x646)
x660 = x55 * (x56 * x659 + x658 * x87)
x661 = x21 * x509 + x22 * x431 + x660
x662 = x55 * (x494 + x650 * x91)
x663 = x21 * x516 + x22 * x435 + x662
x664 = x55 * (x503 + x655 * x91)
x665 = x21 * x521 + x22 * x439 + x664
x666 = x55 * (x512 + x659 * x91)
x667 = x21 * x526 + x22 * x443 + x666
x668 = x55 * (x102 * x659 + x127 * x394)
x669 = x21 * x531 + x22 * x447 + x668
x670 = x153 * x536 - x539 * x9
x671 = x6 * x670
x672 = x153 * x538 - x390 * x549
x673 = x5 * x670 - x672 * x82
x674 = x22 * x459 + x55 * (x178 * x671 + x56**2 * (x4 * x673 + 2.0 * x671))
x675 = x22 * x460 + x674
x676 = x537 + x670 * x9
x677 = x552 + x673 * x9
x678 = x22 * x471 + x55 * (x202 * x676 + x56 * (x56 * x677 + x676 * x87))
x679 = x22 * x472 + x678
x680 = x12 * x670 + x640
x681 = x12 * x673 + x465
x682 = x22 * x481 + x55 * (x202 * x680 + x56 * (x56 * x681 + x680 * x87))
x683 = x22 * x482 + x682
x684 = x555 + x676 * x91
x685 = x91 * (x552 + x677)
x686 = x22 * x490 + x55 * (x56 * x685 + x684 * x87)
x687 = x22 * x491 + x686
x688 = x562 + x680 * x91
x689 = x563 * x87 + x681 * x91
x690 = x22 * x499 + x55 * (x56 * x689 + x688 * x87)
x691 = x22 * x500 + x690
x692 = x102 * x680 + x653
x693 = x102 * x681 + x485
x694 = x22 * x508 + x55 * (x56 * x693 + x692 * x87)
x695 = x22 * x509 + x694
x696 = x22 * x515 + x55 * (x113 * x552 + x685 * x91)
x697 = x22 * x516 + x696
x698 = x22 * x520 + x55 * (x340 * x563 + x689 * x91)
x699 = x22 * x521 + x698
x700 = x22 * x525 + x55 * (x582 * x87 + x693 * x91)
x701 = x22 * x526 + x700
x702 = x22 * x530 + x55 * (x102 * x693 + x512)
x703 = x22 * x531 + x702
x704 = -x12 * x539 + x274 * x536 + 2.0 * x279
x705 = x6 * x704
x706 = x274 * x538 + 2.0 * x302 - x548 * x549
x707 = x5 * x704 - x706 * x82
x708 = x4 * x707
x709 = x22 * x544 + x22 * x545 + x55 * (x178 * x705 + x56**2 * (2.0 * x705 + x708))
x710 = x705 * x91
x711 = x22 * x557 + x22 * x558 + x55 * (x314 * x705 + x56 * (x708 * x91 + x710))
x712 = x12 * x704 + 3.0 * x537
x713 = x712 * x87
x714 = x12 * x707 + 3.0 * x552
x715 = x22 * x565 + x22 * x566 + x55 * (x202 * x712 + x56 * (x56 * x714 + x713))
x716 = x113 * x705
x717 = x22 * x571 + x22 * x572 + x55 * (x113 * x708 + x716)
x718 = x340 * x712
x719 = x22 * x576 + x22 * x577 + x55 * (x314 * x714 + x718)
x720 = x102 * x712 + x561 * x62
x721 = x720 * x87
x722 = x102 * x714 + x563 * x62
x723 = x22 * x583 + x22 * x584 + x55 * (x56 * x722 + x721)
x724 = x134 * x707 + x22 * x588 + x22 * x589
x725 = x139 * x714 + x22 * x592 + x22 * x593
x726 = x119 * x722 + x22 * x596 + x22 * x597
x727 = x22 * x600 + x22 * x601 + x55 * (x102 * x722 + x582 * x62)
x728 = x0 * x179 + x176
x729 = x133 * x4**3
x730 = x0 * x159
x731 = x0 * x203 + x199
x732 = x133 * x7
x733 = x196 * x732
x734 = x0 * x216 + x213
x735 = x12 * x732
x736 = x0 * x225 + x222
x737 = x0 * x201
x738 = x0 * x237 + x234
x739 = x0 * x247 + x244
x740 = x144 * x4
x741 = x0 * x252 + x250
x742 = x117 + x224 * x91
x743 = x0 * x258 + x256
x744 = x124 + x236 * x91
x745 = x0 * x265 + x262
x746 = x127 * x195 + x131
x747 = x0 * x271 + x269
x748 = x378 * x729
x749 = x159 * x21
x750 = x729 * x749 + x748
x751 = x399 * x732
x752 = x21 * x733 + x751
x753 = x378 * x735
x754 = x735 * x749 + x753
x755 = x201 * x416
x756 = x201 * x21
x757 = x224 * x756 + x755
x758 = x201 * x423
x759 = x236 * x756 + x758
x760 = x378 * x740
x761 = x740 * x749 + x760
x762 = x55 * (x224 * x68 + x416 * x91)
x763 = x180 * x742 + x762
x764 = x55 * (x236 * x68 + x423 * x91)
x765 = x180 * x744 + x764
x766 = x127 * x55 * (x397 + x398)
x767 = x180 * x746 + x766
x768 = x149 * x378
x769 = x149 * x749 + x768
x770 = x452 * x729
x771 = x159 * x22
x772 = x729 * x771 + x770
x773 = x468 * x732
x774 = x22 * x733 + x773
x775 = x478 * x732
x776 = x735 * x771 + x775
x777 = x201 * x488
x778 = x201 * x22
x779 = x224 * x778 + x777
x780 = x201 * x497
x781 = x236 * x778 + x780
x782 = x201 * x506
x783 = x740 * x771 + x782
x784 = x55 * (x333 + x488 * x91)
x785 = x300 * x742 + x784
x786 = x55 * (x341 + x497 * x91)
x787 = x300 * x744 + x786
x788 = x55 * (x351 + x506 * x91)
x789 = x300 * x746 + x788
x790 = x55 * (x102 * x506 + x246)
x791 = x149 * x771 + x790
x792 = x604 * x729
x793 = x21 * x748 + x792
x794 = x21 * x750 + x793
x795 = x612 * x732
x796 = x21 * x751 + x795
x797 = x21 * x752 + x796
x798 = x604 * x735
x799 = x21 * x753 + x798
x800 = x21 * x754 + x799
x801 = x201 * x620
x802 = x21 * x755 + x801
x803 = x21 * x757 + x802
x804 = x201 * x624
x805 = x21 * x758 + x804
x806 = x21 * x759 + x805
x807 = x604 * x740
x808 = x21 * x760 + x807
x809 = x21 * x761 + x808
x810 = x55 * (x416 * x62 + x620 * x91)
x811 = x21 * x762 + x810
x812 = x21 * x763 + x811
x813 = x55 * (x423 * x62 + x624 * x91)
x814 = x21 * x764 + x813
x815 = x21 * x765 + x814
x816 = x127 * x55 * (x610 + x611)
x817 = x21 * x766 + x816
x818 = x21 * x767 + x817
x819 = x149 * x604
x820 = x21 * x768 + x819
x821 = x21 * x769 + x820
x822 = x634 * x729
x823 = x22 * x748 + x822
x824 = x21 * x772 + x823
x825 = x641 * x732
x826 = x22 * x751 + x825
x827 = x21 * x774 + x826
x828 = x645 * x732
x829 = x22 * x753 + x828
x830 = x21 * x776 + x829
x831 = x201 * x649
x832 = x22 * x755 + x831
x833 = x21 * x779 + x832
x834 = x201 * x654
x835 = x22 * x758 + x834
x836 = x21 * x781 + x835
x837 = x201 * x658
x838 = x22 * x760 + x837
x839 = x21 * x783 + x838
x840 = x55 * (x488 * x68 + x649 * x91)
x841 = x22 * x762 + x840
x842 = x21 * x785 + x841
x843 = x55 * (x497 * x68 + x654 * x91)
x844 = x22 * x764 + x843
x845 = x21 * x787 + x844
x846 = x506 * x68
x847 = x55 * (x658 * x91 + x846)
x848 = x22 * x766 + x847
x849 = x21 * x789 + x848
x850 = x55 * (x102 * x658 + x430)
x851 = x22 * x768 + x850
x852 = x21 * x791 + x851
x853 = x670 * x729
x854 = x22 * x770 + x853
x855 = x22 * x772 + x854
x856 = x676 * x732
x857 = x22 * x773 + x856
x858 = x22 * x774 + x857
x859 = x680 * x732
x860 = x22 * x775 + x859
x861 = x22 * x776 + x860
x862 = x201 * x684
x863 = x22 * x777 + x862
x864 = x22 * x779 + x863
x865 = x201 * x688
x866 = x22 * x780 + x865
x867 = x22 * x781 + x866
x868 = x201 * x692
x869 = x22 * x782 + x868
x870 = x22 * x783 + x869
x871 = x55 * (x570 + x684 * x91)
x872 = x22 * x784 + x871
x873 = x22 * x785 + x872
x874 = x55 * (x575 + x688 * x91)
x875 = x22 * x786 + x874
x876 = x22 * x787 + x875
x877 = x55 * (x581 + x692 * x91)
x878 = x22 * x788 + x877
x879 = x22 * x789 + x878
x880 = x55 * (x102 * x692 + x846)
x881 = x22 * x790 + x880
x882 = x22 * x791 + x881
x883 = x153 * x604 + 3.0 * x389 - x390 * x606
x884 = x883 * x9
x885 = 4.0 * x605
x886 = x884 + x885
x887 = 4.0 * x613 + x886 * x91
x888 = x102 * (x884 + x885)
x889 = x153 * x634 - x390 * x636 + 2.0 * x462
x890 = x729 * x889
x891 = 3.0 * x635 + x889 * x9
x892 = x732 * x891
x893 = x12 * x889 + x605
x894 = x732 * x893
x895 = x62 * x641 + x891 * x91
x896 = x201 * x895
x897 = x62 * x645 + x893 * x91
x898 = x201 * x897
x899 = x102 * x893 + x618
x900 = x201 * x899
x901 = x55 * (x62 * x649 + x895 * x91)
x902 = x55 * (x62 * x654 + x897 * x91)
x903 = x55 * (x62 * x658 + x899 * x91)
x904 = x55 * (x102 * x899 + x628)
x905 = x153 * x670 - x390 * x672 + x547
x906 = x22 * x822 + x729 * x905
x907 = 2.0 * x671 + x9 * x905
x908 = x22 * x825 + x732 * x907
x909 = x12 * x905 + 2.0 * x635
x910 = x22 * x828 + x732 * x909
x911 = x676 * x68 + x907 * x91
x912 = x201 * x911 + x22 * x831
x913 = x68 * x680 + x909 * x91
x914 = x201 * x913 + x22 * x834
x915 = x102 * x909 + x645 * x68
x916 = x201 * x915 + x22 * x837
x917 = x22 * x840 + x55 * (x68 * x684 + x91 * x911)
x918 = x22 * x843 + x55 * (x68 * x688 + x91 * x913)
x919 = x22 * x847 + x55 * (x68 * x692 + x91 * x915)
x920 = x22 * x850 + x55 * (x102 * x915 + x658 * x68)
x921 = x153 * x704 - x390 * x706
x922 = x22 * x853 + x22 * x854 + x729 * x921
x923 = x705 + x9 * x921
x924 = x22 * x856 + x22 * x857 + x732 * x923
x925 = x12 * x921 + 3.0 * x671
x926 = x22 * x859 + x22 * x860 + x732 * x925
x927 = x710 + x91 * x923
x928 = x201 * x927 + x22 * x862 + x22 * x863
x929 = x713 + x91 * x925
x930 = x201 * x929 + x22 * x865 + x22 * x866
x931 = x102 * x925 + x62 * x680
x932 = x201 * x931 + x22 * x868 + x22 * x869
x933 = x22 * x871 + x22 * x872 + x55 * (x716 + x91 * x927)
x934 = x22 * x874 + x22 * x875 + x55 * (x718 + x91 * x929)
x935 = x22 * x877 + x22 * x878 + x55 * (x721 + x91 * x931)
x936 = x22 * x880 + x22 * x881 + x55 * (x102 * x931 + x62 * x692)
x937 = x0 * x299 + x297
x938 = x0 * x280
x939 = x0 * x315 + x312
x940 = x732 * x9
x941 = x0 * x327 + x325
x942 = x0 * x322
x943 = x0 * x334 + x331
x944 = x139 * x4
x945 = x0 * x342 + x338
x946 = x133 * x99
x947 = x0 * x352 + x348
x948 = x0 * x358 + x356
x949 = x0 * x364 + x362
x950 = x0 * x369 + x367
x951 = x119 * x350
x952 = x0 * x374 + x372
x953 = x102 * x350 + x131
x954 = x21 * x299 + x459
x955 = x21 * x280
x956 = x729 * x955 + x770
x957 = x21 * x315 + x471
x958 = x773 + x940 * x955
x959 = x21 * x327 + x481
x960 = x21 * x322
x961 = x732 * x960 + x775
x962 = x21 * x334 + x490
x963 = x777 + x944 * x955
x964 = x21 * x342 + x499
x965 = x780 + x946 * x960
x966 = x21 * x352 + x508
x967 = x350 * x756 + x782
x968 = x21 * x358 + x515
x969 = x134 * x955 + x784
x970 = x21 * x364 + x520
x971 = x139 * x960 + x786
x972 = x21 * x369 + x525
x973 = x21 * x951 + x788
x974 = x21 * x374 + x530
x975 = x180 * x953 + x790
x976 = x536 * x729
x977 = x22 * x280
x978 = x729 * x977 + x976
x979 = x536 * x940
x980 = x940 * x977 + x979
x981 = x561 * x732
x982 = x22 * x322
x983 = x732 * x982 + x981
x984 = x536 * x944
x985 = x944 * x977 + x984
x986 = x561 * x946
x987 = x946 * x982 + x986
x988 = x201 * x580
x989 = x350 * x778 + x988
x990 = x134 * x536
x991 = x134 * x977 + x990
x992 = x139 * x561
x993 = x139 * x982 + x992
x994 = x119 * x580
x995 = x22 * x951 + x994
x996 = x55 * (x102 * x580 + x350 * x68)
x997 = x300 * x953 + x996
x998 = x21 * x770 + x822
x999 = x21 * x956 + x998
x1000 = x21 * x773 + x825
x1001 = x1000 + x21 * x958
x1002 = x21 * x775 + x828
x1003 = x1002 + x21 * x961
x1004 = x21 * x777 + x831
x1005 = x1004 + x21 * x963
x1006 = x21 * x780 + x834
x1007 = x1006 + x21 * x965
x1008 = x21 * x782 + x837
x1009 = x1008 + x21 * x967
x1010 = x21 * x784 + x840
x1011 = x1010 + x21 * x969
x1012 = x21 * x786 + x843
x1013 = x1012 + x21 * x971
x1014 = x21 * x788 + x847
x1015 = x1014 + x21 * x973
x1016 = x21 * x790 + x850
x1017 = x1016 + x21 * x975
x1018 = x21 * x978 + x854
x1019 = x21 * x980 + x857
x1020 = x21 * x983 + x860
x1021 = x21 * x985 + x863
x1022 = x21 * x987 + x866
x1023 = x21 * x989 + x869
x1024 = x21 * x991 + x872
x1025 = x21 * x993 + x875
x1026 = x21 * x995 + x878
x1027 = x21 * x997 + x881
x1028 = x704 * x729
x1029 = x1028 + x22 * x976
x1030 = x1029 + x22 * x978
x1031 = x704 * x940
x1032 = x1031 + x22 * x979
x1033 = x1032 + x22 * x980
x1034 = x712 * x732
x1035 = x1034 + x22 * x981
x1036 = x1035 + x22 * x983
x1037 = x704 * x944
x1038 = x1037 + x22 * x984
x1039 = x1038 + x22 * x985
x1040 = x712 * x946
x1041 = x1040 + x22 * x986
x1042 = x1041 + x22 * x987
x1043 = x201 * x720
x1044 = x1043 + x22 * x988
x1045 = x1044 + x22 * x989
x1046 = x134 * x704
x1047 = x1046 + x22 * x990
x1048 = x1047 + x22 * x991
x1049 = x139 * x712
x1050 = x1049 + x22 * x992
x1051 = x1050 + x22 * x993
x1052 = x119 * x720
x1053 = x1052 + x22 * x994
x1054 = x1053 + x22 * x995
x1055 = x55 * (x102 * x720 + x580 * x62)
x1056 = x1055 + x22 * x996
x1057 = x1056 + x22 * x997
x1058 = x274 * x704 + 3.0 * x547 - x548 * x706
x1059 = x1058 * x12 + 4.0 * x705
x1060 = x102 * x1059 + 4.0 * x713
# 300 item(s)
result[0, 0, 0] = numpy.sum(
x90
* (
x0 * x70
+ x0 * x75
+ x0 * (x0 * (x74 + x77 * x78) + x75)
+ x55 * (x56 * (x54 * x88 + x56 * (x84 + x86)) + x63 * x88)
)
)
result[0, 0, 1] = numpy.sum(
x101
* (
x0 * x94
+ x0 * x98
+ x0 * (x0 * (x100 * x78 + x97) + x98)
+ x55 * (x56 * x91 * (x84 + x86) + x88 * x92)
)
)
result[0, 0, 2] = numpy.sum(
x101
* (
x0 * x105
+ x0 * x109
+ x0 * (x0 * (x108 + x111 * x78) + x109)
+ x55 * (x102 * x56 * (x84 + x86) + x103 * x88)
)
)
result[0, 0, 3] = numpy.sum(
x101
* (
x0 * x114
+ x0 * x116
+ x0 * (x0 * (x115 + x118 * x78) + x116)
+ x113 * x55 * (x84 + x86)
)
)
result[0, 0, 4] = numpy.sum(
x126
* (
x0 * x121
+ x0 * x123
+ x0 * (x0 * (x122 + x125 * x78) + x123)
+ x120 * x55 * (x84 + x86)
)
)
result[0, 0, 5] = numpy.sum(
x101
* (
x0 * x128
+ x0 * x130
+ x0 * (x0 * (x129 + x132 * x78) + x130)
+ x127 * x55 * (x84 + x86)
)
)
result[0, 0, 6] = numpy.sum(
x90
* (x0 * x135 + x0 * x137 + x0 * (x0 * (x134 * x138 + x136) + x137) + x134 * x83)
)
result[0, 0, 7] = numpy.sum(
x101
* (x0 * x141 + x0 * x143 + x0 * (x0 * (x138 * x140 + x142) + x143) + x140 * x83)
)
result[0, 0, 8] = numpy.sum(
x101
* (x0 * x146 + x0 * x148 + x0 * (x0 * (x138 * x145 + x147) + x148) + x145 * x83)
)
result[0, 0, 9] = numpy.sum(
x90
* (x0 * x150 + x0 * x152 + x0 * (x0 * (x138 * x149 + x151) + x152) + x149 * x83)
)
result[0, 1, 0] = numpy.sum(
x101 * (x0 * x177 + x0 * (x0 * x181 + x177) + x188 + x21 * x70)
)
result[0, 1, 1] = numpy.sum(
x208 * (x0 * x200 + x0 * (x0 * x204 + x200) + x207 + x21 * x94)
)
result[0, 1, 2] = numpy.sum(
x208 * (x0 * x214 + x0 * (x0 * x217 + x214) + x105 * x21 + x218)
)
result[0, 1, 3] = numpy.sum(
x208 * (x0 * x223 + x0 * (x0 * x226 + x223) + x114 * x21 + x228)
)
result[0, 1, 4] = numpy.sum(
x242 * (x0 * x235 + x0 * (x0 * x238 + x235) + x121 * x21 + x241)
)
result[0, 1, 5] = numpy.sum(
x208 * (x0 * x245 + x0 * (x0 * x248 + x245) + x128 * x21 + x249)
)
result[0, 1, 6] = numpy.sum(
x101 * (x0 * x251 + x0 * (x0 * x254 + x251) + x135 * x21 + x255)
)
result[0, 1, 7] = numpy.sum(
x208 * (x0 * x257 + x0 * (x0 * x259 + x257) + x141 * x21 + x260)
)
result[0, 1, 8] = numpy.sum(
x208 * (x0 * x263 + x0 * (x0 * x266 + x263) + x146 * x21 + x268)
)
result[0, 1, 9] = numpy.sum(
x101 * (x0 * x270 + x0 * (x0 * x272 + x270) + x150 * x21 + x273)
)
result[0, 2, 0] = numpy.sum(
x101 * (x0 * x298 + x0 * (x0 * x301 + x298) + x22 * x70 + x308)
)
result[0, 2, 1] = numpy.sum(
x208 * (x0 * x313 + x0 * (x0 * x316 + x313) + x22 * x94 + x317)
)
result[0, 2, 2] = numpy.sum(
x208 * (x0 * x326 + x0 * (x0 * x328 + x326) + x105 * x22 + x330)
)
result[0, 2, 3] = numpy.sum(
x208 * (x0 * x332 + x0 * (x0 * x335 + x332) + x114 * x22 + x336)
)
result[0, 2, 4] = numpy.sum(
x242 * (x0 * x339 + x0 * (x0 * x343 + x339) + x121 * x22 + x344)
)
result[0, 2, 5] = numpy.sum(
x208 * (x0 * x349 + x0 * (x0 * x353 + x349) + x128 * x22 + x355)
)
result[0, 2, 6] = numpy.sum(
x101 * (x0 * x357 + x0 * (x0 * x360 + x357) + x135 * x22 + x361)
)
result[0, 2, 7] = numpy.sum(
x208 * (x0 * x363 + x0 * (x0 * x365 + x363) + x141 * x22 + x366)
)
result[0, 2, 8] = numpy.sum(
x208 * (x0 * x368 + x0 * (x0 * x370 + x368) + x146 * x22 + x371)
)
result[0, 2, 9] = numpy.sum(
x101 * (x0 * x373 + x0 * (x0 * x375 + x373) + x150 * x22 + x376)
)
result[0, 3, 0] = numpy.sum(x101 * (x0 * x388 + x177 * x21 + x396))
result[0, 3, 1] = numpy.sum(x208 * (x0 * x405 + x200 * x21 + x409))
result[0, 3, 2] = numpy.sum(x208 * (x0 * x414 + x21 * x214 + x415))
result[0, 3, 3] = numpy.sum(x208 * (x0 * x420 + x21 * x223 + x422))
result[0, 3, 4] = numpy.sum(x242 * (x0 * x427 + x21 * x235 + x429))
result[0, 3, 5] = numpy.sum(x208 * (x0 * x433 + x21 * x245 + x434))
result[0, 3, 6] = numpy.sum(x101 * (x0 * x437 + x21 * x251 + x438))
result[0, 3, 7] = numpy.sum(x208 * (x0 * x441 + x21 * x257 + x442))
result[0, 3, 8] = numpy.sum(x208 * (x0 * x445 + x21 * x263 + x446))
result[0, 3, 9] = numpy.sum(x101 * (x0 * x449 + x21 * x270 + x450))
result[0, 4, 0] = numpy.sum(x126 * (x0 * x461 + x21 * x298 + x467))
result[0, 4, 1] = numpy.sum(x242 * (x0 * x473 + x21 * x313 + x477))
result[0, 4, 2] = numpy.sum(x242 * (x0 * x483 + x21 * x326 + x487))
result[0, 4, 3] = numpy.sum(x242 * (x0 * x492 + x21 * x332 + x496))
result[0, 4, 4] = numpy.sum(x89 * (x0 * x501 + x21 * x339 + x505))
result[0, 4, 5] = numpy.sum(x242 * (x0 * x510 + x21 * x349 + x514))
result[0, 4, 6] = numpy.sum(x126 * (x0 * x517 + x21 * x357 + x519))
result[0, 4, 7] = numpy.sum(x242 * (x0 * x522 + x21 * x363 + x524))
result[0, 4, 8] = numpy.sum(x242 * (x0 * x527 + x21 * x368 + x529))
result[0, 4, 9] = numpy.sum(x126 * (x0 * x532 + x21 * x373 + x534))
result[0, 5, 0] = numpy.sum(x101 * (x0 * x546 + x22 * x298 + x554))
result[0, 5, 1] = numpy.sum(x208 * (x0 * x559 + x22 * x313 + x560))
result[0, 5, 2] = numpy.sum(x208 * (x0 * x567 + x22 * x326 + x569))
result[0, 5, 3] = numpy.sum(x208 * (x0 * x573 + x22 * x332 + x574))
result[0, 5, 4] = numpy.sum(x242 * (x0 * x578 + x22 * x339 + x579))
result[0, 5, 5] = numpy.sum(x208 * (x0 * x585 + x22 * x349 + x587))
result[0, 5, 6] = numpy.sum(x101 * (x0 * x590 + x22 * x357 + x591))
result[0, 5, 7] = numpy.sum(x208 * (x0 * x594 + x22 * x363 + x595))
result[0, 5, 8] = numpy.sum(x208 * (x0 * x598 + x22 * x368 + x599))
result[0, 5, 9] = numpy.sum(x101 * (x0 * x602 + x22 * x373 + x603))
result[0, 6, 0] = numpy.sum(x90 * (x21 * x388 + x609))
result[0, 6, 1] = numpy.sum(x101 * (x21 * x405 + x617))
result[0, 6, 2] = numpy.sum(x101 * (x21 * x414 + x619))
result[0, 6, 3] = numpy.sum(x101 * (x21 * x420 + x623))
result[0, 6, 4] = numpy.sum(x126 * (x21 * x427 + x627))
result[0, 6, 5] = numpy.sum(x101 * (x21 * x433 + x629))
result[0, 6, 6] = numpy.sum(x90 * (x21 * x437 + x630))
result[0, 6, 7] = numpy.sum(x101 * (x21 * x441 + x631))
result[0, 6, 8] = numpy.sum(x101 * (x21 * x445 + x632))
result[0, 6, 9] = numpy.sum(x90 * (x21 * x449 + x633))
result[0, 7, 0] = numpy.sum(x101 * (x21 * x461 + x639))
result[0, 7, 1] = numpy.sum(x208 * (x21 * x473 + x644))
result[0, 7, 2] = numpy.sum(x208 * (x21 * x483 + x648))
result[0, 7, 3] = numpy.sum(x208 * (x21 * x492 + x652))
result[0, 7, 4] = numpy.sum(x242 * (x21 * x501 + x657))
result[0, 7, 5] = numpy.sum(x208 * (x21 * x510 + x661))
result[0, 7, 6] = numpy.sum(x101 * (x21 * x517 + x663))
result[0, 7, 7] = numpy.sum(x208 * (x21 * x522 + x665))
result[0, 7, 8] = numpy.sum(x208 * (x21 * x527 + x667))
result[0, 7, 9] = numpy.sum(x101 * (x21 * x532 + x669))
result[0, 8, 0] = numpy.sum(x101 * (x21 * x546 + x675))
result[0, 8, 1] = numpy.sum(x208 * (x21 * x559 + x679))
result[0, 8, 2] = numpy.sum(x208 * (x21 * x567 + x683))
result[0, 8, 3] = numpy.sum(x208 * (x21 * x573 + x687))
result[0, 8, 4] = numpy.sum(x242 * (x21 * x578 + x691))
result[0, 8, 5] = numpy.sum(x208 * (x21 * x585 + x695))
result[0, 8, 6] = numpy.sum(x101 * (x21 * x590 + x697))
result[0, 8, 7] = numpy.sum(x208 * (x21 * x594 + x699))
result[0, 8, 8] = numpy.sum(x208 * (x21 * x598 + x701))
result[0, 8, 9] = numpy.sum(x101 * (x21 * x602 + x703))
result[0, 9, 0] = numpy.sum(x90 * (x22 * x546 + x709))
result[0, 9, 1] = numpy.sum(x101 * (x22 * x559 + x711))
result[0, 9, 2] = numpy.sum(x101 * (x22 * x567 + x715))
result[0, 9, 3] = numpy.sum(x101 * (x22 * x573 + x717))
result[0, 9, 4] = numpy.sum(x126 * (x22 * x578 + x719))
result[0, 9, 5] = numpy.sum(x101 * (x22 * x585 + x723))
result[0, 9, 6] = numpy.sum(x90 * (x22 * x590 + x724))
result[0, 9, 7] = numpy.sum(x101 * (x22 * x594 + x725))
result[0, 9, 8] = numpy.sum(x101 * (x22 * x598 + x726))
result[0, 9, 9] = numpy.sum(x90 * (x22 * x602 + x727))
result[1, 0, 0] = numpy.sum(
x90 * (x0 * x176 + x0 * x728 + x0 * (x0 * (x179 + x729 * x730) + x728) + x188)
)
result[1, 0, 1] = numpy.sum(
x101 * (x0 * x199 + x0 * x731 + x0 * (x0 * (x0 * x733 + x203) + x731) + x207)
)
result[1, 0, 2] = numpy.sum(
x101 * (x0 * x213 + x0 * x734 + x0 * (x0 * (x216 + x730 * x735) + x734) + x218)
)
result[1, 0, 3] = numpy.sum(
x101 * (x0 * x222 + x0 * x736 + x0 * (x0 * (x224 * x737 + x225) + x736) + x228)
)
result[1, 0, 4] = numpy.sum(
x126 * (x0 * x234 + x0 * x738 + x0 * (x0 * (x236 * x737 + x237) + x738) + x241)
)
result[1, 0, 5] = numpy.sum(
x101 * (x0 * x244 + x0 * x739 + x0 * (x0 * (x247 + x730 * x740) + x739) + x249)
)
result[1, 0, 6] = numpy.sum(
x90 * (x0 * x250 + x0 * x741 + x0 * (x0 * (x252 + x742 * x78) + x741) + x255)
)
result[1, 0, 7] = numpy.sum(
x101 * (x0 * x256 + x0 * x743 + x0 * (x0 * (x258 + x744 * x78) + x743) + x260)
)
result[1, 0, 8] = numpy.sum(
x101 * (x0 * x262 + x0 * x745 + x0 * (x0 * (x265 + x746 * x78) + x745) + x268)
)
result[1, 0, 9] = numpy.sum(
x90 * (x0 * x269 + x0 * x747 + x0 * (x0 * (x149 * x730 + x271) + x747) + x273)
)
result[1, 1, 0] = numpy.sum(x101 * (x0 * x387 + x0 * (x0 * x750 + x387) + x396))
result[1, 1, 1] = numpy.sum(x208 * (x0 * x404 + x0 * (x0 * x752 + x404) + x409))
result[1, 1, 2] = numpy.sum(x208 * (x0 * x413 + x0 * (x0 * x754 + x413) + x415))
result[1, 1, 3] = numpy.sum(x208 * (x0 * x419 + x0 * (x0 * x757 + x419) + x422))
result[1, 1, 4] = numpy.sum(x242 * (x0 * x426 + x0 * (x0 * x759 + x426) + x429))
result[1, 1, 5] = numpy.sum(x208 * (x0 * x432 + x0 * (x0 * x761 + x432) + x434))
result[1, 1, 6] = numpy.sum(x101 * (x0 * x436 + x0 * (x0 * x763 + x436) + x438))
result[1, 1, 7] = numpy.sum(x208 * (x0 * x440 + x0 * (x0 * x765 + x440) + x442))
result[1, 1, 8] = numpy.sum(x208 * (x0 * x444 + x0 * (x0 * x767 + x444) + x446))
result[1, 1, 9] = numpy.sum(x101 * (x0 * x448 + x0 * (x0 * x769 + x448) + x450))
result[1, 2, 0] = numpy.sum(x101 * (x0 * x460 + x0 * (x0 * x772 + x460) + x467))
result[1, 2, 1] = numpy.sum(x208 * (x0 * x472 + x0 * (x0 * x774 + x472) + x477))
result[1, 2, 2] = numpy.sum(x208 * (x0 * x482 + x0 * (x0 * x776 + x482) + x487))
result[1, 2, 3] = numpy.sum(x208 * (x0 * x491 + x0 * (x0 * x779 + x491) + x496))
result[1, 2, 4] = numpy.sum(x242 * (x0 * x500 + x0 * (x0 * x781 + x500) + x505))
result[1, 2, 5] = numpy.sum(x208 * (x0 * x509 + x0 * (x0 * x783 + x509) + x514))
result[1, 2, 6] = numpy.sum(x101 * (x0 * x516 + x0 * (x0 * x785 + x516) + x519))
result[1, 2, 7] = numpy.sum(x208 * (x0 * x521 + x0 * (x0 * x787 + x521) + x524))
result[1, 2, 8] = numpy.sum(x208 * (x0 * x526 + x0 * (x0 * x789 + x526) + x529))
result[1, 2, 9] = numpy.sum(x101 * (x0 * x531 + x0 * (x0 * x791 + x531) + x534))
result[1, 3, 0] = numpy.sum(x101 * (x0 * x794 + x609))
result[1, 3, 1] = numpy.sum(x208 * (x0 * x797 + x617))
result[1, 3, 2] = numpy.sum(x208 * (x0 * x800 + x619))
result[1, 3, 3] = numpy.sum(x208 * (x0 * x803 + x623))
result[1, 3, 4] = numpy.sum(x242 * (x0 * x806 + x627))
result[1, 3, 5] = numpy.sum(x208 * (x0 * x809 + x629))
result[1, 3, 6] = numpy.sum(x101 * (x0 * x812 + x630))
result[1, 3, 7] = numpy.sum(x208 * (x0 * x815 + x631))
result[1, 3, 8] = numpy.sum(x208 * (x0 * x818 + x632))
result[1, 3, 9] = numpy.sum(x101 * (x0 * x821 + x633))
result[1, 4, 0] = numpy.sum(x126 * (x0 * x824 + x639))
result[1, 4, 1] = numpy.sum(x242 * (x0 * x827 + x644))
result[1, 4, 2] = numpy.sum(x242 * (x0 * x830 + x648))
result[1, 4, 3] = numpy.sum(x242 * (x0 * x833 + x652))
result[1, 4, 4] = numpy.sum(x89 * (x0 * x836 + x657))
result[1, 4, 5] = numpy.sum(x242 * (x0 * x839 + x661))
result[1, 4, 6] = numpy.sum(x126 * (x0 * x842 + x663))
result[1, 4, 7] = numpy.sum(x242 * (x0 * x845 + x665))
result[1, 4, 8] = numpy.sum(x242 * (x0 * x849 + x667))
result[1, 4, 9] = numpy.sum(x126 * (x0 * x852 + x669))
result[1, 5, 0] = numpy.sum(x101 * (x0 * x855 + x675))
result[1, 5, 1] = numpy.sum(x208 * (x0 * x858 + x679))
result[1, 5, 2] = numpy.sum(x208 * (x0 * x861 + x683))
result[1, 5, 3] = numpy.sum(x208 * (x0 * x864 + x687))
result[1, 5, 4] = numpy.sum(x242 * (x0 * x867 + x691))
result[1, 5, 5] = numpy.sum(x208 * (x0 * x870 + x695))
result[1, 5, 6] = numpy.sum(x101 * (x0 * x873 + x697))
result[1, 5, 7] = numpy.sum(x208 * (x0 * x876 + x699))
result[1, 5, 8] = numpy.sum(x208 * (x0 * x879 + x701))
result[1, 5, 9] = numpy.sum(x101 * (x0 * x882 + x703))
result[1, 6, 0] = numpy.sum(
x90 * (x21 * x792 + x21 * x793 + x21 * x794 + x729 * x883)
)
result[1, 6, 1] = numpy.sum(
x101 * (x21 * x795 + x21 * x796 + x21 * x797 + x732 * x886)
)
result[1, 6, 2] = numpy.sum(
x101 * (x21 * x798 + x21 * x799 + x21 * x800 + x735 * x883)
)
result[1, 6, 3] = numpy.sum(
x101 * (x201 * x887 + x21 * x801 + x21 * x802 + x21 * x803)
)
result[1, 6, 4] = numpy.sum(
x126 * (x201 * x888 + x21 * x804 + x21 * x805 + x21 * x806)
)
result[1, 6, 5] = numpy.sum(
x101 * (x21 * x807 + x21 * x808 + x21 * x809 + x740 * x883)
)
result[1, 6, 6] = numpy.sum(
x90 * (x21 * x810 + x21 * x811 + x21 * x812 + x55 * (4.0 * x621 + x887 * x91))
)
result[1, 6, 7] = numpy.sum(
x101 * (x21 * x813 + x21 * x814 + x21 * x815 + x55 * (4.0 * x625 + x888 * x91))
)
result[1, 6, 8] = numpy.sum(
x101 * (x127 * x55 * (x884 + x885) + x21 * x816 + x21 * x817 + x21 * x818)
)
result[1, 6, 9] = numpy.sum(
x90 * (x149 * x883 + x21 * x819 + x21 * x820 + x21 * x821)
)
result[1, 7, 0] = numpy.sum(x101 * (x21 * x823 + x21 * x824 + x22 * x792 + x890))
result[1, 7, 1] = numpy.sum(x208 * (x21 * x826 + x21 * x827 + x22 * x795 + x892))
result[1, 7, 2] = numpy.sum(x208 * (x21 * x829 + x21 * x830 + x22 * x798 + x894))
result[1, 7, 3] = numpy.sum(x208 * (x21 * x832 + x21 * x833 + x22 * x801 + x896))
result[1, 7, 4] = numpy.sum(x242 * (x21 * x835 + x21 * x836 + x22 * x804 + x898))
result[1, 7, 5] = numpy.sum(x208 * (x21 * x838 + x21 * x839 + x22 * x807 + x900))
result[1, 7, 6] = numpy.sum(x101 * (x21 * x841 + x21 * x842 + x22 * x810 + x901))
result[1, 7, 7] = numpy.sum(x208 * (x21 * x844 + x21 * x845 + x22 * x813 + x902))
result[1, 7, 8] = numpy.sum(x208 * (x21 * x848 + x21 * x849 + x22 * x816 + x903))
result[1, 7, 9] = numpy.sum(x101 * (x21 * x851 + x21 * x852 + x22 * x819 + x904))
result[1, 8, 0] = numpy.sum(x101 * (x21 * x855 + x22 * x823 + x906))
result[1, 8, 1] = numpy.sum(x208 * (x21 * x858 + x22 * x826 + x908))
result[1, 8, 2] = numpy.sum(x208 * (x21 * x861 + x22 * x829 + x910))
result[1, 8, 3] = numpy.sum(x208 * (x21 * x864 + x22 * x832 + x912))
result[1, 8, 4] = numpy.sum(x242 * (x21 * x867 + x22 * x835 + x914))
result[1, 8, 5] = numpy.sum(x208 * (x21 * x870 + x22 * x838 + x916))
result[1, 8, 6] = numpy.sum(x101 * (x21 * x873 + x22 * x841 + x917))
result[1, 8, 7] = numpy.sum(x208 * (x21 * x876 + x22 * x844 + x918))
result[1, 8, 8] = numpy.sum(x208 * (x21 * x879 + x22 * x848 + x919))
result[1, 8, 9] = numpy.sum(x101 * (x21 * x882 + x22 * x851 + x920))
result[1, 9, 0] = numpy.sum(x90 * (x22 * x855 + x922))
result[1, 9, 1] = numpy.sum(x101 * (x22 * x858 + x924))
result[1, 9, 2] = numpy.sum(x101 * (x22 * x861 + x926))
result[1, 9, 3] = numpy.sum(x101 * (x22 * x864 + x928))
result[1, 9, 4] = numpy.sum(x126 * (x22 * x867 + x930))
result[1, 9, 5] = numpy.sum(x101 * (x22 * x870 + x932))
result[1, 9, 6] = numpy.sum(x90 * (x22 * x873 + x933))
result[1, 9, 7] = numpy.sum(x101 * (x22 * x876 + x934))
result[1, 9, 8] = numpy.sum(x101 * (x22 * x879 + x935))
result[1, 9, 9] = numpy.sum(x90 * (x22 * x882 + x936))
result[2, 0, 0] = numpy.sum(
x90 * (x0 * x297 + x0 * x937 + x0 * (x0 * (x299 + x729 * x938) + x937) + x308)
)
result[2, 0, 1] = numpy.sum(
x101 * (x0 * x312 + x0 * x939 + x0 * (x0 * (x315 + x938 * x940) + x939) + x317)
)
result[2, 0, 2] = numpy.sum(
x101 * (x0 * x325 + x0 * x941 + x0 * (x0 * (x327 + x732 * x942) + x941) + x330)
)
result[2, 0, 3] = numpy.sum(
x101 * (x0 * x331 + x0 * x943 + x0 * (x0 * (x334 + x938 * x944) + x943) + x336)
)
result[2, 0, 4] = numpy.sum(
x126 * (x0 * x338 + x0 * x945 + x0 * (x0 * (x342 + x942 * x946) + x945) + x344)
)
result[2, 0, 5] = numpy.sum(
x101 * (x0 * x348 + x0 * x947 + x0 * (x0 * (x350 * x737 + x352) + x947) + x355)
)
result[2, 0, 6] = numpy.sum(
x90 * (x0 * x356 + x0 * x948 + x0 * (x0 * (x134 * x938 + x358) + x948) + x361)
)
result[2, 0, 7] = numpy.sum(
x101 * (x0 * x362 + x0 * x949 + x0 * (x0 * (x139 * x942 + x364) + x949) + x366)
)
result[2, 0, 8] = numpy.sum(
x101 * (x0 * x367 + x0 * x950 + x0 * (x0 * (x0 * x951 + x369) + x950) + x371)
)
result[2, 0, 9] = numpy.sum(
x90 * (x0 * x372 + x0 * x952 + x0 * (x0 * (x374 + x78 * x953) + x952) + x376)
)
result[2, 1, 0] = numpy.sum(
x101 * (x0 * x954 + x0 * (x0 * x956 + x954) + x21 * x297 + x466)
)
result[2, 1, 1] = numpy.sum(
x208 * (x0 * x957 + x0 * (x0 * x958 + x957) + x21 * x312 + x476)
)
result[2, 1, 2] = numpy.sum(
x208 * (x0 * x959 + x0 * (x0 * x961 + x959) + x21 * x325 + x486)
)
result[2, 1, 3] = numpy.sum(
x208 * (x0 * x962 + x0 * (x0 * x963 + x962) + x21 * x331 + x495)
)
result[2, 1, 4] = numpy.sum(
x242 * (x0 * x964 + x0 * (x0 * x965 + x964) + x21 * x338 + x504)
)
result[2, 1, 5] = numpy.sum(
x208 * (x0 * x966 + x0 * (x0 * x967 + x966) + x21 * x348 + x513)
)
result[2, 1, 6] = numpy.sum(
x101 * (x0 * x968 + x0 * (x0 * x969 + x968) + x21 * x356 + x518)
)
result[2, 1, 7] = numpy.sum(
x208 * (x0 * x970 + x0 * (x0 * x971 + x970) + x21 * x362 + x523)
)
result[2, 1, 8] = numpy.sum(
x208 * (x0 * x972 + x0 * (x0 * x973 + x972) + x21 * x367 + x528)
)
result[2, 1, 9] = numpy.sum(
x101 * (x0 * x974 + x0 * (x0 * x975 + x974) + x21 * x372 + x533)
)
result[2, 2, 0] = numpy.sum(x101 * (x0 * x545 + x0 * (x0 * x978 + x545) + x554))
result[2, 2, 1] = numpy.sum(x208 * (x0 * x558 + x0 * (x0 * x980 + x558) + x560))
result[2, 2, 2] = numpy.sum(x208 * (x0 * x566 + x0 * (x0 * x983 + x566) + x569))
result[2, 2, 3] = numpy.sum(x208 * (x0 * x572 + x0 * (x0 * x985 + x572) + x574))
result[2, 2, 4] = numpy.sum(x242 * (x0 * x577 + x0 * (x0 * x987 + x577) + x579))
result[2, 2, 5] = numpy.sum(x208 * (x0 * x584 + x0 * (x0 * x989 + x584) + x587))
result[2, 2, 6] = numpy.sum(x101 * (x0 * x589 + x0 * (x0 * x991 + x589) + x591))
result[2, 2, 7] = numpy.sum(x208 * (x0 * x593 + x0 * (x0 * x993 + x593) + x595))
result[2, 2, 8] = numpy.sum(x208 * (x0 * x597 + x0 * (x0 * x995 + x597) + x599))
result[2, 2, 9] = numpy.sum(x101 * (x0 * x601 + x0 * (x0 * x997 + x601) + x603))
result[2, 3, 0] = numpy.sum(x101 * (x0 * x999 + x21 * x459 + x21 * x954 + x638))
result[2, 3, 1] = numpy.sum(x208 * (x0 * x1001 + x21 * x471 + x21 * x957 + x643))
result[2, 3, 2] = numpy.sum(x208 * (x0 * x1003 + x21 * x481 + x21 * x959 + x647))
result[2, 3, 3] = numpy.sum(x208 * (x0 * x1005 + x21 * x490 + x21 * x962 + x651))
result[2, 3, 4] = numpy.sum(x242 * (x0 * x1007 + x21 * x499 + x21 * x964 + x656))
result[2, 3, 5] = numpy.sum(x208 * (x0 * x1009 + x21 * x508 + x21 * x966 + x660))
result[2, 3, 6] = numpy.sum(x101 * (x0 * x1011 + x21 * x515 + x21 * x968 + x662))
result[2, 3, 7] = numpy.sum(x208 * (x0 * x1013 + x21 * x520 + x21 * x970 + x664))
result[2, 3, 8] = numpy.sum(x208 * (x0 * x1015 + x21 * x525 + x21 * x972 + x666))
result[2, 3, 9] = numpy.sum(x101 * (x0 * x1017 + x21 * x530 + x21 * x974 + x668))
result[2, 4, 0] = numpy.sum(x126 * (x0 * x1018 + x21 * x545 + x674))
result[2, 4, 1] = numpy.sum(x242 * (x0 * x1019 + x21 * x558 + x678))
result[2, 4, 2] = numpy.sum(x242 * (x0 * x1020 + x21 * x566 + x682))
result[2, 4, 3] = numpy.sum(x242 * (x0 * x1021 + x21 * x572 + x686))
result[2, 4, 4] = numpy.sum(x89 * (x0 * x1022 + x21 * x577 + x690))
result[2, 4, 5] = numpy.sum(x242 * (x0 * x1023 + x21 * x584 + x694))
result[2, 4, 6] = numpy.sum(x126 * (x0 * x1024 + x21 * x589 + x696))
result[2, 4, 7] = numpy.sum(x242 * (x0 * x1025 + x21 * x593 + x698))
result[2, 4, 8] = numpy.sum(x242 * (x0 * x1026 + x21 * x597 + x700))
result[2, 4, 9] = numpy.sum(x126 * (x0 * x1027 + x21 * x601 + x702))
result[2, 5, 0] = numpy.sum(x101 * (x0 * x1030 + x709))
result[2, 5, 1] = numpy.sum(x208 * (x0 * x1033 + x711))
result[2, 5, 2] = numpy.sum(x208 * (x0 * x1036 + x715))
result[2, 5, 3] = numpy.sum(x208 * (x0 * x1039 + x717))
result[2, 5, 4] = numpy.sum(x242 * (x0 * x1042 + x719))
result[2, 5, 5] = numpy.sum(x208 * (x0 * x1045 + x723))
result[2, 5, 6] = numpy.sum(x101 * (x0 * x1048 + x724))
result[2, 5, 7] = numpy.sum(x208 * (x0 * x1051 + x725))
result[2, 5, 8] = numpy.sum(x208 * (x0 * x1054 + x726))
result[2, 5, 9] = numpy.sum(x101 * (x0 * x1057 + x727))
result[2, 6, 0] = numpy.sum(x90 * (x21 * x822 + x21 * x998 + x21 * x999 + x890))
result[2, 6, 1] = numpy.sum(x101 * (x1000 * x21 + x1001 * x21 + x21 * x825 + x892))
result[2, 6, 2] = numpy.sum(x101 * (x1002 * x21 + x1003 * x21 + x21 * x828 + x894))
result[2, 6, 3] = numpy.sum(x101 * (x1004 * x21 + x1005 * x21 + x21 * x831 + x896))
result[2, 6, 4] = numpy.sum(x126 * (x1006 * x21 + x1007 * x21 + x21 * x834 + x898))
result[2, 6, 5] = numpy.sum(x101 * (x1008 * x21 + x1009 * x21 + x21 * x837 + x900))
result[2, 6, 6] = numpy.sum(x90 * (x1010 * x21 + x1011 * x21 + x21 * x840 + x901))
result[2, 6, 7] = numpy.sum(x101 * (x1012 * x21 + x1013 * x21 + x21 * x843 + x902))
result[2, 6, 8] = numpy.sum(x101 * (x1014 * x21 + x1015 * x21 + x21 * x847 + x903))
result[2, 6, 9] = numpy.sum(x90 * (x1016 * x21 + x1017 * x21 + x21 * x850 + x904))
result[2, 7, 0] = numpy.sum(x101 * (x1018 * x21 + x21 * x854 + x906))
result[2, 7, 1] = numpy.sum(x208 * (x1019 * x21 + x21 * x857 + x908))
result[2, 7, 2] = numpy.sum(x208 * (x1020 * x21 + x21 * x860 + x910))
result[2, 7, 3] = numpy.sum(x208 * (x1021 * x21 + x21 * x863 + x912))
result[2, 7, 4] = numpy.sum(x242 * (x1022 * x21 + x21 * x866 + x914))
result[2, 7, 5] = numpy.sum(x208 * (x1023 * x21 + x21 * x869 + x916))
result[2, 7, 6] = numpy.sum(x101 * (x1024 * x21 + x21 * x872 + x917))
result[2, 7, 7] = numpy.sum(x208 * (x1025 * x21 + x21 * x875 + x918))
result[2, 7, 8] = numpy.sum(x208 * (x1026 * x21 + x21 * x878 + x919))
result[2, 7, 9] = numpy.sum(x101 * (x1027 * x21 + x21 * x881 + x920))
result[2, 8, 0] = numpy.sum(x101 * (x1030 * x21 + x922))
result[2, 8, 1] = numpy.sum(x208 * (x1033 * x21 + x924))
result[2, 8, 2] = numpy.sum(x208 * (x1036 * x21 + x926))
result[2, 8, 3] = numpy.sum(x208 * (x1039 * x21 + x928))
result[2, 8, 4] = numpy.sum(x242 * (x1042 * x21 + x930))
result[2, 8, 5] = numpy.sum(x208 * (x1045 * x21 + x932))
result[2, 8, 6] = numpy.sum(x101 * (x1048 * x21 + x933))
result[2, 8, 7] = numpy.sum(x208 * (x1051 * x21 + x934))
result[2, 8, 8] = numpy.sum(x208 * (x1054 * x21 + x935))
result[2, 8, 9] = numpy.sum(x101 * (x1057 * x21 + x936))
result[2, 9, 0] = numpy.sum(
x90 * (x1028 * x22 + x1029 * x22 + x1030 * x22 + x1058 * x729)
)
result[2, 9, 1] = numpy.sum(
x101 * (x1031 * x22 + x1032 * x22 + x1033 * x22 + x1058 * x940)
)
result[2, 9, 2] = numpy.sum(
x101 * (x1034 * x22 + x1035 * x22 + x1036 * x22 + x1059 * x732)
)
result[2, 9, 3] = numpy.sum(
x101 * (x1037 * x22 + x1038 * x22 + x1039 * x22 + x1058 * x944)
)
result[2, 9, 4] = numpy.sum(
x126 * (x1040 * x22 + x1041 * x22 + x1042 * x22 + x1059 * x946)
)
result[2, 9, 5] = numpy.sum(
x101 * (x1043 * x22 + x1044 * x22 + x1045 * x22 + x1060 * x201)
)
result[2, 9, 6] = numpy.sum(
x90 * (x1046 * x22 + x1047 * x22 + x1048 * x22 + x1058 * x134)
)
result[2, 9, 7] = numpy.sum(
x101 * (x1049 * x22 + x1050 * x22 + x1051 * x22 + x1059 * x139)
)
result[2, 9, 8] = numpy.sum(
x101 * (x1052 * x22 + x1053 * x22 + x1054 * x22 + x1060 * x119)
)
result[2, 9, 9] = numpy.sum(
x90
* (x1055 * x22 + x1056 * x22 + x1057 * x22 + x55 * (x102 * x1060 + 4.0 * x721))
)
return result
[docs]
def int3c2e3d_sph_134(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (pf|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3, 10, 15), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = -x3 - C[0]
x5 = -x3 - A[0]
x6 = 0.5 / (ax + bx)
x7 = x4**2
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = -x8 - C[1]
x10 = x9**2
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = -x11 - C[2]
x13 = x12**2
x14 = cx + x1
x15 = x14 ** (-1.0)
x16 = cx * x15
x17 = x1 * x16 * (x10 + x13 + x7)
x18 = boys(5, x17)
x19 = x14 ** (-1.5)
x20 = 17.49341832762486
x21 = A[1] - B[1]
x22 = A[2] - B[2]
x23 = numpy.exp(-ax * bx * x2 * (x0**2 + x21**2 + x22**2))
x24 = x20 * x23
x25 = x2 * x24
x26 = 2.0 * x19 * x25
x27 = x18 * x26
x28 = cx ** (-1.0)
x29 = x14 ** (-0.5)
x30 = boys(4, x17)
x31 = 2.0 * x2 * x20 * x23 * x28 * x29 * x30 - x27
x32 = x31 * x6
x33 = -2.0 * x2 * x20 * x23 * x28 * x29 * x30 * x5 + x27 * x4
x34 = -x33
x35 = boys(6, x17)
x36 = x26 * x35
x37 = -2.0 * x18 * x2 * x20 * x23 * x28 * x29 * x5 + x36 * x4
x38 = -x37
x39 = x16 * x38
x40 = x39 * x4
x41 = x32 + x34 * x5 - x40
x42 = 2.0 * x6
x43 = x6 * (2.0 * x18 * x2 * x20 * x23 * x28 * x29 - x36)
x44 = boys(7, x17)
x45 = x26 * x44
x46 = 2.0 * x2 * x20 * x23 * x28 * x29 * x35 * x5 - x4 * x45
x47 = x16 * x46
x48 = x38 * x5 - x4 * x47 + x43
x49 = x16 * x48
x50 = -x4 * x49 + x41 * x5 - x42 * (x33 + x39)
x51 = x4 * x50
x52 = x41 * x6
x53 = 3.0 * x52
x54 = x51 + x53
x55 = x1 * x15
x56 = x4 * x55
x57 = x4 * x41
x58 = x34 * x6
x59 = 2.0 * x58
x60 = x57 + x59
x61 = 3.0 * x6
x62 = x55 * x61
x63 = x54 * x56 + x60 * x62
x64 = x34 * x4
x65 = x28 * x30 * x42
x66 = x25 * x29 * x65
x67 = x64 + x66
x68 = x42 * x55
x69 = x56 * x60 + x67 * x68
x70 = x56 * x63 + x62 * x69
x71 = x24 * x65
x72 = x19 * x71
x73 = x4 * x72 + x56 * x67
x74 = x56 * x69 + x68 * x73
x75 = x55 * (x56 * x70 + x62 * x74)
x76 = x7 * x71
x77 = x1 * x14 ** (-2.5)
x78 = x56 * x73 + x76 * x77
x79 = x55 * (x56 * x74 + x68 * x78)
x80 = x0 * x79 + x75
x81 = x4**3
x82 = x1**2
x83 = x14 ** (-3.5) * x82
x84 = x71 * x83
x85 = x56 * x78 + x81 * x84
x86 = x0 * x55
x87 = -x31 * x6
x88 = x6 * (2.0 * x2 * x20 * x23 * x28 * x29 * x35 - x45)
x89 = x26 * boys(8, x17)
x90 = x16 * x4
x91 = (
x5 * x50
- x61 * (-x34 * x5 + x40 + x49 + x87)
+ x90
* (
x42 * (x37 + x47)
- x48 * x5
+ x90
* (
x46 * x5
+ x88
- x90 * (2.0 * x2 * x20 * x23 * x28 * x29 * x44 * x5 - x4 * x89)
)
)
)
x92 = x4 * x91
x93 = x50 * x6
x94 = 4.0 * x93
x95 = x55 * x6
x96 = 4.0 * x95
x97 = da * db * dc
x98 = 0.009523809523809524 * x97
x99 = 2.645751311064591 * x98
x100 = x55 * x9
x101 = x100 * (x51 + x53)
x102 = x100 * (x57 + x59)
x103 = x101 * x56 + x102 * x62
x104 = x72 * x9
x105 = x100 * x64 + x104
x106 = x102 * x56 + x105 * x68
x107 = x55 * (x103 * x56 + x106 * x62)
x108 = x71 * x77
x109 = x108 * x4
x110 = x105 * x56 + x109 * x9
x111 = x55 * (x106 * x56 + x110 * x68)
x112 = x0 * x111 + x107
x113 = x76 * x83
x114 = x110 * x56 + x113 * x9
x115 = 0.06666666666666667 * x97
x116 = x12 * x55
x117 = x116 * (x51 + x53)
x118 = x116 * (x57 + x59)
x119 = x117 * x56 + x118 * x62
x120 = x12 * x72
x121 = x116 * x64 + x120
x122 = x118 * x56 + x121 * x68
x123 = x55 * (x119 * x56 + x122 * x62)
x124 = x109 * x12 + x121 * x56
x125 = x55 * (x122 * x56 + x124 * x68)
x126 = x0 * x125 + x123
x127 = x113 * x12 + x124 * x56
x128 = x82 / x14**2
x129 = x10 * x128
x130 = x129 * (x51 + x53)
x131 = x129 * (x57 + x59)
x132 = x55 * (x130 * x56 + x131 * x62)
x133 = x10 * x108
x134 = x129 * x64 + x133
x135 = x55 * (x131 * x56 + x134 * x68)
x136 = x0 * x135 + x132
x137 = x10 * x84
x138 = x134 * x56 + x137 * x4
x139 = 3.872983346207417
x140 = 0.02222222222222222 * x139 * x97
x141 = x128 * x9
x142 = x12 * x141
x143 = x142 * (x51 + x53)
x144 = x142 * (x57 + x59)
x145 = x55 * (x143 * x56 + x144 * x62)
x146 = x12 * x9
x147 = x108 * x146
x148 = x142 * x64 + x147
x149 = x55 * (x144 * x56 + x148 * x68)
x150 = x0 * x149 + x145
x151 = x146 * x4 * x84 + x148 * x56
x152 = 2.23606797749979 * x115
x153 = x128 * x13
x154 = x153 * (x51 + x53)
x155 = x153 * (x57 + x59)
x156 = x55 * (x154 * x56 + x155 * x62)
x157 = x108 * x13
x158 = x153 * x64 + x157
x159 = x55 * (x155 * x56 + x158 * x68)
x160 = x0 * x159 + x156
x161 = x13 * x4
x162 = x158 * x56 + x161 * x84
x163 = x9**3
x164 = x1**3 / x14**3
x165 = x163 * x164
x166 = x165 * x55 * (x51 + x53)
x167 = x165 * x55 * (x57 + x59)
x168 = x0 * x167 + x166
x169 = x163 * x84
x170 = x165 * x64 + x169
x171 = x10 * x164
x172 = x12 * x171
x173 = x172 * x55 * (x51 + x53)
x174 = x172 * x55 * (x57 + x59)
x175 = x0 * x174 + x173
x176 = x12 * x137
x177 = x172 * x64 + x176
x178 = x164 * x9
x179 = x13 * x178
x180 = x179 * x55 * (x51 + x53)
x181 = x179 * x55 * (x57 + x59)
x182 = x0 * x181 + x180
x183 = x13 * x84 * x9
x184 = x179 * x64 + x183
x185 = x12**3
x186 = x164 * x185
x187 = x186 * x55 * (x51 + x53)
x188 = x186 * x55 * (x57 + x59)
x189 = x0 * x188 + x187
x190 = x185 * x84
x191 = x186 * x64 + x190
x192 = x1**4 / x14**4
x193 = x192 * x9**4
x194 = x193 * x50
x195 = x193 * x41
x196 = x0 * x195 + x194
x197 = x0 * x34
x198 = x163 * x192
x199 = x12 * x198
x200 = x199 * x50
x201 = x199 * x41
x202 = x0 * x201 + x200
x203 = x192 * x50
x204 = x10 * x13
x205 = x203 * x204
x206 = x192 * x204
x207 = x206 * x41
x208 = x0 * x207 + x205
x209 = x185 * x9
x210 = x203 * x209
x211 = x192 * x209
x212 = x211 * x41
x213 = x0 * x212 + x210
x214 = x12**4 * x192
x215 = x214 * x50
x216 = x214 * x41
x217 = x0 * x216 + x215
x218 = -x8 - A[1]
x219 = -2.0 * x18 * x2 * x20 * x218 * x23 * x28 * x29 + x36 * x9
x220 = -x219
x221 = x16 * x220
x222 = -2.0 * x2 * x20 * x218 * x23 * x28 * x29 * x30 + x27 * x9
x223 = -x6 * (x221 + x222)
x224 = -x222
x225 = x221 * x4 - x224 * x5
x226 = -x225
x227 = 2.0 * x2 * x20 * x218 * x23 * x28 * x29 * x35 - x45 * x9
x228 = x16 * x227
x229 = x220 * x5 - x228 * x4
x230 = x16 * x229
x231 = x223 + x226 * x5 - x230 * x4
x232 = x231 * x4
x233 = x226 * x6
x234 = 2.0 * x233
x235 = x232 + x234
x236 = x224 * x6
x237 = x226 * x4
x238 = x236 + x237
x239 = x235 * x56 + x238 * x68
x240 = x56 * (x236 + x238)
x241 = x239 * x56 + x240 * x68
x242 = x128 * x7
x243 = x236 * x242 + x240 * x56
x244 = x55 * (x241 * x56 + x243 * x68)
x245 = x21 * x79 + x244
x246 = x164 * x81
x247 = x55 * (x236 * x246 + x243 * x56)
x248 = x21 * x55
x249 = x247 + x248 * x85
x250 = -x6 * (x219 + x228)
x251 = 2.0 * x2 * x20 * x218 * x23 * x28 * x29 * x44 - x89 * x9
x252 = (
x231 * x5
- x42 * (x225 + x230)
- x90 * (x229 * x5 + x250 - x90 * (x227 * x5 - x251 * x90))
)
x253 = x252 * x4
x254 = x231 * x6
x255 = 3.0 * x254
x256 = x55 * (
x241 * x62 + x56 * (x239 * x62 + x56 * (x235 * x62 + x56 * (x253 + x255)))
)
x257 = 5.916079783099616 * x98
x258 = x231 * x9
x259 = x258 + x52
x260 = x226 * x9
x261 = x260 + x58
x262 = x261 * x68
x263 = x259 * x56 + x262
x264 = x224 * x9
x265 = x264 + x66
x266 = x265 * x55
x267 = x261 * x56 + x266 * x6
x268 = x263 * x56 + x267 * x68
x269 = x128 * x4
x270 = x265 * x6
x271 = x267 * x56 + x269 * x270
x272 = x55 * (x268 * x56 + x271 * x68)
x273 = x111 * x21 + x272
x274 = x164 * x7
x275 = x55 * (x270 * x274 + x271 * x56)
x276 = x114 * x248 + x275
x277 = x252 * x9
x278 = x277 + x93
x279 = x55 * (x268 * x62 + x56 * (x263 * x62 + x56 * (x259 * x62 + x278 * x56)))
x280 = x116 * x234
x281 = x116 * x232 + x280
x282 = x116 * x236
x283 = x116 * x237 + x282
x284 = x281 * x56 + x283 * x68
x285 = x12 * x236
x286 = x269 * x285 + x283 * x56
x287 = x55 * (x284 * x56 + x286 * x68)
x288 = x125 * x21 + x287
x289 = x55 * (x274 * x285 + x286 * x56)
x290 = x127 * x248 + x289
x291 = x55 * (x284 * x62 + x56 * (x116 * x56 * (x253 + x255) + x281 * x62))
x292 = x100 * (x259 + x52)
x293 = x100 * (x261 + x58)
x294 = x293 * x68
x295 = x292 * x56 + x294
x296 = x104 + x266 * x9
x297 = x293 * x56 + x296 * x95
x298 = x55 * (x295 * x56 + x297 * x68)
x299 = x135 * x21 + x298
x300 = x269 * x6
x301 = x55 * (x296 * x300 + x297 * x56)
x302 = x138 * x248 + x301
x303 = x100 * (x278 + x93)
x304 = x55 * (x295 * x62 + x56 * (x292 * x62 + x303 * x56))
x305 = 1.732050807568877
x306 = 0.1111111111111111 * x305 * x97
x307 = x116 * x52
x308 = x116 * x258 + x307
x309 = x116 * x58
x310 = x116 * x260 + x309
x311 = x310 * x68
x312 = x308 * x56 + x311
x313 = x116 * x264 + x120
x314 = x310 * x56 + x313 * x95
x315 = x55 * (x312 * x56 + x314 * x68)
x316 = x149 * x21 + x315
x317 = x55 * (x300 * x313 + x314 * x56)
x318 = x151 * x248 + x317
x319 = x116 * x93
x320 = x116 * x277 + x319
x321 = x55 * (x312 * x62 + x56 * (x308 * x62 + x320 * x56))
x322 = 0.3333333333333333 * x97
x323 = x153 * x234
x324 = x153 * x232 + x323
x325 = x153 * x236
x326 = x153 * x237 + x325
x327 = x55 * (x324 * x56 + x326 * x68)
x328 = x159 * x21 + x327
x329 = x161 * x164
x330 = x55 * (x236 * x329 + x326 * x56)
x331 = x162 * x248 + x330
x332 = x55 * (x153 * x56 * (x253 + x255) + x324 * x62)
x333 = x100 * x292 + x129 * x52
x334 = x100 * x293 + x129 * x58
x335 = x334 * x68
x336 = x55 * (x333 * x56 + x335)
x337 = x167 * x21 + x336
x338 = x100 * x296 + x133
x339 = x55 * (x334 * x56 + x338 * x95)
x340 = x170 * x248 + x339
x341 = x100 * x303 + x129 * x93
x342 = x55 * (x333 * x62 + x341 * x56)
x343 = x100 * x308 + x142 * x52
x344 = x100 * x310 + x142 * x58
x345 = x344 * x68
x346 = x55 * (x343 * x56 + x345)
x347 = x174 * x21 + x346
x348 = x100 * x313 + x147
x349 = x55 * (x344 * x56 + x348 * x95)
x350 = x177 * x248 + x349
x351 = x100 * x320 + x142 * x93
x352 = x55 * (x343 * x62 + x351 * x56)
x353 = x153 * x52
x354 = x153 * x258 + x353
x355 = x153 * x58
x356 = x153 * x260 + x355
x357 = x356 * x68
x358 = x55 * (x354 * x56 + x357)
x359 = x181 * x21 + x358
x360 = x153 * x264 + x157
x361 = x55 * (x356 * x56 + x360 * x95)
x362 = x184 * x248 + x361
x363 = x153 * x93
x364 = x153 * x277 + x363
x365 = x55 * (x354 * x62 + x364 * x56)
x366 = x186 * x234
x367 = x55 * (x186 * x232 + x366)
x368 = x188 * x21 + x367
x369 = x186 * x236
x370 = x55 * (x186 * x237 + x369)
x371 = x191 * x248 + x370
x372 = x186 * x55 * (x253 + x255)
x373 = x55 * (x100 * x333 + x165 * x52)
x374 = x195 * x21 + x373
x375 = x55 * (x100 * x334 + x165 * x58)
x376 = x21 * x34
x377 = x193 * x376 + x375
x378 = x55 * (x100 * x341 + x165 * x93)
x379 = x55 * (x100 * x343 + x172 * x52)
x380 = x201 * x21 + x379
x381 = x55 * (x100 * x344 + x172 * x58)
x382 = x199 * x376 + x381
x383 = x55 * (x100 * x351 + x172 * x93)
x384 = x55 * (x100 * x354 + x179 * x52)
x385 = x207 * x21 + x384
x386 = x55 * (x100 * x356 + x179 * x58)
x387 = x206 * x376 + x386
x388 = x55 * (x100 * x364 + x179 * x93)
x389 = x186 * x52
x390 = x55 * (x186 * x258 + x389)
x391 = x21 * x212 + x390
x392 = x186 * x58
x393 = x55 * (x186 * x260 + x392)
x394 = x211 * x376 + x393
x395 = x186 * x93
x396 = x55 * (x186 * x277 + x395)
x397 = x214 * x231
x398 = x21 * x216 + x397
x399 = x214 * x226
x400 = x214 * x376 + x399
x401 = x214 * x252
x402 = -x11 - A[2]
x403 = x12 * x36 - 2.0 * x18 * x2 * x20 * x23 * x28 * x29 * x402
x404 = -x403
x405 = x16 * x404
x406 = x12 * x27 - 2.0 * x2 * x20 * x23 * x28 * x29 * x30 * x402
x407 = -x6 * (x405 + x406)
x408 = -x406
x409 = x4 * x405 - x408 * x5
x410 = -x409
x411 = -x12 * x45 + 2.0 * x2 * x20 * x23 * x28 * x29 * x35 * x402
x412 = x16 * x411
x413 = -x4 * x412 + x404 * x5
x414 = x16 * x413
x415 = -x4 * x414 + x407 + x410 * x5
x416 = x4 * x415
x417 = x410 * x6
x418 = 2.0 * x417
x419 = x416 + x418
x420 = x408 * x6
x421 = x4 * x410
x422 = x420 + x421
x423 = x419 * x56 + x422 * x68
x424 = x56 * (x420 + x422)
x425 = x423 * x56 + x424 * x68
x426 = x242 * x420 + x424 * x56
x427 = x55 * (x425 * x56 + x426 * x68)
x428 = x22 * x79 + x427
x429 = x55 * (x246 * x420 + x426 * x56)
x430 = x22 * x55
x431 = x429 + x430 * x85
x432 = -x6 * (x403 + x412)
x433 = -x12 * x89 + 2.0 * x2 * x20 * x23 * x28 * x29 * x402 * x44
x434 = (
x415 * x5
- x42 * (x409 + x414)
- x90 * (x413 * x5 + x432 - x90 * (x411 * x5 - x433 * x90))
)
x435 = x4 * x434
x436 = x415 * x6
x437 = 3.0 * x436
x438 = x55 * (
x425 * x62 + x56 * (x423 * x62 + x56 * (x419 * x62 + x56 * (x435 + x437)))
)
x439 = x100 * (x416 + x418)
x440 = x100 * x420
x441 = x100 * x421 + x440
x442 = x439 * x56 + x441 * x68
x443 = x141 * x4
x444 = x420 * x443 + x441 * x56
x445 = x55 * (x442 * x56 + x444 * x68)
x446 = x111 * x22 + x445
x447 = x274 * x9
x448 = x55 * (x420 * x447 + x444 * x56)
x449 = x114 * x430 + x448
x450 = x55 * (x442 * x62 + x56 * (x100 * x56 * (x435 + x437) + x439 * x62))
x451 = x12 * x415 + x52
x452 = x12 * x410 + x58
x453 = x452 * x68
x454 = x451 * x56 + x453
x455 = x12 * x408 + x66
x456 = x455 * x95
x457 = x452 * x56 + x456
x458 = x454 * x56 + x457 * x68
x459 = x300 * x455 + x457 * x56
x460 = x55 * (x458 * x56 + x459 * x68)
x461 = x125 * x22 + x460
x462 = x455 * x6
x463 = x55 * (x274 * x462 + x459 * x56)
x464 = x127 * x430 + x463
x465 = x12 * x434 + x93
x466 = x55 * (x458 * x62 + x56 * (x454 * x62 + x56 * (x451 * x62 + x465 * x56)))
x467 = x129 * (x416 + x418)
x468 = x129 * x420
x469 = x129 * x421 + x468
x470 = x55 * (x467 * x56 + x469 * x68)
x471 = x135 * x22 + x470
x472 = x171 * x4
x473 = x55 * (x420 * x472 + x469 * x56)
x474 = x138 * x430 + x473
x475 = x55 * (x129 * x56 * (x435 + x437) + x467 * x62)
x476 = x42 * x452
x477 = x141 * x476 + x443 * x451
x478 = x141 * x462
x479 = x443 * x452 + x478
x480 = x55 * (x477 * x56 + x479 * x68)
x481 = x149 * x22 + x480
x482 = x178 * x4
x483 = x55 * (x462 * x482 + x479 * x56)
x484 = x151 * x430 + x483
x485 = x451 * x61
x486 = x55 * (x477 * x62 + x56 * (x141 * x485 + x443 * x465))
x487 = x116 * x451 + x307
x488 = x116 * x452 + x309
x489 = x488 * x68
x490 = x487 * x56 + x489
x491 = x116 * x455 + x120
x492 = x491 * x95
x493 = x488 * x56 + x492
x494 = x55 * (x490 * x56 + x493 * x68)
x495 = x159 * x22 + x494
x496 = x55 * (x300 * x491 + x493 * x56)
x497 = x162 * x430 + x496
x498 = x116 * x465 + x319
x499 = x55 * (x490 * x62 + x56 * (x487 * x62 + x498 * x56))
x500 = x165 * x55 * (x416 + x418)
x501 = x167 * x22 + x500
x502 = x165 * x420
x503 = x55 * (x165 * x421 + x502)
x504 = x170 * x430 + x503
x505 = x165 * x55 * (x435 + x437)
x506 = x55 * (x171 * x476 + x451 * x472)
x507 = x174 * x22 + x506
x508 = x171 * x462
x509 = x55 * (x452 * x472 + x508)
x510 = x177 * x430 + x509
x511 = x55 * (x171 * x485 + x465 * x472)
x512 = x141 * x42
x513 = x55 * (x443 * x487 + x488 * x512)
x514 = x181 * x22 + x513
x515 = x141 * x6
x516 = x491 * x515
x517 = x55 * (x443 * x488 + x516)
x518 = x184 * x430 + x517
x519 = x55 * (x141 * x487 * x61 + x443 * x498)
x520 = x116 * x487 + x353
x521 = x116 * x488 + x355
x522 = x521 * x68
x523 = x55 * (x520 * x56 + x522)
x524 = x188 * x22 + x523
x525 = x116 * x491 + x157
x526 = x525 * x95
x527 = x55 * (x521 * x56 + x526)
x528 = x191 * x430 + x527
x529 = x116 * x498 + x363
x530 = x55 * (x520 * x62 + x529 * x56)
x531 = x193 * x415
x532 = x195 * x22 + x531
x533 = x193 * x410
x534 = x22 * x34
x535 = x193 * x534 + x533
x536 = x193 * x434
x537 = x198 * x451
x538 = x201 * x22 + x537
x539 = x198 * x452
x540 = x199 * x534 + x539
x541 = x198 * x465
x542 = x171 * x487
x543 = x207 * x22 + x542
x544 = x171 * x488
x545 = x206 * x534 + x544
x546 = x171 * x498
x547 = x141 * x520
x548 = x212 * x22 + x547
x549 = x141 * x521
x550 = x211 * x534 + x549
x551 = x141 * x529
x552 = x55 * (x116 * x520 + x389)
x553 = x216 * x22 + x552
x554 = x55 * (x116 * x521 + x392)
x555 = x214 * x534 + x554
x556 = x55 * (x116 * x529 + x395)
x557 = x221 * x9
x558 = x218 * x224 + x32 - x557
x559 = x558 * x6
x560 = x218 * x220 - x228 * x9 + x43
x561 = x16 * x560
x562 = -x4 * x561 + x5 * x558
x563 = x4 * x562
x564 = x559 + x563
x565 = x56 * (x559 + x564)
x566 = x242 * x559 + x56 * x565
x567 = x55 * (x246 * x559 + x56 * x566)
x568 = x21 * x247 + x567
x569 = x21 * x249 + x568
x570 = x6 * (x218 * x224 - x557 - x561 - x87)
x571 = x16 * x9
x572 = x218 * x227 - x251 * x571 + x88
x573 = x5 * x562 + x570 - x90 * (x5 * x560 - x572 * x90)
x574 = x4 * x573
x575 = x562 * x6
x576 = 2.0 * x575
x577 = x21 * x244 + x55 * (
x56 * (x56 * (x56 * (x574 + x576) + x564 * x68) + x565 * x68) + x566 * x68
)
x578 = x558 * x9
x579 = 2.0 * x236
x580 = x578 + x579
x581 = x562 * x9
x582 = x234 + x581
x583 = x56 * x582 + x580 * x95
x584 = x300 * x580 + x56 * x583
x585 = x274 * x6
x586 = x55 * (x56 * x584 + x580 * x585)
x587 = x21 * x275 + x586
x588 = x21 * x276 + x587
x589 = x573 * x9
x590 = 2.0 * x254
x591 = x589 + x590
x592 = x21 * x272 + x55 * (
x56 * (x56 * (x56 * x591 + x582 * x68) + x583 * x68) + x584 * x68
)
x593 = x116 * x559
x594 = x116 * x563 + x593
x595 = x12 * x559
x596 = x269 * x595 + x56 * x594
x597 = x55 * (x274 * x595 + x56 * x596)
x598 = x21 * x289 + x597
x599 = x21 * x290 + x598
x600 = x21 * x287 + x55 * (
x56 * (x116 * x56 * (x574 + x576) + x594 * x68) + x596 * x68
)
x601 = x100 * x580 + x266 * x42
x602 = x100 * x582 + x262
x603 = x56 * x602 + x601 * x95
x604 = x55 * (x300 * x601 + x56 * x603)
x605 = x21 * x301 + x604
x606 = x21 * x302 + x605
x607 = x100 * x591 + x259 * x68
x608 = x21 * x298 + x55 * (x56 * (x56 * x607 + x602 * x68) + x603 * x68)
x609 = x116 * (x578 + x579)
x610 = x116 * x581 + x280
x611 = x56 * x610 + x609 * x95
x612 = x55 * (x300 * x609 + x56 * x611)
x613 = x21 * x317 + x612
x614 = x21 * x318 + x613
x615 = x116 * (x589 + x590)
x616 = x21 * x315 + x55 * (x56 * (x56 * x615 + x610 * x68) + x611 * x68)
x617 = x153 * x559
x618 = x153 * x563 + x617
x619 = x55 * (x329 * x559 + x56 * x618)
x620 = x21 * x330 + x619
x621 = x21 * x331 + x620
x622 = x21 * x327 + x55 * (x153 * x56 * (x574 + x576) + x618 * x68)
x623 = x100 * x601 + x296 * x68
x624 = x100 * x602 + x294
x625 = x55 * (x56 * x624 + x623 * x95)
x626 = x21 * x339 + x625
x627 = x21 * x340 + x626
x628 = x100 * x607 + x292 * x68
x629 = x21 * x336 + x55 * (x56 * x628 + x624 * x68)
x630 = x100 * x609 + x313 * x68
x631 = x100 * x610 + x311
x632 = x55 * (x56 * x631 + x630 * x95)
x633 = x21 * x349 + x632
x634 = x21 * x350 + x633
x635 = x100 * x615 + x308 * x68
x636 = x21 * x346 + x55 * (x56 * x635 + x631 * x68)
x637 = x153 * (x578 + x579)
x638 = x153 * x581 + x323
x639 = x55 * (x56 * x638 + x637 * x95)
x640 = x21 * x361 + x639
x641 = x21 * x362 + x640
x642 = x153 * (x589 + x590)
x643 = x21 * x358 + x55 * (x56 * x642 + x638 * x68)
x644 = x186 * x559
x645 = x55 * (x186 * x563 + x644)
x646 = x21 * x370 + x645
x647 = x21 * x371 + x646
x648 = x186 * x55 * (x574 + x576) + x21 * x367
x649 = x55 * (x100 * x624 + x335)
x650 = x21 * x375 + x649
x651 = x21 * x377 + x650
x652 = x21 * x373 + x55 * (x100 * x628 + x333 * x68)
x653 = x55 * (x100 * x631 + x345)
x654 = x21 * x381 + x653
x655 = x21 * x382 + x654
x656 = x21 * x379 + x55 * (x100 * x635 + x343 * x68)
x657 = x55 * (x100 * x638 + x357)
x658 = x21 * x386 + x657
x659 = x21 * x387 + x658
x660 = x21 * x384 + x55 * (x100 * x642 + x354 * x68)
x661 = x55 * (x186 * x581 + x366)
x662 = x21 * x393 + x661
x663 = x21 * x394 + x662
x664 = x186 * x55 * (x589 + x590) + x21 * x390
x665 = x214 * x562
x666 = x21 * x399 + x665
x667 = x21 * x400 + x666
x668 = x21 * x397 + x214 * x573
x669 = -x218 * x408 + x405 * x9
x670 = -x669
x671 = x6 * x670
x672 = x218 * x404 - x412 * x9
x673 = x16 * x672
x674 = -x4 * x673 + x5 * x670
x675 = x4 * x674 + x671
x676 = x56 * (x671 + x675)
x677 = x242 * x671 + x56 * x676
x678 = x55 * (x246 * x671 + x56 * x677)
x679 = x22 * x247 + x678
x680 = x21 * x431 + x679
x681 = -x6 * (x669 + x673)
x682 = x218 * x411 - x433 * x571
x683 = x5 * x674 + x681 - x90 * (x5 * x672 - x682 * x90)
x684 = x42 * x674
x685 = x55 * (
x56 * (x56 * (x56 * (x4 * x683 + x684) + x675 * x68) + x676 * x68) + x677 * x68
)
x686 = x22 * x244 + x685
x687 = 10.2469507659596 * x98
x688 = x420 + x670 * x9
x689 = x417 + x674 * x9
x690 = x56 * x689 + x688 * x95
x691 = x300 * x688 + x56 * x690
x692 = x55 * (x56 * x691 + x585 * x688)
x693 = x22 * x275 + x692
x694 = x21 * x449 + x693
x695 = x436 + x683 * x9
x696 = x68 * x689
x697 = x55 * (x56 * (x56 * (x56 * x695 + x696) + x68 * x690) + x68 * x691)
x698 = x22 * x272 + x697
x699 = x115 * x139
x700 = x12 * x670 + x236
x701 = x12 * x674 + x233
x702 = x56 * x701 + x700 * x95
x703 = x300 * x700 + x56 * x702
x704 = x55 * (x56 * x703 + x585 * x700)
x705 = x22 * x289 + x704
x706 = x21 * x464 + x705
x707 = x12 * x683 + x254
x708 = x68 * x701
x709 = x55 * (x56 * (x56 * (x56 * x707 + x708) + x68 * x702) + x68 * x703)
x710 = x22 * x287 + x709
x711 = x100 * x688 + x440
x712 = x100 * (x417 + x689)
x713 = x56 * x712 + x711 * x95
x714 = x55 * (x300 * x711 + x56 * x713)
x715 = x22 * x301 + x714
x716 = x21 * x474 + x715
x717 = x100 * (x436 + x695)
x718 = x68 * x712
x719 = x55 * (x56 * (x56 * x717 + x718) + x68 * x713)
x720 = x22 * x298 + x719
x721 = x100 * x700 + x456
x722 = x100 * x701 + x452 * x95
x723 = x56 * x722 + x721 * x95
x724 = x55 * (x300 * x721 + x56 * x723)
x725 = x22 * x317 + x724
x726 = x21 * x484 + x725
x727 = x100 * x707 + x451 * x95
x728 = x68 * x722
x729 = x55 * (x56 * (x56 * x727 + x728) + x68 * x723)
x730 = x22 * x315 + x729
x731 = x305 * x322
x732 = x116 * x700 + x282
x733 = x116 * (x233 + x701)
x734 = x56 * x733 + x732 * x95
x735 = x55 * (x300 * x732 + x56 * x734)
x736 = x22 * x330 + x735
x737 = x21 * x497 + x736
x738 = x116 * (x254 + x707)
x739 = x68 * x733
x740 = x55 * (x56 * (x56 * x738 + x739) + x68 * x734)
x741 = x22 * x327 + x740
x742 = x100 * x711 + x468
x743 = x100 * x712 + x129 * x417
x744 = x55 * (x56 * x743 + x742 * x95)
x745 = x22 * x339 + x744
x746 = x21 * x504 + x745
x747 = x100 * x717 + x129 * x436
x748 = x68 * x743
x749 = x55 * (x56 * x747 + x748)
x750 = x22 * x336 + x749
x751 = x100 * x721 + x478
x752 = x100 * x722 + x452 * x515
x753 = x55 * (x56 * x752 + x751 * x95)
x754 = x22 * x349 + x753
x755 = x21 * x510 + x754
x756 = x100 * x727 + x451 * x515
x757 = x68 * x752
x758 = x55 * (x56 * x756 + x757)
x759 = x22 * x346 + x758
x760 = x100 * x732 + x492
x761 = x100 * x733 + x488 * x95
x762 = x55 * (x56 * x761 + x760 * x95)
x763 = x22 * x361 + x762
x764 = x21 * x518 + x763
x765 = x100 * x738 + x487 * x95
x766 = x68 * x761
x767 = x55 * (x56 * x765 + x766)
x768 = x22 * x358 + x767
x769 = x116 * x732 + x325
x770 = x116 * x733 + x153 * x233
x771 = x55 * (x56 * x770 + x769 * x95)
x772 = x22 * x370 + x771
x773 = x21 * x528 + x772
x774 = x116 * x738 + x153 * x254
x775 = x68 * x770
x776 = x55 * (x56 * x774 + x775)
x777 = x22 * x367 + x776
x778 = x55 * (x100 * x743 + x165 * x417)
x779 = x22 * x375 + x778
x780 = x21 * x535 + x779
x781 = x55 * (x100 * x747 + x165 * x436)
x782 = x22 * x373 + x781
x783 = x171 * x6
x784 = x55 * (x100 * x752 + x452 * x783)
x785 = x22 * x381 + x784
x786 = x21 * x540 + x785
x787 = x55 * (x100 * x756 + x451 * x783)
x788 = x22 * x379 + x787
x789 = x55 * (x100 * x761 + x488 * x515)
x790 = x22 * x386 + x789
x791 = x21 * x545 + x790
x792 = x55 * (x100 * x765 + x487 * x515)
x793 = x22 * x384 + x792
x794 = x55 * (x100 * x770 + x521 * x95)
x795 = x22 * x393 + x794
x796 = x21 * x550 + x795
x797 = x55 * (x100 * x774 + x520 * x95)
x798 = x22 * x390 + x797
x799 = x55 * (x116 * x770 + x186 * x233)
x800 = x22 * x399 + x799
x801 = x21 * x555 + x800
x802 = x55 * (x116 * x774 + x186 * x254)
x803 = x22 * x397 + x802
x804 = x12 * x405
x805 = x32 + x402 * x408 - x804
x806 = x6 * x805
x807 = -x12 * x412 + x402 * x404 + x43
x808 = x16 * x807
x809 = -x4 * x808 + x5 * x805
x810 = x4 * x809
x811 = x806 + x810
x812 = x56 * (x806 + x811)
x813 = x242 * x806 + x56 * x812
x814 = x55 * (x246 * x806 + x56 * x813)
x815 = x22 * x429 + x814
x816 = x22 * x431 + x815
x817 = x6 * (x402 * x408 - x804 - x808 - x87)
x818 = x12 * x16
x819 = x402 * x411 - x433 * x818 + x88
x820 = x5 * x809 + x817 - x90 * (x5 * x807 - x819 * x90)
x821 = x4 * x820
x822 = x6 * x809
x823 = 2.0 * x822
x824 = x22 * x427 + x55 * (
x56 * (x56 * (x56 * (x821 + x823) + x68 * x811) + x68 * x812) + x68 * x813
)
x825 = x100 * x806
x826 = x100 * x810 + x825
x827 = x443 * x806 + x56 * x826
x828 = x55 * (x447 * x806 + x56 * x827)
x829 = x22 * x448 + x828
x830 = x22 * x449 + x829
x831 = x22 * x445 + x55 * (
x56 * (x100 * x56 * (x821 + x823) + x68 * x826) + x68 * x827
)
x832 = x12 * x805 + 2.0 * x420
x833 = x832 * x95
x834 = x12 * x809 + x418
x835 = x56 * x834 + x833
x836 = x300 * x832 + x56 * x835
x837 = x55 * (x56 * x836 + x585 * x832)
x838 = x22 * x463 + x837
x839 = x22 * x464 + x838
x840 = x12 * x820 + 2.0 * x436
x841 = x22 * x460 + x55 * (
x56 * (x56 * (x56 * x840 + x68 * x834) + x68 * x835) + x68 * x836
)
x842 = x129 * x806
x843 = x129 * x810 + x842
x844 = x55 * (x472 * x806 + x56 * x843)
x845 = x22 * x473 + x844
x846 = x22 * x474 + x845
x847 = x22 * x470 + x55 * (x129 * x56 * (x821 + x823) + x68 * x843)
x848 = x515 * x832
x849 = x443 * x834 + x848
x850 = x4 * x832
x851 = x55 * (x178 * x6 * x850 + x56 * x849)
x852 = x22 * x483 + x851
x853 = x22 * x484 + x852
x854 = x22 * x480 + x55 * (x56 * (x443 * x840 + x512 * x834) + x68 * x849)
x855 = x116 * x832 + x455 * x68
x856 = x855 * x95
x857 = x116 * x834 + x453
x858 = x56 * x857 + x856
x859 = x55 * (x300 * x855 + x56 * x858)
x860 = x22 * x496 + x859
x861 = x22 * x497 + x860
x862 = x116 * x840 + x451 * x68
x863 = x22 * x494 + x55 * (x56 * (x56 * x862 + x68 * x857) + x68 * x858)
x864 = x165 * x806
x865 = x55 * (x165 * x810 + x864)
x866 = x22 * x503 + x865
x867 = x22 * x504 + x866
x868 = x165 * x55 * (x821 + x823) + x22 * x500
x869 = x783 * x832
x870 = x55 * (x472 * x834 + x869)
x871 = x22 * x509 + x870
x872 = x22 * x510 + x871
x873 = x22 * x506 + x55 * (x171 * x42 * x834 + x472 * x840)
x874 = x515 * x855
x875 = x55 * (x443 * x857 + x874)
x876 = x22 * x517 + x875
x877 = x22 * x518 + x876
x878 = x22 * x513 + x55 * (x443 * x862 + x512 * x857)
x879 = x116 * x855 + x491 * x68
x880 = x879 * x95
x881 = x116 * x857 + x489
x882 = x55 * (x56 * x881 + x880)
x883 = x22 * x527 + x882
x884 = x22 * x528 + x883
x885 = x116 * x862 + x487 * x68
x886 = x22 * x523 + x55 * (x56 * x885 + x68 * x881)
x887 = x193 * x809
x888 = x22 * x533 + x887
x889 = x22 * x535 + x888
x890 = x193 * x820 + x22 * x531
x891 = x198 * x834
x892 = x22 * x539 + x891
x893 = x22 * x540 + x892
x894 = x198 * x840 + x22 * x537
x895 = x171 * x857
x896 = x22 * x544 + x895
x897 = x22 * x545 + x896
x898 = x171 * x862 + x22 * x542
x899 = x141 * x881
x900 = x22 * x549 + x899
x901 = x22 * x550 + x900
x902 = x141 * x885 + x22 * x547
x903 = x55 * (x116 * x881 + x522)
x904 = x22 * x554 + x903
x905 = x22 * x555 + x904
x906 = x22 * x552 + x55 * (x116 * x885 + x520 * x68)
x907 = x218 * x558 + 2.0 * x223 - x561 * x9
x908 = x6 * x907
x909 = x218 * x560 + 2.0 * x250 - x571 * x572
x910 = x5 * x907 - x90 * x909
x911 = x4 * x910
x912 = (
x21 * x567
+ x21 * x568
+ x55 * (x246 * x908 + x56 * (x242 * x908 + x56**2 * (2.0 * x908 + x911)))
)
x913 = x9 * x907
x914 = 3.0 * x559
x915 = x913 + x914
x916 = x915 * x95
x917 = x9 * x910
x918 = 3.0 * x575
x919 = x917 + x918
x920 = (
x21 * x586
+ x21 * x587
+ x55 * (x56 * (x300 * x915 + x56 * (x56 * x919 + x916)) + x585 * x915)
)
x921 = x116 * x908
x922 = x12 * x908
x923 = (
x21 * x597
+ x21 * x598
+ x55 * (x274 * x922 + x56 * (x269 * x922 + x56 * (x116 * x911 + x921)))
)
x924 = x100 * x915 + x580 * x62
x925 = x924 * x95
x926 = x100 * x919 + x582 * x62
x927 = x21 * x604 + x21 * x605 + x55 * (x300 * x924 + x56 * (x56 * x926 + x925))
x928 = x116 * (x913 + x914)
x929 = x928 * x95
x930 = x116 * (x917 + x918)
x931 = x21 * x612 + x21 * x613 + x55 * (x300 * x928 + x56 * (x56 * x930 + x929))
x932 = x153 * x908
x933 = x21 * x619 + x21 * x620 + x55 * (x329 * x908 + x56 * (x153 * x911 + x932))
x934 = x100 * x924 + x601 * x62
x935 = x934 * x95
x936 = x100 * x926 + x602 * x62
x937 = x21 * x625 + x21 * x626 + x55 * (x56 * x936 + x935)
x938 = x100 * x928 + x609 * x62
x939 = x938 * x95
x940 = x100 * x930 + x610 * x62
x941 = x21 * x632 + x21 * x633 + x55 * (x56 * x940 + x939)
x942 = x153 * (x913 + x914)
x943 = x942 * x95
x944 = x153 * (x917 + x918)
x945 = x21 * x639 + x21 * x640 + x55 * (x56 * x944 + x943)
x946 = x186 * x908
x947 = x21 * x645 + x21 * x646 + x55 * (x186 * x911 + x946)
x948 = x21 * x649 + x21 * x650 + x55 * (x100 * x936 + x62 * x624)
x949 = x21 * x653 + x21 * x654 + x55 * (x100 * x940 + x62 * x631)
x950 = x21 * x657 + x21 * x658 + x55 * (x100 * x944 + x62 * x638)
x951 = x186 * x55 * (x917 + x918) + x21 * x661 + x21 * x662
x952 = x21 * x665 + x21 * x666 + x214 * x910
x953 = x218 * x670 + x407 - x673 * x9
x954 = x6 * x953
x955 = x218 * x672 + x432 - x571 * x682
x956 = x5 * x953 - x90 * x955
x957 = x55 * (x246 * x954 + x56 * (x242 * x954 + x56**2 * (x4 * x956 + 2.0 * x954)))
x958 = x21 * x679 + x22 * x567 + x957
x959 = 2.0 * x671
x960 = x9 * x953 + x959
x961 = x684 + x9 * x956
x962 = x55 * (x56 * (x300 * x960 + x56 * (x56 * x961 + x95 * x960)) + x585 * x960)
x963 = x21 * x693 + x22 * x586 + x962
x964 = x12 * x953 + x559
x965 = x12 * x956 + x575
x966 = x55 * (x56 * (x300 * x964 + x56 * (x56 * x965 + x95 * x964)) + x585 * x964)
x967 = x21 * x705 + x22 * x597 + x966
x968 = x100 * x960 + x68 * x688
x969 = x100 * x961 + x696
x970 = x55 * (x300 * x968 + x56 * (x56 * x969 + x95 * x968))
x971 = x21 * x715 + x22 * x604 + x970
x972 = x68 * x700
x973 = x100 * x964 + x972
x974 = x100 * x965 + x708
x975 = x55 * (x300 * x973 + x56 * (x56 * x974 + x95 * x973))
x976 = x21 * x725 + x22 * x612 + x975
x977 = x116 * x964 + x593
x978 = x116 * (x575 + x965)
x979 = x55 * (x300 * x977 + x56 * (x56 * x978 + x95 * x977))
x980 = x21 * x736 + x22 * x619 + x979
x981 = x100 * x968 + x68 * x711
x982 = x100 * x969 + x718
x983 = x55 * (x56 * x982 + x95 * x981)
x984 = x21 * x745 + x22 * x625 + x983
x985 = x100 * x973 + x68 * x721
x986 = x100 * x974 + x728
x987 = x55 * (x56 * x986 + x95 * x985)
x988 = x21 * x754 + x22 * x632 + x987
x989 = x68 * x732
x990 = x100 * x977 + x989
x991 = x100 * x978 + x739
x992 = x55 * (x56 * x991 + x95 * x990)
x993 = x21 * x763 + x22 * x639 + x992
x994 = x116 * x977 + x617
x995 = x116 * x978 + x153 * x575
x996 = x55 * (x56 * x995 + x95 * x994)
x997 = x21 * x772 + x22 * x645 + x996
x998 = x55 * (x100 * x982 + x748)
x999 = x21 * x779 + x22 * x649 + x998
x1000 = x55 * (x100 * x986 + x757)
x1001 = x1000 + x21 * x785 + x22 * x653
x1002 = x55 * (x100 * x991 + x766)
x1003 = x1002 + x21 * x790 + x22 * x657
x1004 = x55 * (x100 * x995 + x775)
x1005 = x1004 + x21 * x795 + x22 * x661
x1006 = x55 * (x116 * x995 + x186 * x575)
x1007 = x1006 + x21 * x800 + x22 * x665
x1008 = x218 * x805 - x808 * x9
x1009 = x1008 * x6
x1010 = x218 * x807 - x571 * x819
x1011 = x1008 * x5 - x1010 * x90
x1012 = x22 * x678 + x55 * (
x1009 * x246 + x56 * (x1009 * x242 + x56**2 * (2.0 * x1009 + x1011 * x4))
)
x1013 = x1012 + x22 * x679
x1014 = x1008 * x9 + x806
x1015 = x1011 * x9 + x822
x1016 = x22 * x692 + x55 * (
x1014 * x585 + x56 * (x1014 * x300 + x56 * (x1014 * x95 + x1015 * x56))
)
x1017 = x1016 + x22 * x693
x1018 = x1008 * x12 + x959
x1019 = x1011 * x12 + x684
x1020 = x22 * x704 + x55 * (
x1018 * x585 + x56 * (x1018 * x300 + x56 * (x1018 * x95 + x1019 * x56))
)
x1021 = x1020 + x22 * x705
x1022 = x100 * x1014 + x825
x1023 = x100 * (x1015 + x822)
x1024 = x22 * x714 + x55 * (x1022 * x300 + x56 * (x1022 * x95 + x1023 * x56))
x1025 = x1024 + x22 * x715
x1026 = x100 * x1018 + x833
x1027 = x100 * x1019 + x834 * x95
x1028 = x22 * x724 + x55 * (x1026 * x300 + x56 * (x1026 * x95 + x1027 * x56))
x1029 = x1028 + x22 * x725
x1030 = x1018 * x116 + x972
x1031 = x1019 * x116 + x708
x1032 = x22 * x735 + x55 * (x1030 * x300 + x56 * (x1030 * x95 + x1031 * x56))
x1033 = x1032 + x22 * x736
x1034 = x100 * x1022 + x842
x1035 = x100 * x1023 + x129 * x822
x1036 = x22 * x744 + x55 * (x1034 * x95 + x1035 * x56)
x1037 = x1036 + x22 * x745
x1038 = x100 * x1026 + x848
x1039 = x100 * x1027 + x515 * x834
x1040 = x22 * x753 + x55 * (x1038 * x95 + x1039 * x56)
x1041 = x1040 + x22 * x754
x1042 = x100 * x1030 + x856
x1043 = x100 * x1031 + x857 * x95
x1044 = x22 * x762 + x55 * (x1042 * x95 + x1043 * x56)
x1045 = x1044 + x22 * x763
x1046 = x1030 * x116 + x989
x1047 = x1031 * x116 + x739
x1048 = x22 * x771 + x55 * (x1046 * x95 + x1047 * x56)
x1049 = x1048 + x22 * x772
x1050 = x22 * x778 + x55 * (x100 * x1035 + x165 * x822)
x1051 = x1050 + x22 * x779
x1052 = x22 * x784 + x55 * (x100 * x1039 + x783 * x834)
x1053 = x1052 + x22 * x785
x1054 = x22 * x789 + x55 * (x100 * x1043 + x515 * x857)
x1055 = x1054 + x22 * x790
x1056 = x22 * x794 + x55 * (x100 * x1047 + x881 * x95)
x1057 = x1056 + x22 * x795
x1058 = x22 * x799 + x55 * (x1047 * x116 + x775)
x1059 = x1058 + x22 * x800
x1060 = -x12 * x808 + x402 * x805 + 2.0 * x407
x1061 = x1060 * x6
x1062 = x402 * x807 + 2.0 * x432 - x818 * x819
x1063 = x1060 * x5 - x1062 * x90
x1064 = x1063 * x4
x1065 = (
x22 * x814
+ x22 * x815
+ x55 * (x1061 * x246 + x56 * (x1061 * x242 + x56**2 * (2.0 * x1061 + x1064)))
)
x1066 = x100 * x1061
x1067 = (
x22 * x828
+ x22 * x829
+ x55 * (x1061 * x447 + x56 * (x1061 * x443 + x56 * (x100 * x1064 + x1066)))
)
x1068 = x1060 * x12 + 3.0 * x806
x1069 = x1068 * x95
x1070 = x1063 * x12 + 3.0 * x822
x1071 = (
x22 * x837
+ x22 * x838
+ x55 * (x1068 * x585 + x56 * (x1068 * x300 + x56 * (x1069 + x1070 * x56)))
)
x1072 = x1061 * x129
x1073 = x22 * x844 + x22 * x845 + x55 * (x1061 * x472 + x56 * (x1064 * x129 + x1072))
x1074 = x1068 * x515
x1075 = (
x22 * x851 + x22 * x852 + x55 * (x1068 * x482 * x6 + x56 * (x1070 * x443 + x1074))
)
x1076 = x1068 * x116 + x62 * x832
x1077 = x1076 * x95
x1078 = x1070 * x116 + x62 * x834
x1079 = x22 * x859 + x22 * x860 + x55 * (x1076 * x300 + x56 * (x1077 + x1078 * x56))
x1080 = x1061 * x165
x1081 = x22 * x865 + x22 * x866 + x55 * (x1064 * x165 + x1080)
x1082 = x1068 * x783
x1083 = x22 * x870 + x22 * x871 + x55 * (x1070 * x472 + x1082)
x1084 = x1076 * x515
x1085 = x22 * x875 + x22 * x876 + x55 * (x1078 * x443 + x1084)
x1086 = x1076 * x116 + x62 * x855
x1087 = x1086 * x95
x1088 = x1078 * x116 + x62 * x857
x1089 = x22 * x882 + x22 * x883 + x55 * (x1087 + x1088 * x56)
x1090 = x1063 * x193 + x22 * x887 + x22 * x888
x1091 = x1070 * x198 + x22 * x891 + x22 * x892
x1092 = x1078 * x171 + x22 * x895 + x22 * x896
x1093 = x1088 * x141 + x22 * x899 + x22 * x900
x1094 = x22 * x903 + x22 * x904 + x55 * (x1088 * x116 + x62 * x881)
x1095 = x0 * x247 + x244
x1096 = x192 * x4**4
x1097 = x0 * x224
x1098 = x0 * x275 + x272
x1099 = x192 * x81
x1100 = x1099 * x265
x1101 = x0 * x289 + x287
x1102 = x1099 * x12
x1103 = x0 * x301 + x298
x1104 = x0 * x274
x1105 = x0 * x317 + x315
x1106 = x0 * x330 + x327
x1107 = x13 * x7
x1108 = x1097 * x192
x1109 = x0 * x339 + x336
x1110 = x0 * x269
x1111 = x0 * x349 + x346
x1112 = x0 * x361 + x358
x1113 = x0 * x370 + x367
x1114 = x185 * x4
x1115 = x0 * x375 + x373
x1116 = x100 * x338 + x169
x1117 = x0 * x381 + x379
x1118 = x100 * x348 + x176
x1119 = x0 * x386 + x384
x1120 = x100 * x360 + x183
x1121 = x0 * x393 + x390
x1122 = x186 * x264 + x190
x1123 = x0 * x399 + x397
x1124 = x1096 * x558
x1125 = x21 * x224
x1126 = x1096 * x1125 + x1124
x1127 = x1099 * x580
x1128 = x1100 * x21 + x1127
x1129 = x1102 * x558
x1130 = x1102 * x1125 + x1129
x1131 = x274 * x601
x1132 = x21 * x274
x1133 = x1131 + x1132 * x296
x1134 = x274 * x609
x1135 = x1132 * x313 + x1134
x1136 = x192 * x558
x1137 = x1107 * x1136
x1138 = x1125 * x192
x1139 = x1107 * x1138 + x1137
x1140 = x269 * x623
x1141 = x21 * x269
x1142 = x1140 + x1141 * x338
x1143 = x269 * x630
x1144 = x1141 * x348 + x1143
x1145 = x269 * x637
x1146 = x1141 * x360 + x1145
x1147 = x1114 * x1136
x1148 = x1114 * x1138 + x1147
x1149 = x55 * (x100 * x623 + x338 * x68)
x1150 = x1116 * x248 + x1149
x1151 = x55 * (x100 * x630 + x348 * x68)
x1152 = x1118 * x248 + x1151
x1153 = x55 * (x100 * x637 + x360 * x68)
x1154 = x1120 * x248 + x1153
x1155 = x186 * x55 * (x578 + x579)
x1156 = x1122 * x248 + x1155
x1157 = x214 * x558
x1158 = x1125 * x214 + x1157
x1159 = x1096 * x670
x1160 = x22 * x224
x1161 = x1096 * x1160 + x1159
x1162 = x1099 * x688
x1163 = x1100 * x22 + x1162
x1164 = x1099 * x700
x1165 = x1102 * x1160 + x1164
x1166 = x274 * x711
x1167 = x22 * x274
x1168 = x1166 + x1167 * x296
x1169 = x274 * x721
x1170 = x1167 * x313 + x1169
x1171 = x274 * x732
x1172 = x1160 * x192
x1173 = x1107 * x1172 + x1171
x1174 = x269 * x742
x1175 = x22 * x269
x1176 = x1174 + x1175 * x338
x1177 = x269 * x751
x1178 = x1175 * x348 + x1177
x1179 = x269 * x760
x1180 = x1175 * x360 + x1179
x1181 = x269 * x769
x1182 = x1114 * x1172 + x1181
x1183 = x55 * (x100 * x742 + x502)
x1184 = x1116 * x430 + x1183
x1185 = x55 * (x100 * x751 + x508)
x1186 = x1118 * x430 + x1185
x1187 = x55 * (x100 * x760 + x516)
x1188 = x1120 * x430 + x1187
x1189 = x55 * (x100 * x769 + x526)
x1190 = x1122 * x430 + x1189
x1191 = x55 * (x116 * x769 + x369)
x1192 = x1160 * x214 + x1191
x1193 = x1096 * x907
x1194 = x1124 * x21 + x1193
x1195 = x1126 * x21 + x1194
x1196 = x1099 * x915
x1197 = x1127 * x21 + x1196
x1198 = x1128 * x21 + x1197
x1199 = x1102 * x907
x1200 = x1129 * x21 + x1199
x1201 = x1130 * x21 + x1200
x1202 = x274 * x924
x1203 = x1131 * x21 + x1202
x1204 = x1133 * x21 + x1203
x1205 = x274 * x928
x1206 = x1134 * x21 + x1205
x1207 = x1135 * x21 + x1206
x1208 = x192 * x907
x1209 = x1107 * x1208
x1210 = x1137 * x21 + x1209
x1211 = x1139 * x21 + x1210
x1212 = x269 * x934
x1213 = x1140 * x21 + x1212
x1214 = x1142 * x21 + x1213
x1215 = x269 * x938
x1216 = x1143 * x21 + x1215
x1217 = x1144 * x21 + x1216
x1218 = x269 * x942
x1219 = x1145 * x21 + x1218
x1220 = x1146 * x21 + x1219
x1221 = x1114 * x1208
x1222 = x1147 * x21 + x1221
x1223 = x1148 * x21 + x1222
x1224 = x55 * (x100 * x934 + x62 * x623)
x1225 = x1149 * x21 + x1224
x1226 = x1150 * x21 + x1225
x1227 = x55 * (x100 * x938 + x62 * x630)
x1228 = x1151 * x21 + x1227
x1229 = x1152 * x21 + x1228
x1230 = x55 * (x100 * x942 + x62 * x637)
x1231 = x1153 * x21 + x1230
x1232 = x1154 * x21 + x1231
x1233 = x186 * x55 * (x913 + x914)
x1234 = x1155 * x21 + x1233
x1235 = x1156 * x21 + x1234
x1236 = x214 * x907
x1237 = x1157 * x21 + x1236
x1238 = x1158 * x21 + x1237
x1239 = x1096 * x953
x1240 = x1124 * x22 + x1239
x1241 = x1161 * x21 + x1240
x1242 = x1099 * x960
x1243 = x1127 * x22 + x1242
x1244 = x1163 * x21 + x1243
x1245 = x1099 * x964
x1246 = x1129 * x22 + x1245
x1247 = x1165 * x21 + x1246
x1248 = x274 * x968
x1249 = x1131 * x22 + x1248
x1250 = x1168 * x21 + x1249
x1251 = x274 * x973
x1252 = x1134 * x22 + x1251
x1253 = x1170 * x21 + x1252
x1254 = x274 * x977
x1255 = x1137 * x22 + x1254
x1256 = x1173 * x21 + x1255
x1257 = x269 * x981
x1258 = x1140 * x22 + x1257
x1259 = x1176 * x21 + x1258
x1260 = x269 * x985
x1261 = x1143 * x22 + x1260
x1262 = x1178 * x21 + x1261
x1263 = x269 * x990
x1264 = x1145 * x22 + x1263
x1265 = x1180 * x21 + x1264
x1266 = x269 * x994
x1267 = x1147 * x22 + x1266
x1268 = x1182 * x21 + x1267
x1269 = x55 * (x100 * x981 + x68 * x742)
x1270 = x1149 * x22 + x1269
x1271 = x1184 * x21 + x1270
x1272 = x55 * (x100 * x985 + x68 * x751)
x1273 = x1151 * x22 + x1272
x1274 = x1186 * x21 + x1273
x1275 = x55 * (x100 * x990 + x68 * x760)
x1276 = x1153 * x22 + x1275
x1277 = x1188 * x21 + x1276
x1278 = x68 * x769
x1279 = x55 * (x100 * x994 + x1278)
x1280 = x1155 * x22 + x1279
x1281 = x1190 * x21 + x1280
x1282 = x55 * (x116 * x994 + x644)
x1283 = x1157 * x22 + x1282
x1284 = x1192 * x21 + x1283
x1285 = x1008 * x1096
x1286 = x1159 * x22 + x1285
x1287 = x1161 * x22 + x1286
x1288 = x1014 * x1099
x1289 = x1162 * x22 + x1288
x1290 = x1163 * x22 + x1289
x1291 = x1018 * x1099
x1292 = x1164 * x22 + x1291
x1293 = x1165 * x22 + x1292
x1294 = x1022 * x274
x1295 = x1166 * x22 + x1294
x1296 = x1168 * x22 + x1295
x1297 = x1026 * x274
x1298 = x1169 * x22 + x1297
x1299 = x1170 * x22 + x1298
x1300 = x1030 * x274
x1301 = x1171 * x22 + x1300
x1302 = x1173 * x22 + x1301
x1303 = x1034 * x269
x1304 = x1174 * x22 + x1303
x1305 = x1176 * x22 + x1304
x1306 = x1038 * x269
x1307 = x1177 * x22 + x1306
x1308 = x1178 * x22 + x1307
x1309 = x1042 * x269
x1310 = x1179 * x22 + x1309
x1311 = x1180 * x22 + x1310
x1312 = x1046 * x269
x1313 = x1181 * x22 + x1312
x1314 = x1182 * x22 + x1313
x1315 = x55 * (x100 * x1034 + x864)
x1316 = x1183 * x22 + x1315
x1317 = x1184 * x22 + x1316
x1318 = x55 * (x100 * x1038 + x869)
x1319 = x1185 * x22 + x1318
x1320 = x1186 * x22 + x1319
x1321 = x55 * (x100 * x1042 + x874)
x1322 = x1187 * x22 + x1321
x1323 = x1188 * x22 + x1322
x1324 = x55 * (x100 * x1046 + x880)
x1325 = x1189 * x22 + x1324
x1326 = x1190 * x22 + x1325
x1327 = x55 * (x1046 * x116 + x1278)
x1328 = x1191 * x22 + x1327
x1329 = x1192 * x22 + x1328
x1330 = x218 * x907 + 3.0 * x570 - x571 * x909
x1331 = x1330 * x9
x1332 = 4.0 * x908
x1333 = x1331 + x1332
x1334 = x100 * x1333 + 4.0 * x916
x1335 = x116 * (x1331 + x1332)
x1336 = x1330 * x192
x1337 = x100 * x1334 + 4.0 * x925
x1338 = x100 * x1335 + 4.0 * x929
x1339 = x153 * (x1331 + x1332)
x1340 = x218 * x953 - x571 * x955 + 2.0 * x681
x1341 = x1096 * x1340
x1342 = x1340 * x9 + 3.0 * x954
x1343 = x1099 * x1342
x1344 = x12 * x1340 + x908
x1345 = x1099 * x1344
x1346 = x100 * x1342 + x62 * x960
x1347 = x1346 * x274
x1348 = x100 * x1344 + x62 * x964
x1349 = x1348 * x274
x1350 = x116 * x1344 + x921
x1351 = x1350 * x274
x1352 = x100 * x1346 + x62 * x968
x1353 = x1352 * x269
x1354 = x100 * x1348 + x62 * x973
x1355 = x1354 * x269
x1356 = x100 * x1350 + x62 * x977
x1357 = x1356 * x269
x1358 = x116 * x1350 + x932
x1359 = x1358 * x269
x1360 = x55 * (x100 * x1352 + x62 * x981)
x1361 = x55 * (x100 * x1354 + x62 * x985)
x1362 = x55 * (x100 * x1356 + x62 * x990)
x1363 = x55 * (x100 * x1358 + x62 * x994)
x1364 = x55 * (x116 * x1358 + x946)
x1365 = x1008 * x218 - x1010 * x571 + x817
x1366 = x1096 * x1365 + x1239 * x22
x1367 = 2.0 * x1009 + x1365 * x9
x1368 = x1099 * x1367 + x1242 * x22
x1369 = x12 * x1365 + 2.0 * x954
x1370 = x1099 * x1369 + x1245 * x22
x1371 = x100 * x1367 + x1014 * x68
x1372 = x1248 * x22 + x1371 * x274
x1373 = x100 * x1369 + x1018 * x68
x1374 = x1251 * x22 + x1373 * x274
x1375 = x116 * x1369 + x68 * x964
x1376 = x1254 * x22 + x1375 * x274
x1377 = x100 * x1371 + x1022 * x68
x1378 = x1257 * x22 + x1377 * x269
x1379 = x100 * x1373 + x1026 * x68
x1380 = x1260 * x22 + x1379 * x269
x1381 = x100 * x1375 + x1030 * x68
x1382 = x1263 * x22 + x1381 * x269
x1383 = x116 * x1375 + x68 * x977
x1384 = x1266 * x22 + x1383 * x269
x1385 = x1269 * x22 + x55 * (x100 * x1377 + x1034 * x68)
x1386 = x1272 * x22 + x55 * (x100 * x1379 + x1038 * x68)
x1387 = x1275 * x22 + x55 * (x100 * x1381 + x1042 * x68)
x1388 = x1279 * x22 + x55 * (x100 * x1383 + x1046 * x68)
x1389 = x1282 * x22 + x55 * (x116 * x1383 + x68 * x994)
x1390 = x1060 * x218 - x1062 * x571
x1391 = x1096 * x1390 + x1285 * x22 + x1286 * x22
x1392 = x1061 + x1390 * x9
x1393 = x1099 * x1392 + x1288 * x22 + x1289 * x22
x1394 = 3.0 * x1009 + x12 * x1390
x1395 = x1099 * x1394 + x1291 * x22 + x1292 * x22
x1396 = x100 * x1392 + x1066
x1397 = x1294 * x22 + x1295 * x22 + x1396 * x274
x1398 = x100 * x1394 + x1069
x1399 = x1297 * x22 + x1298 * x22 + x1398 * x274
x1400 = x1018 * x62 + x116 * x1394
x1401 = x1300 * x22 + x1301 * x22 + x1400 * x274
x1402 = x100 * x1396 + x1072
x1403 = x1303 * x22 + x1304 * x22 + x1402 * x269
x1404 = x100 * x1398 + x1074
x1405 = x1306 * x22 + x1307 * x22 + x1404 * x269
x1406 = x100 * x1400 + x1077
x1407 = x1309 * x22 + x1310 * x22 + x1406 * x269
x1408 = x1030 * x62 + x116 * x1400
x1409 = x1312 * x22 + x1313 * x22 + x1408 * x269
x1410 = x1315 * x22 + x1316 * x22 + x55 * (x100 * x1402 + x1080)
x1411 = x1318 * x22 + x1319 * x22 + x55 * (x100 * x1404 + x1082)
x1412 = x1321 * x22 + x1322 * x22 + x55 * (x100 * x1406 + x1084)
x1413 = x1324 * x22 + x1325 * x22 + x55 * (x100 * x1408 + x1087)
x1414 = x1327 * x22 + x1328 * x22 + x55 * (x1046 * x62 + x116 * x1408)
x1415 = x0 * x429 + x427
x1416 = x0 * x408
x1417 = x0 * x448 + x445
x1418 = x1099 * x9
x1419 = x0 * x463 + x460
x1420 = x0 * x455
x1421 = x0 * x473 + x470
x1422 = x192 * x7
x1423 = x10 * x1422
x1424 = x0 * x483 + x480
x1425 = x1422 * x9
x1426 = x0 * x496 + x494
x1427 = x0 * x503 + x500
x1428 = x198 * x4
x1429 = x0 * x509 + x506
x1430 = x10 * x192
x1431 = x1430 * x4
x1432 = x0 * x517 + x513
x1433 = x482 * x491
x1434 = x0 * x527 + x523
x1435 = x0 * x533 + x531
x1436 = x0 * x539 + x537
x1437 = x0 * x544 + x542
x1438 = x171 * x491
x1439 = x0 * x549 + x547
x1440 = x141 * x525
x1441 = x0 * x554 + x552
x1442 = x116 * x525 + x190
x1443 = x21 * x429 + x678
x1444 = x21 * x408
x1445 = x1096 * x1444 + x1159
x1446 = x21 * x448 + x692
x1447 = x1162 + x1418 * x1444
x1448 = x21 * x463 + x704
x1449 = x21 * x455
x1450 = x1099 * x1449 + x1164
x1451 = x21 * x473 + x714
x1452 = x1166 + x1423 * x1444
x1453 = x21 * x483 + x724
x1454 = x1169 + x1425 * x1449
x1455 = x21 * x496 + x735
x1456 = x1132 * x491 + x1171
x1457 = x21 * x503 + x744
x1458 = x1174 + x1428 * x1444
x1459 = x21 * x509 + x753
x1460 = x1177 + x1431 * x1449
x1461 = x21 * x517 + x762
x1462 = x1179 + x1433 * x21
x1463 = x21 * x527 + x771
x1464 = x1141 * x525 + x1181
x1465 = x21 * x533 + x778
x1466 = x1183 + x1444 * x193
x1467 = x21 * x539 + x784
x1468 = x1185 + x1449 * x198
x1469 = x21 * x544 + x789
x1470 = x1187 + x1438 * x21
x1471 = x21 * x549 + x794
x1472 = x1189 + x1440 * x21
x1473 = x21 * x554 + x799
x1474 = x1191 + x1442 * x248
x1475 = x1096 * x805
x1476 = x22 * x408
x1477 = x1096 * x1476 + x1475
x1478 = x1418 * x805
x1479 = x1418 * x1476 + x1478
x1480 = x1099 * x832
x1481 = x22 * x455
x1482 = x1099 * x1481 + x1480
x1483 = x1423 * x805
x1484 = x1423 * x1476 + x1483
x1485 = x1425 * x832
x1486 = x1425 * x1481 + x1485
x1487 = x274 * x855
x1488 = x1167 * x491 + x1487
x1489 = x1428 * x805
x1490 = x1428 * x1476 + x1489
x1491 = x1430 * x850
x1492 = x1431 * x1481 + x1491
x1493 = x482 * x855
x1494 = x1433 * x22 + x1493
x1495 = x269 * x879
x1496 = x1175 * x525 + x1495
x1497 = x193 * x805
x1498 = x1476 * x193 + x1497
x1499 = x198 * x832
x1500 = x1481 * x198 + x1499
x1501 = x171 * x855
x1502 = x1438 * x22 + x1501
x1503 = x141 * x879
x1504 = x1440 * x22 + x1503
x1505 = x55 * (x116 * x879 + x525 * x68)
x1506 = x1442 * x430 + x1505
x1507 = x1159 * x21 + x1239
x1508 = x1445 * x21 + x1507
x1509 = x1162 * x21 + x1242
x1510 = x1447 * x21 + x1509
x1511 = x1164 * x21 + x1245
x1512 = x1450 * x21 + x1511
x1513 = x1166 * x21 + x1248
x1514 = x1452 * x21 + x1513
x1515 = x1169 * x21 + x1251
x1516 = x1454 * x21 + x1515
x1517 = x1171 * x21 + x1254
x1518 = x1456 * x21 + x1517
x1519 = x1174 * x21 + x1257
x1520 = x1458 * x21 + x1519
x1521 = x1177 * x21 + x1260
x1522 = x1460 * x21 + x1521
x1523 = x1179 * x21 + x1263
x1524 = x1462 * x21 + x1523
x1525 = x1181 * x21 + x1266
x1526 = x1464 * x21 + x1525
x1527 = x1183 * x21 + x1269
x1528 = x1466 * x21 + x1527
x1529 = x1185 * x21 + x1272
x1530 = x1468 * x21 + x1529
x1531 = x1187 * x21 + x1275
x1532 = x1470 * x21 + x1531
x1533 = x1189 * x21 + x1279
x1534 = x1472 * x21 + x1533
x1535 = x1191 * x21 + x1282
x1536 = x1474 * x21 + x1535
x1537 = x1286 + x1477 * x21
x1538 = x1289 + x1479 * x21
x1539 = x1292 + x1482 * x21
x1540 = x1295 + x1484 * x21
x1541 = x1298 + x1486 * x21
x1542 = x1301 + x1488 * x21
x1543 = x1304 + x1490 * x21
x1544 = x1307 + x1492 * x21
x1545 = x1310 + x1494 * x21
x1546 = x1313 + x1496 * x21
x1547 = x1316 + x1498 * x21
x1548 = x1319 + x1500 * x21
x1549 = x1322 + x1502 * x21
x1550 = x1325 + x1504 * x21
x1551 = x1328 + x1506 * x21
x1552 = x1060 * x1096
x1553 = x1475 * x22 + x1552
x1554 = x1477 * x22 + x1553
x1555 = x1060 * x1418
x1556 = x1478 * x22 + x1555
x1557 = x1479 * x22 + x1556
x1558 = x1068 * x1099
x1559 = x1480 * x22 + x1558
x1560 = x1482 * x22 + x1559
x1561 = x1060 * x1423
x1562 = x1483 * x22 + x1561
x1563 = x1484 * x22 + x1562
x1564 = x1068 * x1425
x1565 = x1485 * x22 + x1564
x1566 = x1486 * x22 + x1565
x1567 = x1076 * x274
x1568 = x1487 * x22 + x1567
x1569 = x1488 * x22 + x1568
x1570 = x1060 * x1428
x1571 = x1489 * x22 + x1570
x1572 = x1490 * x22 + x1571
x1573 = x1068 * x1431
x1574 = x1491 * x22 + x1573
x1575 = x1492 * x22 + x1574
x1576 = x1076 * x482
x1577 = x1493 * x22 + x1576
x1578 = x1494 * x22 + x1577
x1579 = x1086 * x269
x1580 = x1495 * x22 + x1579
x1581 = x1496 * x22 + x1580
x1582 = x1060 * x193
x1583 = x1497 * x22 + x1582
x1584 = x1498 * x22 + x1583
x1585 = x1068 * x198
x1586 = x1499 * x22 + x1585
x1587 = x1500 * x22 + x1586
x1588 = x1076 * x171
x1589 = x1501 * x22 + x1588
x1590 = x1502 * x22 + x1589
x1591 = x1086 * x141
x1592 = x1503 * x22 + x1591
x1593 = x1504 * x22 + x1592
x1594 = x55 * (x1086 * x116 + x62 * x879)
x1595 = x1505 * x22 + x1594
x1596 = x1506 * x22 + x1595
x1597 = x1060 * x402 - x1062 * x818 + 3.0 * x817
x1598 = 4.0 * x1061 + x12 * x1597
x1599 = 4.0 * x1069 + x116 * x1598
x1600 = 4.0 * x1077 + x116 * x1599
# 450 item(s)
result[0, 0, 0] = numpy.sum(
x99
* (
x0 * x75
+ x0 * x80
+ x0 * (x0 * (x79 + x85 * x86) + x80)
+ x55
* (x56 * (x56 * (x54 * x96 + x56 * (x92 + x94)) + x63 * x96) + x70 * x96)
)
)
result[0, 0, 1] = numpy.sum(
x115
* (
x0 * x107
+ x0 * x112
+ x0 * (x0 * (x111 + x114 * x86) + x112)
+ x55 * (x103 * x96 + x56 * (x100 * x56 * (x92 + x94) + x101 * x96))
)
)
result[0, 0, 2] = numpy.sum(
x115
* (
x0 * x123
+ x0 * x126
+ x0 * (x0 * (x125 + x127 * x86) + x126)
+ x55 * (x119 * x96 + x56 * (x116 * x56 * (x92 + x94) + x117 * x96))
)
)
result[0, 0, 3] = numpy.sum(
x140
* (
x0 * x132
+ x0 * x136
+ x0 * (x0 * (x135 + x138 * x86) + x136)
+ x55 * (x129 * x56 * (x92 + x94) + x130 * x96)
)
)
result[0, 0, 4] = numpy.sum(
x152
* (
x0 * x145
+ x0 * x150
+ x0 * (x0 * (x149 + x151 * x86) + x150)
+ x55 * (x142 * x56 * (x92 + x94) + x143 * x96)
)
)
result[0, 0, 5] = numpy.sum(
x140
* (
x0 * x156
+ x0 * x160
+ x0 * (x0 * (x159 + x162 * x86) + x160)
+ x55 * (x153 * x56 * (x92 + x94) + x154 * x96)
)
)
result[0, 0, 6] = numpy.sum(
x115
* (
x0 * x166
+ x0 * x168
+ x0 * (x0 * (x167 + x170 * x86) + x168)
+ x165 * x55 * (x92 + x94)
)
)
result[0, 0, 7] = numpy.sum(
x152
* (
x0 * x173
+ x0 * x175
+ x0 * (x0 * (x174 + x177 * x86) + x175)
+ x172 * x55 * (x92 + x94)
)
)
result[0, 0, 8] = numpy.sum(
x152
* (
x0 * x180
+ x0 * x182
+ x0 * (x0 * (x181 + x184 * x86) + x182)
+ x179 * x55 * (x92 + x94)
)
)
result[0, 0, 9] = numpy.sum(
x115
* (
x0 * x187
+ x0 * x189
+ x0 * (x0 * (x188 + x191 * x86) + x189)
+ x186 * x55 * (x92 + x94)
)
)
result[0, 0, 10] = numpy.sum(
x99
* (x0 * x194 + x0 * x196 + x0 * (x0 * (x193 * x197 + x195) + x196) + x193 * x91)
)
result[0, 0, 11] = numpy.sum(
x115
* (x0 * x200 + x0 * x202 + x0 * (x0 * (x197 * x199 + x201) + x202) + x199 * x91)
)
result[0, 0, 12] = numpy.sum(
x140
* (x0 * x205 + x0 * x208 + x0 * (x0 * (x197 * x206 + x207) + x208) + x206 * x91)
)
result[0, 0, 13] = numpy.sum(
x115
* (x0 * x210 + x0 * x213 + x0 * (x0 * (x197 * x211 + x212) + x213) + x211 * x91)
)
result[0, 0, 14] = numpy.sum(
x99
* (x0 * x215 + x0 * x217 + x0 * (x0 * (x197 * x214 + x216) + x217) + x214 * x91)
)
result[0, 1, 0] = numpy.sum(
x257 * (x0 * x245 + x0 * (x0 * x249 + x245) + x21 * x75 + x256)
)
result[0, 1, 1] = numpy.sum(
x152 * (x0 * x273 + x0 * (x0 * x276 + x273) + x107 * x21 + x279)
)
result[0, 1, 2] = numpy.sum(
x152 * (x0 * x288 + x0 * (x0 * x290 + x288) + x123 * x21 + x291)
)
result[0, 1, 3] = numpy.sum(
x306 * (x0 * x299 + x0 * (x0 * x302 + x299) + x132 * x21 + x304)
)
result[0, 1, 4] = numpy.sum(
x322 * (x0 * x316 + x0 * (x0 * x318 + x316) + x145 * x21 + x321)
)
result[0, 1, 5] = numpy.sum(
x306 * (x0 * x328 + x0 * (x0 * x331 + x328) + x156 * x21 + x332)
)
result[0, 1, 6] = numpy.sum(
x152 * (x0 * x337 + x0 * (x0 * x340 + x337) + x166 * x21 + x342)
)
result[0, 1, 7] = numpy.sum(
x322 * (x0 * x347 + x0 * (x0 * x350 + x347) + x173 * x21 + x352)
)
result[0, 1, 8] = numpy.sum(
x322 * (x0 * x359 + x0 * (x0 * x362 + x359) + x180 * x21 + x365)
)
result[0, 1, 9] = numpy.sum(
x152 * (x0 * x368 + x0 * (x0 * x371 + x368) + x187 * x21 + x372)
)
result[0, 1, 10] = numpy.sum(
x257 * (x0 * x374 + x0 * (x0 * x377 + x374) + x194 * x21 + x378)
)
result[0, 1, 11] = numpy.sum(
x152 * (x0 * x380 + x0 * (x0 * x382 + x380) + x200 * x21 + x383)
)
result[0, 1, 12] = numpy.sum(
x306 * (x0 * x385 + x0 * (x0 * x387 + x385) + x205 * x21 + x388)
)
result[0, 1, 13] = numpy.sum(
x152 * (x0 * x391 + x0 * (x0 * x394 + x391) + x21 * x210 + x396)
)
result[0, 1, 14] = numpy.sum(
x257 * (x0 * x398 + x0 * (x0 * x400 + x398) + x21 * x215 + x401)
)
result[0, 2, 0] = numpy.sum(
x257 * (x0 * x428 + x0 * (x0 * x431 + x428) + x22 * x75 + x438)
)
result[0, 2, 1] = numpy.sum(
x152 * (x0 * x446 + x0 * (x0 * x449 + x446) + x107 * x22 + x450)
)
result[0, 2, 2] = numpy.sum(
x152 * (x0 * x461 + x0 * (x0 * x464 + x461) + x123 * x22 + x466)
)
result[0, 2, 3] = numpy.sum(
x306 * (x0 * x471 + x0 * (x0 * x474 + x471) + x132 * x22 + x475)
)
result[0, 2, 4] = numpy.sum(
x322 * (x0 * x481 + x0 * (x0 * x484 + x481) + x145 * x22 + x486)
)
result[0, 2, 5] = numpy.sum(
x306 * (x0 * x495 + x0 * (x0 * x497 + x495) + x156 * x22 + x499)
)
result[0, 2, 6] = numpy.sum(
x152 * (x0 * x501 + x0 * (x0 * x504 + x501) + x166 * x22 + x505)
)
result[0, 2, 7] = numpy.sum(
x322 * (x0 * x507 + x0 * (x0 * x510 + x507) + x173 * x22 + x511)
)
result[0, 2, 8] = numpy.sum(
x322 * (x0 * x514 + x0 * (x0 * x518 + x514) + x180 * x22 + x519)
)
result[0, 2, 9] = numpy.sum(
x152 * (x0 * x524 + x0 * (x0 * x528 + x524) + x187 * x22 + x530)
)
result[0, 2, 10] = numpy.sum(
x257 * (x0 * x532 + x0 * (x0 * x535 + x532) + x194 * x22 + x536)
)
result[0, 2, 11] = numpy.sum(
x152 * (x0 * x538 + x0 * (x0 * x540 + x538) + x200 * x22 + x541)
)
result[0, 2, 12] = numpy.sum(
x306 * (x0 * x543 + x0 * (x0 * x545 + x543) + x205 * x22 + x546)
)
result[0, 2, 13] = numpy.sum(
x152 * (x0 * x548 + x0 * (x0 * x550 + x548) + x210 * x22 + x551)
)
result[0, 2, 14] = numpy.sum(
x257 * (x0 * x553 + x0 * (x0 * x555 + x553) + x215 * x22 + x556)
)
result[0, 3, 0] = numpy.sum(x257 * (x0 * x569 + x21 * x245 + x577))
result[0, 3, 1] = numpy.sum(x152 * (x0 * x588 + x21 * x273 + x592))
result[0, 3, 2] = numpy.sum(x152 * (x0 * x599 + x21 * x288 + x600))
result[0, 3, 3] = numpy.sum(x306 * (x0 * x606 + x21 * x299 + x608))
result[0, 3, 4] = numpy.sum(x322 * (x0 * x614 + x21 * x316 + x616))
result[0, 3, 5] = numpy.sum(x306 * (x0 * x621 + x21 * x328 + x622))
result[0, 3, 6] = numpy.sum(x152 * (x0 * x627 + x21 * x337 + x629))
result[0, 3, 7] = numpy.sum(x322 * (x0 * x634 + x21 * x347 + x636))
result[0, 3, 8] = numpy.sum(x322 * (x0 * x641 + x21 * x359 + x643))
result[0, 3, 9] = numpy.sum(x152 * (x0 * x647 + x21 * x368 + x648))
result[0, 3, 10] = numpy.sum(x257 * (x0 * x651 + x21 * x374 + x652))
result[0, 3, 11] = numpy.sum(x152 * (x0 * x655 + x21 * x380 + x656))
result[0, 3, 12] = numpy.sum(x306 * (x0 * x659 + x21 * x385 + x660))
result[0, 3, 13] = numpy.sum(x152 * (x0 * x663 + x21 * x391 + x664))
result[0, 3, 14] = numpy.sum(x257 * (x0 * x667 + x21 * x398 + x668))
result[0, 4, 0] = numpy.sum(x687 * (x0 * x680 + x21 * x428 + x686))
result[0, 4, 1] = numpy.sum(x699 * (x0 * x694 + x21 * x446 + x698))
result[0, 4, 2] = numpy.sum(x699 * (x0 * x706 + x21 * x461 + x710))
result[0, 4, 3] = numpy.sum(x322 * (x0 * x716 + x21 * x471 + x720))
result[0, 4, 4] = numpy.sum(x731 * (x0 * x726 + x21 * x481 + x730))
result[0, 4, 5] = numpy.sum(x322 * (x0 * x737 + x21 * x495 + x741))
result[0, 4, 6] = numpy.sum(x699 * (x0 * x746 + x21 * x501 + x750))
result[0, 4, 7] = numpy.sum(x731 * (x0 * x755 + x21 * x507 + x759))
result[0, 4, 8] = numpy.sum(x731 * (x0 * x764 + x21 * x514 + x768))
result[0, 4, 9] = numpy.sum(x699 * (x0 * x773 + x21 * x524 + x777))
result[0, 4, 10] = numpy.sum(x687 * (x0 * x780 + x21 * x532 + x782))
result[0, 4, 11] = numpy.sum(x699 * (x0 * x786 + x21 * x538 + x788))
result[0, 4, 12] = numpy.sum(x322 * (x0 * x791 + x21 * x543 + x793))
result[0, 4, 13] = numpy.sum(x699 * (x0 * x796 + x21 * x548 + x798))
result[0, 4, 14] = numpy.sum(x687 * (x0 * x801 + x21 * x553 + x803))
result[0, 5, 0] = numpy.sum(x257 * (x0 * x816 + x22 * x428 + x824))
result[0, 5, 1] = numpy.sum(x152 * (x0 * x830 + x22 * x446 + x831))
result[0, 5, 2] = numpy.sum(x152 * (x0 * x839 + x22 * x461 + x841))
result[0, 5, 3] = numpy.sum(x306 * (x0 * x846 + x22 * x471 + x847))
result[0, 5, 4] = numpy.sum(x322 * (x0 * x853 + x22 * x481 + x854))
result[0, 5, 5] = numpy.sum(x306 * (x0 * x861 + x22 * x495 + x863))
result[0, 5, 6] = numpy.sum(x152 * (x0 * x867 + x22 * x501 + x868))
result[0, 5, 7] = numpy.sum(x322 * (x0 * x872 + x22 * x507 + x873))
result[0, 5, 8] = numpy.sum(x322 * (x0 * x877 + x22 * x514 + x878))
result[0, 5, 9] = numpy.sum(x152 * (x0 * x884 + x22 * x524 + x886))
result[0, 5, 10] = numpy.sum(x257 * (x0 * x889 + x22 * x532 + x890))
result[0, 5, 11] = numpy.sum(x152 * (x0 * x893 + x22 * x538 + x894))
result[0, 5, 12] = numpy.sum(x306 * (x0 * x897 + x22 * x543 + x898))
result[0, 5, 13] = numpy.sum(x152 * (x0 * x901 + x22 * x548 + x902))
result[0, 5, 14] = numpy.sum(x257 * (x0 * x905 + x22 * x553 + x906))
result[0, 6, 0] = numpy.sum(x99 * (x21 * x569 + x912))
result[0, 6, 1] = numpy.sum(x115 * (x21 * x588 + x920))
result[0, 6, 2] = numpy.sum(x115 * (x21 * x599 + x923))
result[0, 6, 3] = numpy.sum(x140 * (x21 * x606 + x927))
result[0, 6, 4] = numpy.sum(x152 * (x21 * x614 + x931))
result[0, 6, 5] = numpy.sum(x140 * (x21 * x621 + x933))
result[0, 6, 6] = numpy.sum(x115 * (x21 * x627 + x937))
result[0, 6, 7] = numpy.sum(x152 * (x21 * x634 + x941))
result[0, 6, 8] = numpy.sum(x152 * (x21 * x641 + x945))
result[0, 6, 9] = numpy.sum(x115 * (x21 * x647 + x947))
result[0, 6, 10] = numpy.sum(x99 * (x21 * x651 + x948))
result[0, 6, 11] = numpy.sum(x115 * (x21 * x655 + x949))
result[0, 6, 12] = numpy.sum(x140 * (x21 * x659 + x950))
result[0, 6, 13] = numpy.sum(x115 * (x21 * x663 + x951))
result[0, 6, 14] = numpy.sum(x99 * (x21 * x667 + x952))
result[0, 7, 0] = numpy.sum(x257 * (x21 * x680 + x958))
result[0, 7, 1] = numpy.sum(x152 * (x21 * x694 + x963))
result[0, 7, 2] = numpy.sum(x152 * (x21 * x706 + x967))
result[0, 7, 3] = numpy.sum(x306 * (x21 * x716 + x971))
result[0, 7, 4] = numpy.sum(x322 * (x21 * x726 + x976))
result[0, 7, 5] = numpy.sum(x306 * (x21 * x737 + x980))
result[0, 7, 6] = numpy.sum(x152 * (x21 * x746 + x984))
result[0, 7, 7] = numpy.sum(x322 * (x21 * x755 + x988))
result[0, 7, 8] = numpy.sum(x322 * (x21 * x764 + x993))
result[0, 7, 9] = numpy.sum(x152 * (x21 * x773 + x997))
result[0, 7, 10] = numpy.sum(x257 * (x21 * x780 + x999))
result[0, 7, 11] = numpy.sum(x152 * (x1001 + x21 * x786))
result[0, 7, 12] = numpy.sum(x306 * (x1003 + x21 * x791))
result[0, 7, 13] = numpy.sum(x152 * (x1005 + x21 * x796))
result[0, 7, 14] = numpy.sum(x257 * (x1007 + x21 * x801))
result[0, 8, 0] = numpy.sum(x257 * (x1013 + x21 * x816))
result[0, 8, 1] = numpy.sum(x152 * (x1017 + x21 * x830))
result[0, 8, 2] = numpy.sum(x152 * (x1021 + x21 * x839))
result[0, 8, 3] = numpy.sum(x306 * (x1025 + x21 * x846))
result[0, 8, 4] = numpy.sum(x322 * (x1029 + x21 * x853))
result[0, 8, 5] = numpy.sum(x306 * (x1033 + x21 * x861))
result[0, 8, 6] = numpy.sum(x152 * (x1037 + x21 * x867))
result[0, 8, 7] = numpy.sum(x322 * (x1041 + x21 * x872))
result[0, 8, 8] = numpy.sum(x322 * (x1045 + x21 * x877))
result[0, 8, 9] = numpy.sum(x152 * (x1049 + x21 * x884))
result[0, 8, 10] = numpy.sum(x257 * (x1051 + x21 * x889))
result[0, 8, 11] = numpy.sum(x152 * (x1053 + x21 * x893))
result[0, 8, 12] = numpy.sum(x306 * (x1055 + x21 * x897))
result[0, 8, 13] = numpy.sum(x152 * (x1057 + x21 * x901))
result[0, 8, 14] = numpy.sum(x257 * (x1059 + x21 * x905))
result[0, 9, 0] = numpy.sum(x99 * (x1065 + x22 * x816))
result[0, 9, 1] = numpy.sum(x115 * (x1067 + x22 * x830))
result[0, 9, 2] = numpy.sum(x115 * (x1071 + x22 * x839))
result[0, 9, 3] = numpy.sum(x140 * (x1073 + x22 * x846))
result[0, 9, 4] = numpy.sum(x152 * (x1075 + x22 * x853))
result[0, 9, 5] = numpy.sum(x140 * (x1079 + x22 * x861))
result[0, 9, 6] = numpy.sum(x115 * (x1081 + x22 * x867))
result[0, 9, 7] = numpy.sum(x152 * (x1083 + x22 * x872))
result[0, 9, 8] = numpy.sum(x152 * (x1085 + x22 * x877))
result[0, 9, 9] = numpy.sum(x115 * (x1089 + x22 * x884))
result[0, 9, 10] = numpy.sum(x99 * (x1090 + x22 * x889))
result[0, 9, 11] = numpy.sum(x115 * (x1091 + x22 * x893))
result[0, 9, 12] = numpy.sum(x140 * (x1092 + x22 * x897))
result[0, 9, 13] = numpy.sum(x115 * (x1093 + x22 * x901))
result[0, 9, 14] = numpy.sum(x99 * (x1094 + x22 * x905))
result[1, 0, 0] = numpy.sum(
x99 * (x0 * x1095 + x0 * x244 + x0 * (x0 * (x1096 * x1097 + x247) + x1095) + x256)
)
result[1, 0, 1] = numpy.sum(
x115 * (x0 * x1098 + x0 * x272 + x0 * (x0 * (x0 * x1100 + x275) + x1098) + x279)
)
result[1, 0, 2] = numpy.sum(
x115
* (x0 * x1101 + x0 * x287 + x0 * (x0 * (x1097 * x1102 + x289) + x1101) + x291)
)
result[1, 0, 3] = numpy.sum(
x140 * (x0 * x1103 + x0 * x298 + x0 * (x0 * (x1104 * x296 + x301) + x1103) + x304)
)
result[1, 0, 4] = numpy.sum(
x152 * (x0 * x1105 + x0 * x315 + x0 * (x0 * (x1104 * x313 + x317) + x1105) + x321)
)
result[1, 0, 5] = numpy.sum(
x140
* (x0 * x1106 + x0 * x327 + x0 * (x0 * (x1107 * x1108 + x330) + x1106) + x332)
)
result[1, 0, 6] = numpy.sum(
x115 * (x0 * x1109 + x0 * x336 + x0 * (x0 * (x1110 * x338 + x339) + x1109) + x342)
)
result[1, 0, 7] = numpy.sum(
x152 * (x0 * x1111 + x0 * x346 + x0 * (x0 * (x1110 * x348 + x349) + x1111) + x352)
)
result[1, 0, 8] = numpy.sum(
x152 * (x0 * x1112 + x0 * x358 + x0 * (x0 * (x1110 * x360 + x361) + x1112) + x365)
)
result[1, 0, 9] = numpy.sum(
x115
* (x0 * x1113 + x0 * x367 + x0 * (x0 * (x1108 * x1114 + x370) + x1113) + x372)
)
result[1, 0, 10] = numpy.sum(
x99 * (x0 * x1115 + x0 * x373 + x0 * (x0 * (x1116 * x86 + x375) + x1115) + x378)
)
result[1, 0, 11] = numpy.sum(
x115 * (x0 * x1117 + x0 * x379 + x0 * (x0 * (x1118 * x86 + x381) + x1117) + x383)
)
result[1, 0, 12] = numpy.sum(
x140 * (x0 * x1119 + x0 * x384 + x0 * (x0 * (x1120 * x86 + x386) + x1119) + x388)
)
result[1, 0, 13] = numpy.sum(
x115 * (x0 * x1121 + x0 * x390 + x0 * (x0 * (x1122 * x86 + x393) + x1121) + x396)
)
result[1, 0, 14] = numpy.sum(
x99 * (x0 * x1123 + x0 * x397 + x0 * (x0 * (x1097 * x214 + x399) + x1123) + x401)
)
result[1, 1, 0] = numpy.sum(x257 * (x0 * x568 + x0 * (x0 * x1126 + x568) + x577))
result[1, 1, 1] = numpy.sum(x152 * (x0 * x587 + x0 * (x0 * x1128 + x587) + x592))
result[1, 1, 2] = numpy.sum(x152 * (x0 * x598 + x0 * (x0 * x1130 + x598) + x600))
result[1, 1, 3] = numpy.sum(x306 * (x0 * x605 + x0 * (x0 * x1133 + x605) + x608))
result[1, 1, 4] = numpy.sum(x322 * (x0 * x613 + x0 * (x0 * x1135 + x613) + x616))
result[1, 1, 5] = numpy.sum(x306 * (x0 * x620 + x0 * (x0 * x1139 + x620) + x622))
result[1, 1, 6] = numpy.sum(x152 * (x0 * x626 + x0 * (x0 * x1142 + x626) + x629))
result[1, 1, 7] = numpy.sum(x322 * (x0 * x633 + x0 * (x0 * x1144 + x633) + x636))
result[1, 1, 8] = numpy.sum(x322 * (x0 * x640 + x0 * (x0 * x1146 + x640) + x643))
result[1, 1, 9] = numpy.sum(x152 * (x0 * x646 + x0 * (x0 * x1148 + x646) + x648))
result[1, 1, 10] = numpy.sum(x257 * (x0 * x650 + x0 * (x0 * x1150 + x650) + x652))
result[1, 1, 11] = numpy.sum(x152 * (x0 * x654 + x0 * (x0 * x1152 + x654) + x656))
result[1, 1, 12] = numpy.sum(x306 * (x0 * x658 + x0 * (x0 * x1154 + x658) + x660))
result[1, 1, 13] = numpy.sum(x152 * (x0 * x662 + x0 * (x0 * x1156 + x662) + x664))
result[1, 1, 14] = numpy.sum(x257 * (x0 * x666 + x0 * (x0 * x1158 + x666) + x668))
result[1, 2, 0] = numpy.sum(x257 * (x0 * x679 + x0 * (x0 * x1161 + x679) + x686))
result[1, 2, 1] = numpy.sum(x152 * (x0 * x693 + x0 * (x0 * x1163 + x693) + x698))
result[1, 2, 2] = numpy.sum(x152 * (x0 * x705 + x0 * (x0 * x1165 + x705) + x710))
result[1, 2, 3] = numpy.sum(x306 * (x0 * x715 + x0 * (x0 * x1168 + x715) + x720))
result[1, 2, 4] = numpy.sum(x322 * (x0 * x725 + x0 * (x0 * x1170 + x725) + x730))
result[1, 2, 5] = numpy.sum(x306 * (x0 * x736 + x0 * (x0 * x1173 + x736) + x741))
result[1, 2, 6] = numpy.sum(x152 * (x0 * x745 + x0 * (x0 * x1176 + x745) + x750))
result[1, 2, 7] = numpy.sum(x322 * (x0 * x754 + x0 * (x0 * x1178 + x754) + x759))
result[1, 2, 8] = numpy.sum(x322 * (x0 * x763 + x0 * (x0 * x1180 + x763) + x768))
result[1, 2, 9] = numpy.sum(x152 * (x0 * x772 + x0 * (x0 * x1182 + x772) + x777))
result[1, 2, 10] = numpy.sum(x257 * (x0 * x779 + x0 * (x0 * x1184 + x779) + x782))
result[1, 2, 11] = numpy.sum(x152 * (x0 * x785 + x0 * (x0 * x1186 + x785) + x788))
result[1, 2, 12] = numpy.sum(x306 * (x0 * x790 + x0 * (x0 * x1188 + x790) + x793))
result[1, 2, 13] = numpy.sum(x152 * (x0 * x795 + x0 * (x0 * x1190 + x795) + x798))
result[1, 2, 14] = numpy.sum(x257 * (x0 * x800 + x0 * (x0 * x1192 + x800) + x803))
result[1, 3, 0] = numpy.sum(x257 * (x0 * x1195 + x912))
result[1, 3, 1] = numpy.sum(x152 * (x0 * x1198 + x920))
result[1, 3, 2] = numpy.sum(x152 * (x0 * x1201 + x923))
result[1, 3, 3] = numpy.sum(x306 * (x0 * x1204 + x927))
result[1, 3, 4] = numpy.sum(x322 * (x0 * x1207 + x931))
result[1, 3, 5] = numpy.sum(x306 * (x0 * x1211 + x933))
result[1, 3, 6] = numpy.sum(x152 * (x0 * x1214 + x937))
result[1, 3, 7] = numpy.sum(x322 * (x0 * x1217 + x941))
result[1, 3, 8] = numpy.sum(x322 * (x0 * x1220 + x945))
result[1, 3, 9] = numpy.sum(x152 * (x0 * x1223 + x947))
result[1, 3, 10] = numpy.sum(x257 * (x0 * x1226 + x948))
result[1, 3, 11] = numpy.sum(x152 * (x0 * x1229 + x949))
result[1, 3, 12] = numpy.sum(x306 * (x0 * x1232 + x950))
result[1, 3, 13] = numpy.sum(x152 * (x0 * x1235 + x951))
result[1, 3, 14] = numpy.sum(x257 * (x0 * x1238 + x952))
result[1, 4, 0] = numpy.sum(x687 * (x0 * x1241 + x958))
result[1, 4, 1] = numpy.sum(x699 * (x0 * x1244 + x963))
result[1, 4, 2] = numpy.sum(x699 * (x0 * x1247 + x967))
result[1, 4, 3] = numpy.sum(x322 * (x0 * x1250 + x971))
result[1, 4, 4] = numpy.sum(x731 * (x0 * x1253 + x976))
result[1, 4, 5] = numpy.sum(x322 * (x0 * x1256 + x980))
result[1, 4, 6] = numpy.sum(x699 * (x0 * x1259 + x984))
result[1, 4, 7] = numpy.sum(x731 * (x0 * x1262 + x988))
result[1, 4, 8] = numpy.sum(x731 * (x0 * x1265 + x993))
result[1, 4, 9] = numpy.sum(x699 * (x0 * x1268 + x997))
result[1, 4, 10] = numpy.sum(x687 * (x0 * x1271 + x999))
result[1, 4, 11] = numpy.sum(x699 * (x0 * x1274 + x1001))
result[1, 4, 12] = numpy.sum(x322 * (x0 * x1277 + x1003))
result[1, 4, 13] = numpy.sum(x699 * (x0 * x1281 + x1005))
result[1, 4, 14] = numpy.sum(x687 * (x0 * x1284 + x1007))
result[1, 5, 0] = numpy.sum(x257 * (x0 * x1287 + x1013))
result[1, 5, 1] = numpy.sum(x152 * (x0 * x1290 + x1017))
result[1, 5, 2] = numpy.sum(x152 * (x0 * x1293 + x1021))
result[1, 5, 3] = numpy.sum(x306 * (x0 * x1296 + x1025))
result[1, 5, 4] = numpy.sum(x322 * (x0 * x1299 + x1029))
result[1, 5, 5] = numpy.sum(x306 * (x0 * x1302 + x1033))
result[1, 5, 6] = numpy.sum(x152 * (x0 * x1305 + x1037))
result[1, 5, 7] = numpy.sum(x322 * (x0 * x1308 + x1041))
result[1, 5, 8] = numpy.sum(x322 * (x0 * x1311 + x1045))
result[1, 5, 9] = numpy.sum(x152 * (x0 * x1314 + x1049))
result[1, 5, 10] = numpy.sum(x257 * (x0 * x1317 + x1051))
result[1, 5, 11] = numpy.sum(x152 * (x0 * x1320 + x1053))
result[1, 5, 12] = numpy.sum(x306 * (x0 * x1323 + x1055))
result[1, 5, 13] = numpy.sum(x152 * (x0 * x1326 + x1057))
result[1, 5, 14] = numpy.sum(x257 * (x0 * x1329 + x1059))
result[1, 6, 0] = numpy.sum(
x99 * (x1096 * x1330 + x1193 * x21 + x1194 * x21 + x1195 * x21)
)
result[1, 6, 1] = numpy.sum(
x115 * (x1099 * x1333 + x1196 * x21 + x1197 * x21 + x1198 * x21)
)
result[1, 6, 2] = numpy.sum(
x115 * (x1102 * x1330 + x1199 * x21 + x1200 * x21 + x1201 * x21)
)
result[1, 6, 3] = numpy.sum(
x140 * (x1202 * x21 + x1203 * x21 + x1204 * x21 + x1334 * x274)
)
result[1, 6, 4] = numpy.sum(
x152 * (x1205 * x21 + x1206 * x21 + x1207 * x21 + x1335 * x274)
)
result[1, 6, 5] = numpy.sum(
x140 * (x1107 * x1336 + x1209 * x21 + x1210 * x21 + x1211 * x21)
)
result[1, 6, 6] = numpy.sum(
x115 * (x1212 * x21 + x1213 * x21 + x1214 * x21 + x1337 * x269)
)
result[1, 6, 7] = numpy.sum(
x152 * (x1215 * x21 + x1216 * x21 + x1217 * x21 + x1338 * x269)
)
result[1, 6, 8] = numpy.sum(
x152 * (x1218 * x21 + x1219 * x21 + x1220 * x21 + x1339 * x269)
)
result[1, 6, 9] = numpy.sum(
x115 * (x1114 * x1336 + x1221 * x21 + x1222 * x21 + x1223 * x21)
)
result[1, 6, 10] = numpy.sum(
x99
* (x1224 * x21 + x1225 * x21 + x1226 * x21 + x55 * (x100 * x1337 + 4.0 * x935))
)
result[1, 6, 11] = numpy.sum(
x115
* (x1227 * x21 + x1228 * x21 + x1229 * x21 + x55 * (x100 * x1338 + 4.0 * x939))
)
result[1, 6, 12] = numpy.sum(
x140
* (x1230 * x21 + x1231 * x21 + x1232 * x21 + x55 * (x100 * x1339 + 4.0 * x943))
)
result[1, 6, 13] = numpy.sum(
x115 * (x1233 * x21 + x1234 * x21 + x1235 * x21 + x186 * x55 * (x1331 + x1332))
)
result[1, 6, 14] = numpy.sum(
x99 * (x1236 * x21 + x1237 * x21 + x1238 * x21 + x1330 * x214)
)
result[1, 7, 0] = numpy.sum(x257 * (x1193 * x22 + x1240 * x21 + x1241 * x21 + x1341))
result[1, 7, 1] = numpy.sum(x152 * (x1196 * x22 + x1243 * x21 + x1244 * x21 + x1343))
result[1, 7, 2] = numpy.sum(x152 * (x1199 * x22 + x1246 * x21 + x1247 * x21 + x1345))
result[1, 7, 3] = numpy.sum(x306 * (x1202 * x22 + x1249 * x21 + x1250 * x21 + x1347))
result[1, 7, 4] = numpy.sum(x322 * (x1205 * x22 + x1252 * x21 + x1253 * x21 + x1349))
result[1, 7, 5] = numpy.sum(x306 * (x1209 * x22 + x1255 * x21 + x1256 * x21 + x1351))
result[1, 7, 6] = numpy.sum(x152 * (x1212 * x22 + x1258 * x21 + x1259 * x21 + x1353))
result[1, 7, 7] = numpy.sum(x322 * (x1215 * x22 + x1261 * x21 + x1262 * x21 + x1355))
result[1, 7, 8] = numpy.sum(x322 * (x1218 * x22 + x1264 * x21 + x1265 * x21 + x1357))
result[1, 7, 9] = numpy.sum(x152 * (x1221 * x22 + x1267 * x21 + x1268 * x21 + x1359))
result[1, 7, 10] = numpy.sum(x257 * (x1224 * x22 + x1270 * x21 + x1271 * x21 + x1360))
result[1, 7, 11] = numpy.sum(x152 * (x1227 * x22 + x1273 * x21 + x1274 * x21 + x1361))
result[1, 7, 12] = numpy.sum(x306 * (x1230 * x22 + x1276 * x21 + x1277 * x21 + x1362))
result[1, 7, 13] = numpy.sum(x152 * (x1233 * x22 + x1280 * x21 + x1281 * x21 + x1363))
result[1, 7, 14] = numpy.sum(x257 * (x1236 * x22 + x1283 * x21 + x1284 * x21 + x1364))
result[1, 8, 0] = numpy.sum(x257 * (x1240 * x22 + x1287 * x21 + x1366))
result[1, 8, 1] = numpy.sum(x152 * (x1243 * x22 + x1290 * x21 + x1368))
result[1, 8, 2] = numpy.sum(x152 * (x1246 * x22 + x1293 * x21 + x1370))
result[1, 8, 3] = numpy.sum(x306 * (x1249 * x22 + x1296 * x21 + x1372))
result[1, 8, 4] = numpy.sum(x322 * (x1252 * x22 + x1299 * x21 + x1374))
result[1, 8, 5] = numpy.sum(x306 * (x1255 * x22 + x1302 * x21 + x1376))
result[1, 8, 6] = numpy.sum(x152 * (x1258 * x22 + x1305 * x21 + x1378))
result[1, 8, 7] = numpy.sum(x322 * (x1261 * x22 + x1308 * x21 + x1380))
result[1, 8, 8] = numpy.sum(x322 * (x1264 * x22 + x1311 * x21 + x1382))
result[1, 8, 9] = numpy.sum(x152 * (x1267 * x22 + x1314 * x21 + x1384))
result[1, 8, 10] = numpy.sum(x257 * (x1270 * x22 + x1317 * x21 + x1385))
result[1, 8, 11] = numpy.sum(x152 * (x1273 * x22 + x1320 * x21 + x1386))
result[1, 8, 12] = numpy.sum(x306 * (x1276 * x22 + x1323 * x21 + x1387))
result[1, 8, 13] = numpy.sum(x152 * (x1280 * x22 + x1326 * x21 + x1388))
result[1, 8, 14] = numpy.sum(x257 * (x1283 * x22 + x1329 * x21 + x1389))
result[1, 9, 0] = numpy.sum(x99 * (x1287 * x22 + x1391))
result[1, 9, 1] = numpy.sum(x115 * (x1290 * x22 + x1393))
result[1, 9, 2] = numpy.sum(x115 * (x1293 * x22 + x1395))
result[1, 9, 3] = numpy.sum(x140 * (x1296 * x22 + x1397))
result[1, 9, 4] = numpy.sum(x152 * (x1299 * x22 + x1399))
result[1, 9, 5] = numpy.sum(x140 * (x1302 * x22 + x1401))
result[1, 9, 6] = numpy.sum(x115 * (x1305 * x22 + x1403))
result[1, 9, 7] = numpy.sum(x152 * (x1308 * x22 + x1405))
result[1, 9, 8] = numpy.sum(x152 * (x1311 * x22 + x1407))
result[1, 9, 9] = numpy.sum(x115 * (x1314 * x22 + x1409))
result[1, 9, 10] = numpy.sum(x99 * (x1317 * x22 + x1410))
result[1, 9, 11] = numpy.sum(x115 * (x1320 * x22 + x1411))
result[1, 9, 12] = numpy.sum(x140 * (x1323 * x22 + x1412))
result[1, 9, 13] = numpy.sum(x115 * (x1326 * x22 + x1413))
result[1, 9, 14] = numpy.sum(x99 * (x1329 * x22 + x1414))
result[2, 0, 0] = numpy.sum(
x99 * (x0 * x1415 + x0 * x427 + x0 * (x0 * (x1096 * x1416 + x429) + x1415) + x438)
)
result[2, 0, 1] = numpy.sum(
x115
* (x0 * x1417 + x0 * x445 + x0 * (x0 * (x1416 * x1418 + x448) + x1417) + x450)
)
result[2, 0, 2] = numpy.sum(
x115
* (x0 * x1419 + x0 * x460 + x0 * (x0 * (x1099 * x1420 + x463) + x1419) + x466)
)
result[2, 0, 3] = numpy.sum(
x140
* (x0 * x1421 + x0 * x470 + x0 * (x0 * (x1416 * x1423 + x473) + x1421) + x475)
)
result[2, 0, 4] = numpy.sum(
x152
* (x0 * x1424 + x0 * x480 + x0 * (x0 * (x1420 * x1425 + x483) + x1424) + x486)
)
result[2, 0, 5] = numpy.sum(
x140 * (x0 * x1426 + x0 * x494 + x0 * (x0 * (x1104 * x491 + x496) + x1426) + x499)
)
result[2, 0, 6] = numpy.sum(
x115
* (x0 * x1427 + x0 * x500 + x0 * (x0 * (x1416 * x1428 + x503) + x1427) + x505)
)
result[2, 0, 7] = numpy.sum(
x152
* (x0 * x1429 + x0 * x506 + x0 * (x0 * (x1420 * x1431 + x509) + x1429) + x511)
)
result[2, 0, 8] = numpy.sum(
x152 * (x0 * x1432 + x0 * x513 + x0 * (x0 * (x0 * x1433 + x517) + x1432) + x519)
)
result[2, 0, 9] = numpy.sum(
x115 * (x0 * x1434 + x0 * x523 + x0 * (x0 * (x1110 * x525 + x527) + x1434) + x530)
)
result[2, 0, 10] = numpy.sum(
x99 * (x0 * x1435 + x0 * x531 + x0 * (x0 * (x1416 * x193 + x533) + x1435) + x536)
)
result[2, 0, 11] = numpy.sum(
x115 * (x0 * x1436 + x0 * x537 + x0 * (x0 * (x1420 * x198 + x539) + x1436) + x541)
)
result[2, 0, 12] = numpy.sum(
x140 * (x0 * x1437 + x0 * x542 + x0 * (x0 * (x0 * x1438 + x544) + x1437) + x546)
)
result[2, 0, 13] = numpy.sum(
x115 * (x0 * x1439 + x0 * x547 + x0 * (x0 * (x0 * x1440 + x549) + x1439) + x551)
)
result[2, 0, 14] = numpy.sum(
x99 * (x0 * x1441 + x0 * x552 + x0 * (x0 * (x1442 * x86 + x554) + x1441) + x556)
)
result[2, 1, 0] = numpy.sum(
x257 * (x0 * x1443 + x0 * (x0 * x1445 + x1443) + x21 * x427 + x685)
)
result[2, 1, 1] = numpy.sum(
x152 * (x0 * x1446 + x0 * (x0 * x1447 + x1446) + x21 * x445 + x697)
)
result[2, 1, 2] = numpy.sum(
x152 * (x0 * x1448 + x0 * (x0 * x1450 + x1448) + x21 * x460 + x709)
)
result[2, 1, 3] = numpy.sum(
x306 * (x0 * x1451 + x0 * (x0 * x1452 + x1451) + x21 * x470 + x719)
)
result[2, 1, 4] = numpy.sum(
x322 * (x0 * x1453 + x0 * (x0 * x1454 + x1453) + x21 * x480 + x729)
)
result[2, 1, 5] = numpy.sum(
x306 * (x0 * x1455 + x0 * (x0 * x1456 + x1455) + x21 * x494 + x740)
)
result[2, 1, 6] = numpy.sum(
x152 * (x0 * x1457 + x0 * (x0 * x1458 + x1457) + x21 * x500 + x749)
)
result[2, 1, 7] = numpy.sum(
x322 * (x0 * x1459 + x0 * (x0 * x1460 + x1459) + x21 * x506 + x758)
)
result[2, 1, 8] = numpy.sum(
x322 * (x0 * x1461 + x0 * (x0 * x1462 + x1461) + x21 * x513 + x767)
)
result[2, 1, 9] = numpy.sum(
x152 * (x0 * x1463 + x0 * (x0 * x1464 + x1463) + x21 * x523 + x776)
)
result[2, 1, 10] = numpy.sum(
x257 * (x0 * x1465 + x0 * (x0 * x1466 + x1465) + x21 * x531 + x781)
)
result[2, 1, 11] = numpy.sum(
x152 * (x0 * x1467 + x0 * (x0 * x1468 + x1467) + x21 * x537 + x787)
)
result[2, 1, 12] = numpy.sum(
x306 * (x0 * x1469 + x0 * (x0 * x1470 + x1469) + x21 * x542 + x792)
)
result[2, 1, 13] = numpy.sum(
x152 * (x0 * x1471 + x0 * (x0 * x1472 + x1471) + x21 * x547 + x797)
)
result[2, 1, 14] = numpy.sum(
x257 * (x0 * x1473 + x0 * (x0 * x1474 + x1473) + x21 * x552 + x802)
)
result[2, 2, 0] = numpy.sum(x257 * (x0 * x815 + x0 * (x0 * x1477 + x815) + x824))
result[2, 2, 1] = numpy.sum(x152 * (x0 * x829 + x0 * (x0 * x1479 + x829) + x831))
result[2, 2, 2] = numpy.sum(x152 * (x0 * x838 + x0 * (x0 * x1482 + x838) + x841))
result[2, 2, 3] = numpy.sum(x306 * (x0 * x845 + x0 * (x0 * x1484 + x845) + x847))
result[2, 2, 4] = numpy.sum(x322 * (x0 * x852 + x0 * (x0 * x1486 + x852) + x854))
result[2, 2, 5] = numpy.sum(x306 * (x0 * x860 + x0 * (x0 * x1488 + x860) + x863))
result[2, 2, 6] = numpy.sum(x152 * (x0 * x866 + x0 * (x0 * x1490 + x866) + x868))
result[2, 2, 7] = numpy.sum(x322 * (x0 * x871 + x0 * (x0 * x1492 + x871) + x873))
result[2, 2, 8] = numpy.sum(x322 * (x0 * x876 + x0 * (x0 * x1494 + x876) + x878))
result[2, 2, 9] = numpy.sum(x152 * (x0 * x883 + x0 * (x0 * x1496 + x883) + x886))
result[2, 2, 10] = numpy.sum(x257 * (x0 * x888 + x0 * (x0 * x1498 + x888) + x890))
result[2, 2, 11] = numpy.sum(x152 * (x0 * x892 + x0 * (x0 * x1500 + x892) + x894))
result[2, 2, 12] = numpy.sum(x306 * (x0 * x896 + x0 * (x0 * x1502 + x896) + x898))
result[2, 2, 13] = numpy.sum(x152 * (x0 * x900 + x0 * (x0 * x1504 + x900) + x902))
result[2, 2, 14] = numpy.sum(x257 * (x0 * x904 + x0 * (x0 * x1506 + x904) + x906))
result[2, 3, 0] = numpy.sum(x257 * (x0 * x1508 + x1443 * x21 + x21 * x678 + x957))
result[2, 3, 1] = numpy.sum(x152 * (x0 * x1510 + x1446 * x21 + x21 * x692 + x962))
result[2, 3, 2] = numpy.sum(x152 * (x0 * x1512 + x1448 * x21 + x21 * x704 + x966))
result[2, 3, 3] = numpy.sum(x306 * (x0 * x1514 + x1451 * x21 + x21 * x714 + x970))
result[2, 3, 4] = numpy.sum(x322 * (x0 * x1516 + x1453 * x21 + x21 * x724 + x975))
result[2, 3, 5] = numpy.sum(x306 * (x0 * x1518 + x1455 * x21 + x21 * x735 + x979))
result[2, 3, 6] = numpy.sum(x152 * (x0 * x1520 + x1457 * x21 + x21 * x744 + x983))
result[2, 3, 7] = numpy.sum(x322 * (x0 * x1522 + x1459 * x21 + x21 * x753 + x987))
result[2, 3, 8] = numpy.sum(x322 * (x0 * x1524 + x1461 * x21 + x21 * x762 + x992))
result[2, 3, 9] = numpy.sum(x152 * (x0 * x1526 + x1463 * x21 + x21 * x771 + x996))
result[2, 3, 10] = numpy.sum(x257 * (x0 * x1528 + x1465 * x21 + x21 * x778 + x998))
result[2, 3, 11] = numpy.sum(x152 * (x0 * x1530 + x1000 + x1467 * x21 + x21 * x784))
result[2, 3, 12] = numpy.sum(x306 * (x0 * x1532 + x1002 + x1469 * x21 + x21 * x789))
result[2, 3, 13] = numpy.sum(x152 * (x0 * x1534 + x1004 + x1471 * x21 + x21 * x794))
result[2, 3, 14] = numpy.sum(x257 * (x0 * x1536 + x1006 + x1473 * x21 + x21 * x799))
result[2, 4, 0] = numpy.sum(x687 * (x0 * x1537 + x1012 + x21 * x815))
result[2, 4, 1] = numpy.sum(x699 * (x0 * x1538 + x1016 + x21 * x829))
result[2, 4, 2] = numpy.sum(x699 * (x0 * x1539 + x1020 + x21 * x838))
result[2, 4, 3] = numpy.sum(x322 * (x0 * x1540 + x1024 + x21 * x845))
result[2, 4, 4] = numpy.sum(x731 * (x0 * x1541 + x1028 + x21 * x852))
result[2, 4, 5] = numpy.sum(x322 * (x0 * x1542 + x1032 + x21 * x860))
result[2, 4, 6] = numpy.sum(x699 * (x0 * x1543 + x1036 + x21 * x866))
result[2, 4, 7] = numpy.sum(x731 * (x0 * x1544 + x1040 + x21 * x871))
result[2, 4, 8] = numpy.sum(x731 * (x0 * x1545 + x1044 + x21 * x876))
result[2, 4, 9] = numpy.sum(x699 * (x0 * x1546 + x1048 + x21 * x883))
result[2, 4, 10] = numpy.sum(x687 * (x0 * x1547 + x1050 + x21 * x888))
result[2, 4, 11] = numpy.sum(x699 * (x0 * x1548 + x1052 + x21 * x892))
result[2, 4, 12] = numpy.sum(x322 * (x0 * x1549 + x1054 + x21 * x896))
result[2, 4, 13] = numpy.sum(x699 * (x0 * x1550 + x1056 + x21 * x900))
result[2, 4, 14] = numpy.sum(x687 * (x0 * x1551 + x1058 + x21 * x904))
result[2, 5, 0] = numpy.sum(x257 * (x0 * x1554 + x1065))
result[2, 5, 1] = numpy.sum(x152 * (x0 * x1557 + x1067))
result[2, 5, 2] = numpy.sum(x152 * (x0 * x1560 + x1071))
result[2, 5, 3] = numpy.sum(x306 * (x0 * x1563 + x1073))
result[2, 5, 4] = numpy.sum(x322 * (x0 * x1566 + x1075))
result[2, 5, 5] = numpy.sum(x306 * (x0 * x1569 + x1079))
result[2, 5, 6] = numpy.sum(x152 * (x0 * x1572 + x1081))
result[2, 5, 7] = numpy.sum(x322 * (x0 * x1575 + x1083))
result[2, 5, 8] = numpy.sum(x322 * (x0 * x1578 + x1085))
result[2, 5, 9] = numpy.sum(x152 * (x0 * x1581 + x1089))
result[2, 5, 10] = numpy.sum(x257 * (x0 * x1584 + x1090))
result[2, 5, 11] = numpy.sum(x152 * (x0 * x1587 + x1091))
result[2, 5, 12] = numpy.sum(x306 * (x0 * x1590 + x1092))
result[2, 5, 13] = numpy.sum(x152 * (x0 * x1593 + x1093))
result[2, 5, 14] = numpy.sum(x257 * (x0 * x1596 + x1094))
result[2, 6, 0] = numpy.sum(x99 * (x1239 * x21 + x1341 + x1507 * x21 + x1508 * x21))
result[2, 6, 1] = numpy.sum(x115 * (x1242 * x21 + x1343 + x1509 * x21 + x1510 * x21))
result[2, 6, 2] = numpy.sum(x115 * (x1245 * x21 + x1345 + x1511 * x21 + x1512 * x21))
result[2, 6, 3] = numpy.sum(x140 * (x1248 * x21 + x1347 + x1513 * x21 + x1514 * x21))
result[2, 6, 4] = numpy.sum(x152 * (x1251 * x21 + x1349 + x1515 * x21 + x1516 * x21))
result[2, 6, 5] = numpy.sum(x140 * (x1254 * x21 + x1351 + x1517 * x21 + x1518 * x21))
result[2, 6, 6] = numpy.sum(x115 * (x1257 * x21 + x1353 + x1519 * x21 + x1520 * x21))
result[2, 6, 7] = numpy.sum(x152 * (x1260 * x21 + x1355 + x1521 * x21 + x1522 * x21))
result[2, 6, 8] = numpy.sum(x152 * (x1263 * x21 + x1357 + x1523 * x21 + x1524 * x21))
result[2, 6, 9] = numpy.sum(x115 * (x1266 * x21 + x1359 + x1525 * x21 + x1526 * x21))
result[2, 6, 10] = numpy.sum(x99 * (x1269 * x21 + x1360 + x1527 * x21 + x1528 * x21))
result[2, 6, 11] = numpy.sum(x115 * (x1272 * x21 + x1361 + x1529 * x21 + x1530 * x21))
result[2, 6, 12] = numpy.sum(x140 * (x1275 * x21 + x1362 + x1531 * x21 + x1532 * x21))
result[2, 6, 13] = numpy.sum(x115 * (x1279 * x21 + x1363 + x1533 * x21 + x1534 * x21))
result[2, 6, 14] = numpy.sum(x99 * (x1282 * x21 + x1364 + x1535 * x21 + x1536 * x21))
result[2, 7, 0] = numpy.sum(x257 * (x1286 * x21 + x1366 + x1537 * x21))
result[2, 7, 1] = numpy.sum(x152 * (x1289 * x21 + x1368 + x1538 * x21))
result[2, 7, 2] = numpy.sum(x152 * (x1292 * x21 + x1370 + x1539 * x21))
result[2, 7, 3] = numpy.sum(x306 * (x1295 * x21 + x1372 + x1540 * x21))
result[2, 7, 4] = numpy.sum(x322 * (x1298 * x21 + x1374 + x1541 * x21))
result[2, 7, 5] = numpy.sum(x306 * (x1301 * x21 + x1376 + x1542 * x21))
result[2, 7, 6] = numpy.sum(x152 * (x1304 * x21 + x1378 + x1543 * x21))
result[2, 7, 7] = numpy.sum(x322 * (x1307 * x21 + x1380 + x1544 * x21))
result[2, 7, 8] = numpy.sum(x322 * (x1310 * x21 + x1382 + x1545 * x21))
result[2, 7, 9] = numpy.sum(x152 * (x1313 * x21 + x1384 + x1546 * x21))
result[2, 7, 10] = numpy.sum(x257 * (x1316 * x21 + x1385 + x1547 * x21))
result[2, 7, 11] = numpy.sum(x152 * (x1319 * x21 + x1386 + x1548 * x21))
result[2, 7, 12] = numpy.sum(x306 * (x1322 * x21 + x1387 + x1549 * x21))
result[2, 7, 13] = numpy.sum(x152 * (x1325 * x21 + x1388 + x1550 * x21))
result[2, 7, 14] = numpy.sum(x257 * (x1328 * x21 + x1389 + x1551 * x21))
result[2, 8, 0] = numpy.sum(x257 * (x1391 + x1554 * x21))
result[2, 8, 1] = numpy.sum(x152 * (x1393 + x1557 * x21))
result[2, 8, 2] = numpy.sum(x152 * (x1395 + x1560 * x21))
result[2, 8, 3] = numpy.sum(x306 * (x1397 + x1563 * x21))
result[2, 8, 4] = numpy.sum(x322 * (x1399 + x1566 * x21))
result[2, 8, 5] = numpy.sum(x306 * (x1401 + x1569 * x21))
result[2, 8, 6] = numpy.sum(x152 * (x1403 + x1572 * x21))
result[2, 8, 7] = numpy.sum(x322 * (x1405 + x1575 * x21))
result[2, 8, 8] = numpy.sum(x322 * (x1407 + x1578 * x21))
result[2, 8, 9] = numpy.sum(x152 * (x1409 + x1581 * x21))
result[2, 8, 10] = numpy.sum(x257 * (x1410 + x1584 * x21))
result[2, 8, 11] = numpy.sum(x152 * (x1411 + x1587 * x21))
result[2, 8, 12] = numpy.sum(x306 * (x1412 + x1590 * x21))
result[2, 8, 13] = numpy.sum(x152 * (x1413 + x1593 * x21))
result[2, 8, 14] = numpy.sum(x257 * (x1414 + x1596 * x21))
result[2, 9, 0] = numpy.sum(
x99 * (x1096 * x1597 + x1552 * x22 + x1553 * x22 + x1554 * x22)
)
result[2, 9, 1] = numpy.sum(
x115 * (x1418 * x1597 + x1555 * x22 + x1556 * x22 + x1557 * x22)
)
result[2, 9, 2] = numpy.sum(
x115 * (x1099 * x1598 + x1558 * x22 + x1559 * x22 + x1560 * x22)
)
result[2, 9, 3] = numpy.sum(
x140 * (x1423 * x1597 + x1561 * x22 + x1562 * x22 + x1563 * x22)
)
result[2, 9, 4] = numpy.sum(
x152 * (x1425 * x1598 + x1564 * x22 + x1565 * x22 + x1566 * x22)
)
result[2, 9, 5] = numpy.sum(
x140 * (x1567 * x22 + x1568 * x22 + x1569 * x22 + x1599 * x274)
)
result[2, 9, 6] = numpy.sum(
x115 * (x1428 * x1597 + x1570 * x22 + x1571 * x22 + x1572 * x22)
)
result[2, 9, 7] = numpy.sum(
x152 * (x1431 * x1598 + x1573 * x22 + x1574 * x22 + x1575 * x22)
)
result[2, 9, 8] = numpy.sum(
x152 * (x1576 * x22 + x1577 * x22 + x1578 * x22 + x1599 * x482)
)
result[2, 9, 9] = numpy.sum(
x115 * (x1579 * x22 + x1580 * x22 + x1581 * x22 + x1600 * x269)
)
result[2, 9, 10] = numpy.sum(
x99 * (x1582 * x22 + x1583 * x22 + x1584 * x22 + x1597 * x193)
)
result[2, 9, 11] = numpy.sum(
x115 * (x1585 * x22 + x1586 * x22 + x1587 * x22 + x1598 * x198)
)
result[2, 9, 12] = numpy.sum(
x140 * (x1588 * x22 + x1589 * x22 + x1590 * x22 + x1599 * x171)
)
result[2, 9, 13] = numpy.sum(
x115 * (x141 * x1600 + x1591 * x22 + x1592 * x22 + x1593 * x22)
)
result[2, 9, 14] = numpy.sum(
x99
* (x1594 * x22 + x1595 * x22 + x1596 * x22 + x55 * (4.0 * x1087 + x116 * x1600))
)
return result
[docs]
def int3c2e3d_sph_200(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ds|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 1, 1), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = cx + x0
x3 = x2 ** (-1.0)
x4 = -x1 * (ax * A[0] + bx * B[0])
x5 = x4 + C[0]
x6 = -x5
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x3
x14 = x0 * x13 * (x12**2 + x6**2 + x9**2)
x15 = boys(1, x14)
x16 = x15 * x3
x17 = cx ** (-1.0)
x18 = x17 * boys(0, x14)
x19 = x1 * (x16 - x18)
x20 = x4 + A[0]
x21 = -x20
x22 = x3 * boys(2, x14)
x23 = x15 * x17
x24 = x13 * x5
x25 = (
17.49341832762486
* da
* db
* dc
* x1
* x2 ** (-0.5)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
)
x26 = 0.5773502691896258 * x25
x27 = x7 + A[1]
x28 = -x27
x29 = x16 * x9 - x18 * x28
x30 = x22 * x9 - x23 * x28
x31 = 2.0 * x25
x32 = x10 + A[2]
x33 = -x32
x34 = x12 * x16 - x18 * x33
x35 = x12 * x22 - x23 * x33
x36 = x13 * x8
# 6 item(s)
result[0, 0, 0] = numpy.sum(
x26
* (-x19 + 2.0 * x20 * (x16 * x6 - x18 * x21) + 2.0 * x24 * (x21 * x23 - x22 * x6))
)
result[1, 0, 0] = numpy.sum(x31 * (x20 * x29 - x24 * x30))
result[2, 0, 0] = numpy.sum(x31 * (x20 * x34 - x24 * x35))
result[3, 0, 0] = numpy.sum(x26 * (-x19 + 2.0 * x27 * x29 - 2.0 * x30 * x36))
result[4, 0, 0] = numpy.sum(x31 * (x27 * x34 - x35 * x36))
result[5, 0, 0] = numpy.sum(x26 * (-2.0 * x11 * x13 * x35 - x19 + 2.0 * x32 * x34))
return result
[docs]
def int3c2e3d_sph_201(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ds|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 1, 3), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = cx + x0
x5 = x4 ** (-1.0)
x6 = -x3
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x5
x14 = x0 * x13
x15 = x14 * (x12**2 + x6**2 + x9**2)
x16 = boys(2, x15)
x17 = x16 * x5
x18 = cx ** (-1.0)
x19 = x18 * boys(1, x15)
x20 = x1 * (x17 - x19)
x21 = x2 + A[0]
x22 = -x21
x23 = x17 * x6 - x19 * x22
x24 = x5 * boys(3, x15)
x25 = x16 * x18
x26 = x13 * x3
x27 = x20 - 2.0 * x21 * x23 - 2.0 * x26 * (x22 * x25 - x24 * x6)
x28 = (
17.49341832762486
* da
* db
* dc
* x4 ** (-1.5)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
)
x29 = 0.5773502691896258 * x28
x30 = x27 * x29
x31 = x14 * (x11**2 + x3**2 + x8**2)
x32 = x5 * boys(2, x31)
x33 = x7 + A[1]
x34 = boys(1, x31)
x35 = x1 * (-x18 * x33 * x34 + x32 * x8)
x36 = -x33
x37 = x17 * x9 - x19 * x36
x38 = x24 * x9 - x25 * x36
x39 = -2.0 * x21 * x37 + 2.0 * x26 * x38
x40 = x1 * (-x18 * x21 * x34 + x3 * x32)
x41 = x10 + A[2]
x42 = x1 * (x11 * x32 - x18 * x34 * x41)
x43 = -x41
x44 = x12 * x17 - x19 * x43
x45 = x12 * x24 - x25 * x43
x46 = -2.0 * x21 * x44 + 2.0 * x26 * x45
x47 = 2.0 * x37
x48 = x13 * x8
x49 = x20 - x33 * x47 + 2.0 * x38 * x48
x50 = x29 * x49
x51 = -2.0 * x33 * x44 + 2.0 * x45 * x48
x52 = 2.0 * x44
x53 = 2.0 * x11 * x13 * x45 + x20 - x41 * x52
x54 = x29 * x53
# 18 item(s)
result[0, 0, 0] = numpy.sum(x29 * (-2.0 * x1 * x23 + x27 * x3))
result[0, 0, 1] = numpy.sum(x30 * x8)
result[0, 0, 2] = numpy.sum(x11 * x30)
result[1, 0, 0] = numpy.sum(x28 * (x3 * x39 + x35))
result[1, 0, 1] = numpy.sum(x28 * (x39 * x8 + x40))
result[1, 0, 2] = numpy.sum(x11 * x28 * x39)
result[2, 0, 0] = numpy.sum(x28 * (x3 * x46 + x42))
result[2, 0, 1] = numpy.sum(x28 * x46 * x8)
result[2, 0, 2] = numpy.sum(x28 * (x11 * x46 + x40))
result[3, 0, 0] = numpy.sum(x3 * x50)
result[3, 0, 1] = numpy.sum(x29 * (-x1 * x47 + x49 * x8))
result[3, 0, 2] = numpy.sum(x11 * x50)
result[4, 0, 0] = numpy.sum(x28 * x3 * x51)
result[4, 0, 1] = numpy.sum(x28 * (x42 + x51 * x8))
result[4, 0, 2] = numpy.sum(x28 * (x11 * x51 + x35))
result[5, 0, 0] = numpy.sum(x3 * x54)
result[5, 0, 1] = numpy.sum(x54 * x8)
result[5, 0, 2] = numpy.sum(x29 * (-x1 * x52 + x11 * x53))
return result
[docs]
def int3c2e3d_sph_202(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ds|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 1, 6), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = x2 + C[0]
x4 = -x3
x5 = cx + x0
x6 = x5 ** (-1.0)
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x6
x14 = x0 * x13
x15 = x14 * (x12**2 + x4**2 + x9**2)
x16 = boys(3, x15)
x17 = x16 * x6
x18 = x2 + A[0]
x19 = -x18
x20 = cx ** (-1.0)
x21 = x20 * boys(2, x15)
x22 = x17 * x4 - x19 * x21
x23 = x3**2
x24 = x8**2
x25 = x11**2
x26 = x14 * (x23 + x24 + x25)
x27 = boys(2, x26)
x28 = x1 * x20 * x27
x29 = x1 * (x17 - x21)
x30 = x6 * boys(4, x15)
x31 = x13 * x3
x32 = -2.0 * x18 * x22 + x29 - 2.0 * x31 * (x16 * x19 * x20 - x30 * x4)
x33 = x1 * x22
x34 = 2.0 * x33
x35 = (
17.49341832762486
* da
* db
* dc
* x0
* x5 ** (-2.5)
* numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
)
x36 = 0.3333333333333333 * x35
x37 = x6 * boys(3, x26)
x38 = x18 * x20 * x27 - x3 * x37
x39 = 1.732050807568877
x40 = x36 * x39
x41 = x40 * (2.0 * x1 * x38 - x3 * x32)
x42 = x32 * x36
x43 = x11 * x39
x44 = x7 + A[1]
x45 = -x44
x46 = x17 * x9 - x21 * x45
x47 = x1 * x46
x48 = 2.0 * x47
x49 = -x48
x50 = -x16 * x20 * x45 + x30 * x9
x51 = x13 * x4
x52 = 2.0 * x19 * x46 - 2.0 * x50 * x51
x53 = x3 * x52
x54 = x3 * x40
x55 = -x33
x56 = x52 * x8
x57 = x55 + x56
x58 = 2.0 * x46
x59 = x1 * (x28 + x58 * x8)
x60 = -x47
x61 = x11 * x35
x62 = -x34
x63 = x40 * x8
x64 = 0.6666666666666667 * x35 * x39
x65 = x10 + A[2]
x66 = -x65
x67 = x12 * x17 - x21 * x66
x68 = x1 * x67
x69 = 2.0 * x68
x70 = -x69
x71 = -x67
x72 = x12 * x30 - x16 * x20 * x66
x73 = -x72
x74 = -2.0 * x19 * x71 + 2.0 * x51 * x73
x75 = x3 * x74
x76 = x35 * x8
x77 = x11 * x74
x78 = 2.0 * x11
x79 = x1 * (x28 + x67 * x78)
x80 = -0.5 * x79
x81 = -x18 * x67 + x31 * x72
x82 = x11 * x40
x83 = 2.0 * x8
x84 = x13 * x50 * x83 + x29 - x44 * x58
x85 = x36 * x84
x86 = x48 - x8 * x84
x87 = x20 * x27 * x44 - x37 * x8
x88 = x13 * x72
x89 = -x44 * x67 + x8 * x88
x90 = x3 * x35
x91 = x13 * x73 * x9 - x45 * x71
x92 = x78 * x91
x93 = x29 - 2.0 * x65 * x67 + x78 * x88
x94 = x36 * x93
x95 = -x11 * x93 + x69
# 36 item(s)
result[0, 0, 0] = numpy.sum(
x36 * (x1 * (2.0 * x22 * x3 + x28) - x3 * (x3 * x32 - x34))
)
result[0, 0, 1] = numpy.sum(x41 * x8)
result[0, 0, 2] = numpy.sum(x11 * x41)
result[0, 0, 3] = numpy.sum(-x24 * x42)
result[0, 0, 4] = numpy.sum(-x42 * x43 * x8)
result[0, 0, 5] = numpy.sum(-x25 * x42)
result[1, 0, 0] = numpy.sum(-x54 * (x49 + x53))
result[1, 0, 1] = numpy.sum(0.5 * x35 * (-2.0 * x3 * x57 + x59))
result[1, 0, 2] = numpy.sum(-x61 * (x53 + x60))
result[1, 0, 3] = numpy.sum(-x63 * (x56 + x62))
result[1, 0, 4] = numpy.sum(-x57 * x61)
result[1, 0, 5] = numpy.sum(x25 * x64 * (x18 * x46 - x31 * x50))
result[2, 0, 0] = numpy.sum(-x54 * (x70 + x75))
result[2, 0, 1] = numpy.sum(x76 * (x68 - x75))
result[2, 0, 2] = numpy.sum(-x35 * (x3 * (x55 + x77) + x80))
result[2, 0, 3] = numpy.sum(-x24 * x64 * x81)
result[2, 0, 4] = numpy.sum(x76 * (x1 * x38 - x78 * x81))
result[2, 0, 5] = numpy.sum(-x82 * (x62 + x77))
result[3, 0, 0] = numpy.sum(-x23 * x85)
result[3, 0, 1] = numpy.sum(x54 * x86)
result[3, 0, 2] = numpy.sum(-x3 * x43 * x85)
result[3, 0, 3] = numpy.sum(x36 * (x59 + x8 * x86))
result[3, 0, 4] = numpy.sum(x82 * (2.0 * x1 * x87 - x8 * x84))
result[3, 0, 5] = numpy.sum(-x25 * x85)
result[4, 0, 0] = numpy.sum(-x23 * x64 * x89)
result[4, 0, 1] = numpy.sum(x90 * (-x1 * (x11 * x37 - x20 * x27 * x65) - x83 * x89))
result[4, 0, 2] = numpy.sum(x90 * (x1 * x87 - x78 * x89))
result[4, 0, 3] = numpy.sum(-x63 * (x70 + x83 * x91))
result[4, 0, 4] = numpy.sum(-x35 * (x8 * (x60 + x92) + x80))
result[4, 0, 5] = numpy.sum(-x82 * (x49 + x92))
result[5, 0, 0] = numpy.sum(-x23 * x94)
result[5, 0, 1] = numpy.sum(-x3 * x39 * x8 * x94)
result[5, 0, 2] = numpy.sum(x54 * x95)
result[5, 0, 3] = numpy.sum(-x24 * x94)
result[5, 0, 4] = numpy.sum(x63 * x95)
result[5, 0, 5] = numpy.sum(x36 * (x11 * x95 + x79))
return result
[docs]
def int3c2e3d_sph_203(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ds|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 1, 10), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = 0.5 / (ax + bx)
x5 = x3**2
x6 = -x1 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = x7**2
x9 = -x1 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = x10**2
x12 = cx + x0
x13 = x12 ** (-1.0)
x14 = cx * x13
x15 = x0 * x14 * (x11 + x5 + x8)
x16 = boys(4, x15)
x17 = x12 ** (-1.5)
x18 = 17.49341832762486
x19 = numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
x20 = 2.0 * x1 * x18 * x19
x21 = x17 * x20
x22 = x16 * x21
x23 = cx ** (-1.0)
x24 = x12 ** (-0.5)
x25 = boys(3, x15)
x26 = x4 * (2.0 * x1 * x18 * x19 * x23 * x24 * x25 - x22)
x27 = -x2 - A[0]
x28 = 2.0 * x1 * x18 * x19 * x23 * x24 * x25 * x27 - x22 * x3
x29 = x21 * boys(5, x15)
x30 = x14 * x3
x31 = (
x26 + x27 * x28 - x30 * (2.0 * x1 * x16 * x18 * x19 * x23 * x24 * x27 - x29 * x3)
)
x32 = x3 * x31
x33 = x28 * x4
x34 = 2.0 * x33
x35 = x0 * x13
x36 = x3 * x35
x37 = x28 * x3
x38 = x23 * x25
x39 = x20 * x24 * x38 * x4
x40 = x37 + x39
x41 = x35 * x4
x42 = 2.0 * x41
x43 = 2.0 * x17 * x18 * x19 * x38 * x4
x44 = 2.23606797749979
x45 = da * db * dc
x46 = x35 * x45
x47 = 0.06666666666666667 * x46
x48 = x44 * x47
x49 = x35 * x7
x50 = x43 * x7
x51 = 0.3333333333333333 * x46
x52 = x10 * x35
x53 = x10 * x43
x54 = x0**2 / x12**2
x55 = x32 * x54
x56 = x54 * x8
x57 = x54 * x7
x58 = x10 * x57
x59 = 1.732050807568877
x60 = x51 * x59
x61 = x11 * x54
x62 = x0**3 / x12**3
x63 = 0.06666666666666667 * x45 * x62
x64 = x63 * x7**3
x65 = x31 * x44
x66 = 0.3333333333333333 * x45
x67 = x62 * x66
x68 = x67 * x8
x69 = x10**3 * x63
x70 = -x6 - A[1]
x71 = 2.0 * x1 * x18 * x19 * x23 * x24 * x25 * x70 - x22 * x7
x72 = x4 * x71
x73 = 2.0 * x1 * x16 * x18 * x19 * x23 * x24 * x70 - x29 * x7
x74 = x27 * x71 - x30 * x73
x75 = x3 * x74
x76 = x54 * x72
x77 = 3.872983346207417
x78 = x47 * x77
x79 = x7 * x71
x80 = x39 + x79
x81 = x35 * x80
x82 = x4 * x81
x83 = x7 * x74
x84 = x33 + x83
x85 = x4 * x54
x86 = x3 * x85
x87 = x52 * x72
x88 = x41 * (x50 + x7 * x81)
x89 = x49 * (x33 + x84)
x90 = x41 * (x52 * x79 + x53)
x91 = x33 * x52
x92 = x52 * x83 + x91
x93 = x11 * x76
x94 = x33 * x61
x95 = -x9 - A[2]
x96 = 2.0 * x1 * x18 * x19 * x23 * x24 * x25 * x95 - x10 * x22
x97 = x4 * x96
x98 = 2.0 * x1 * x16 * x18 * x19 * x23 * x24 * x95 - x10 * x29
x99 = x27 * x96 - x30 * x98
x100 = x3 * x99
x101 = x54 * x97
x102 = x49 * x97
x103 = x3 * x7
x104 = x10 * x96 + x39
x105 = x104 * x41
x106 = x10 * x99 + x33
x107 = x56 * x97
x108 = x104 * x7 * x85
x109 = x41 * (x104 * x52 + x53)
x110 = x106 * x52 + x91
x111 = x57 * x66
x112 = x14 * x7
x113 = -x112 * x73 + x26 + x70 * x71
x114 = x113 * x44
x115 = x3**3 * x63
x116 = x113 * x7
x117 = 2.0 * x72
x118 = x116 + x117
x119 = x5 * x67
x120 = x118 * x49 + 2.0 * x82
x121 = x3 * x45
x122 = x121 * x54
x123 = 0.3333333333333333 * x122
x124 = x52 * (x116 + x117)
x125 = x123 * x59
x126 = 0.3333333333333333 * x121 * x62
x127 = -x112 * x98 + x70 * x96
x128 = x127 * x7 + x97
x129 = x119 * x59
x130 = x10 * x127 + x72
x131 = x102 + x128 * x49
x132 = x105 + x130 * x49
x133 = x130 * x52 + x87
x134 = -x10 * x14 * x98 + x26 + x95 * x96
x135 = x134 * x44
x136 = x10 * x134 + 2.0 * x97
x137 = 2.0 * x105 + x136 * x52
# 60 item(s)
result[0, 0, 0] = numpy.sum(
x48 * (x36 * (x36 * (x32 + x34) + x40 * x42) + x42 * (x3 * x43 + x36 * x40))
)
result[0, 0, 1] = numpy.sum(x51 * (x36 * x49 * (x32 + x34) + x42 * (x37 * x49 + x50)))
result[0, 0, 2] = numpy.sum(x51 * (x36 * x52 * (x32 + x34) + x42 * (x37 * x52 + x53)))
result[0, 0, 3] = numpy.sum(x51 * (x34 * x56 + x55 * x8))
result[0, 0, 4] = numpy.sum(x60 * (x10 * x55 * x7 + x34 * x58))
result[0, 0, 5] = numpy.sum(x51 * (x11 * x55 + x34 * x61))
result[0, 0, 6] = numpy.sum(x64 * x65)
result[0, 0, 7] = numpy.sum(x10 * x31 * x68)
result[0, 0, 8] = numpy.sum(x11 * x31 * x67 * x7)
result[0, 0, 9] = numpy.sum(x65 * x69)
result[1, 0, 0] = numpy.sum(x78 * (x36**2 * (2.0 * x72 + x75) + x5 * x76))
result[1, 0, 1] = numpy.sum(x60 * (x36 * (x36 * x84 + x82) + x80 * x86))
result[1, 0, 2] = numpy.sum(x60 * (x10 * x3 * x76 + x36 * (x52 * x75 + x87)))
result[1, 0, 3] = numpy.sum(x60 * (x36 * x89 + x88))
result[1, 0, 4] = numpy.sum(x46 * (x36 * x92 + x90))
result[1, 0, 5] = numpy.sum(x60 * (x61 * x75 + x93))
result[1, 0, 6] = numpy.sum(x78 * (x33 * x56 + x49 * x89))
result[1, 0, 7] = numpy.sum(x60 * (x33 * x58 + x49 * x92))
result[1, 0, 8] = numpy.sum(x60 * (x61 * x83 + x94))
result[1, 0, 9] = numpy.sum(x69 * x74 * x77)
result[2, 0, 0] = numpy.sum(x78 * (x101 * x5 + x36**2 * (x100 + 2.0 * x97)))
result[2, 0, 1] = numpy.sum(x60 * (x101 * x103 + x36 * (x100 * x49 + x102)))
result[2, 0, 2] = numpy.sum(x60 * (x104 * x86 + x36 * (x105 + x106 * x36)))
result[2, 0, 3] = numpy.sum(x60 * (x100 * x56 + x107))
result[2, 0, 4] = numpy.sum(x46 * (x106 * x3 * x57 + x108))
result[2, 0, 5] = numpy.sum(x60 * (x109 + x110 * x36))
result[2, 0, 6] = numpy.sum(x64 * x77 * x99)
result[2, 0, 7] = numpy.sum(x106 * x59 * x68)
result[2, 0, 8] = numpy.sum(x110 * x111 * x59)
result[2, 0, 9] = numpy.sum(x78 * (x110 * x52 + x94))
result[3, 0, 0] = numpy.sum(x114 * x115)
result[3, 0, 1] = numpy.sum(x118 * x119)
result[3, 0, 2] = numpy.sum(x10 * x113 * x119)
result[3, 0, 3] = numpy.sum(x120 * x123)
result[3, 0, 4] = numpy.sum(x124 * x125)
result[3, 0, 5] = numpy.sum(x11 * x113 * x126)
result[3, 0, 6] = numpy.sum(x48 * (x120 * x49 + 2.0 * x88))
result[3, 0, 7] = numpy.sum(x51 * (x124 * x49 + 2.0 * x90))
result[3, 0, 8] = numpy.sum(x51 * x61 * (x116 + x117))
result[3, 0, 9] = numpy.sum(x114 * x69)
result[4, 0, 0] = numpy.sum(x115 * x127 * x77)
result[4, 0, 1] = numpy.sum(x128 * x129)
result[4, 0, 2] = numpy.sum(x129 * x130)
result[4, 0, 3] = numpy.sum(x125 * x131)
result[4, 0, 4] = numpy.sum(x122 * x132)
result[4, 0, 5] = numpy.sum(x125 * x133)
result[4, 0, 6] = numpy.sum(x78 * (x107 + x131 * x49))
result[4, 0, 7] = numpy.sum(x60 * (x108 + x132 * x49))
result[4, 0, 8] = numpy.sum(x60 * (x109 + x133 * x49))
result[4, 0, 9] = numpy.sum(x78 * (x133 * x52 + x93))
result[5, 0, 0] = numpy.sum(x115 * x135)
result[5, 0, 1] = numpy.sum(x119 * x134 * x7)
result[5, 0, 2] = numpy.sum(x119 * x136)
result[5, 0, 3] = numpy.sum(x126 * x134 * x8)
result[5, 0, 4] = numpy.sum(x103 * x136 * x59 * x67)
result[5, 0, 5] = numpy.sum(x123 * x137)
result[5, 0, 6] = numpy.sum(x135 * x64)
result[5, 0, 7] = numpy.sum(x136 * x68)
result[5, 0, 8] = numpy.sum(x111 * x137)
result[5, 0, 9] = numpy.sum(x48 * (2.0 * x109 + x137 * x52))
return result
[docs]
def int3c2e3d_sph_204(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (ds|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 1, 15), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = 0.5 / (ax + bx)
x5 = x3**2
x6 = -x1 * (ax * A[1] + bx * B[1])
x7 = -x6 - C[1]
x8 = x7**2
x9 = -x1 * (ax * A[2] + bx * B[2])
x10 = -x9 - C[2]
x11 = x10**2
x12 = cx + x0
x13 = x12 ** (-1.0)
x14 = cx * x13
x15 = x0 * x14 * (x11 + x5 + x8)
x16 = boys(5, x15)
x17 = x12 ** (-1.5)
x18 = 17.49341832762486
x19 = numpy.exp(
-ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)
)
x20 = 2.0 * x18 * x19
x21 = x1 * x20
x22 = x17 * x21
x23 = x16 * x22
x24 = cx ** (-1.0)
x25 = x12 ** (-0.5)
x26 = boys(4, x15)
x27 = x4 * (2.0 * x1 * x18 * x19 * x24 * x25 * x26 - x23)
x28 = -x2 - A[0]
x29 = 2.0 * x1 * x18 * x19 * x24 * x25 * x26 * x28 - x23 * x3
x30 = x22 * boys(6, x15)
x31 = x14 * x3
x32 = (
x27 + x28 * x29 - x31 * (2.0 * x1 * x16 * x18 * x19 * x24 * x25 * x28 - x3 * x30)
)
x33 = x3 * x32
x34 = x29 * x4
x35 = 2.0 * x34
x36 = x0 * x13
x37 = x3 * x36
x38 = x29 * x3
x39 = x24 * x26
x40 = x21 * x25 * x39 * x4
x41 = x38 + x40
x42 = x36 * x4
x43 = 2.0 * x42
x44 = x20 * x39 * x4
x45 = x17 * x44
x46 = x3 * x45 + x37 * x41
x47 = x0 * x12 ** (-2.5) * x44
x48 = 5.916079783099616
x49 = da * db * dc
x50 = x36 * x49
x51 = 0.009523809523809524 * x50
x52 = x48 * x51
x53 = x36 * x7
x54 = x45 * x7
x55 = x38 * x53 + x54
x56 = x3 * x7
x57 = 2.23606797749979
x58 = 0.06666666666666667 * x50
x59 = x57 * x58
x60 = x10 * x36
x61 = x10 * x45
x62 = x38 * x60 + x61
x63 = x0**2 / x12**2
x64 = x33 * x8
x65 = x63 * x8
x66 = x38 * x63
x67 = x47 * x8
x68 = 1.732050807568877
x69 = 0.1111111111111111 * x68
x70 = x50 * x69
x71 = x63 * x7
x72 = x10 * x71
x73 = x10 * x7
x74 = x47 * x73
x75 = 0.3333333333333333 * x50
x76 = x11 * x63
x77 = x11 * x47
x78 = x7**3
x79 = x0**3 / x12**3
x80 = x33 * x79
x81 = x78 * x79
x82 = x79 * x8
x83 = x10 * x82
x84 = x11 * x7
x85 = x79 * x84
x86 = x10**3
x87 = x79 * x86
x88 = x0**4 / x12**4
x89 = x49 * x88
x90 = 0.009523809523809524 * x89
x91 = x7**4 * x90
x92 = x32 * x48
x93 = 0.06666666666666667 * x57
x94 = x89 * x93
x95 = x78 * x94
x96 = x11 * x69 * x89
x97 = x86 * x94
x98 = x10**4 * x90
x99 = -x6 - A[1]
x100 = 2.0 * x1 * x18 * x19 * x24 * x25 * x26 * x99 - x23 * x7
x101 = x100 * x4
x102 = 2.0 * x1 * x16 * x18 * x19 * x24 * x25 * x99 - x30 * x7
x103 = x100 * x28 - x102 * x31
x104 = x103 * x3
x105 = x5 * x63
x106 = x3**3
x107 = x101 * x79
x108 = 10.2469507659596
x109 = x108 * x51
x110 = x100 * x7
x111 = x110 + x40
x112 = x111 * x36
x113 = x112 * x4
x114 = x103 * x7
x115 = x114 + x34
x116 = x111 * x4
x117 = x3 * x63
x118 = x5 * x79
x119 = 3.872983346207417
x120 = x119 * x58
x121 = x101 * x60
x122 = x112 * x7 + x54
x123 = x122 * x42
x124 = x53 * (x115 + x34)
x125 = x117 * x4
x126 = x110 * x60 + x61
x127 = x126 * x42
x128 = x34 * x60
x129 = x114 * x60 + x128
x130 = x68 * x75
x131 = x101 * x76
x132 = x42 * (x122 * x53 + x67)
x133 = x124 * x53 + x34 * x65
x134 = x42 * (x126 * x53 + x74)
x135 = x129 * x53 + x34 * x72
x136 = x42 * (x110 * x76 + x77)
x137 = x34 * x76
x138 = x114 * x76 + x137
x139 = x107 * x86
x140 = x34 * x87
x141 = -x9 - A[2]
x142 = 2.0 * x1 * x141 * x18 * x19 * x24 * x25 * x26 - x10 * x23
x143 = x142 * x4
x144 = 2.0 * x1 * x141 * x16 * x18 * x19 * x24 * x25 - x10 * x30
x145 = x142 * x28 - x144 * x31
x146 = x145 * x3
x147 = x143 * x79
x148 = x143 * x53
x149 = x117 * x7
x150 = x10 * x142 + x40
x151 = x150 * x42
x152 = x10 * x145 + x34
x153 = x150 * x4
x154 = x143 * x65
x155 = x3 * x8
x156 = x153 * x71
x157 = x56 * x79
x158 = x150 * x60 + x61
x159 = x158 * x42
x160 = x128 + x152 * x60
x161 = x143 * x81
x162 = x153 * x82
x163 = x158 * x4 * x71
x164 = x42 * (x158 * x60 + x77)
x165 = x137 + x160 * x60
x166 = 0.06666666666666667 * x119
x167 = x166 * x89
x168 = 0.3333333333333333 * x49
x169 = x166 * x49
x170 = x14 * x7
x171 = x100 * x99 - x102 * x170 + x27
x172 = x171 * x48
x173 = x3**4 * x90
x174 = x171 * x7
x175 = 2.0 * x101
x176 = x174 + x175
x177 = x106 * x94
x178 = 2.0 * x113 + x176 * x53
x179 = x49 * x69
x180 = x118 * x179
x181 = x60 * (x174 + x175)
x182 = x118 * x168
x183 = 2.0 * x123 + x178 * x53
x184 = x49 * x93
x185 = x117 * x184
x186 = 2.0 * x127 + x181 * x53
x187 = x117 * x168
x188 = x76 * (x174 + x175)
x189 = x142 * x99 - x144 * x170
x190 = x143 + x189 * x7
x191 = x106 * x167
x192 = x10 * x189 + x101
x193 = x148 + x190 * x53
x194 = x151 + x192 * x53
x195 = x121 + x192 * x60
x196 = x154 + x193 * x53
x197 = x117 * x169
x198 = x156 + x194 * x53
x199 = x187 * x68
x200 = x159 + x195 * x53
x201 = x131 + x195 * x60
x202 = -x10 * x14 * x144 + x141 * x142 + x27
x203 = x202 * x48
x204 = x10 * x202 + 2.0 * x143
x205 = x168 * x204 * x88
x206 = 2.0 * x151 + x204 * x60
x207 = 2.0 * x159 + x206 * x60
# 90 item(s)
result[0, 0, 0] = numpy.sum(
x52
* (
x37 * (x37 * (x37 * (x33 + x35) + x41 * x43) + x43 * x46)
+ x43 * (x37 * x46 + x47 * x5)
)
)
result[0, 0, 1] = numpy.sum(
x59
* (x37 * (x37 * x53 * (x33 + x35) + x43 * x55) + x43 * (x37 * x55 + x47 * x56))
)
result[0, 0, 2] = numpy.sum(
x59
* (
x37 * (x37 * x60 * (x33 + x35) + x43 * x62)
+ x43 * (x10 * x3 * x47 + x37 * x62)
)
)
result[0, 0, 3] = numpy.sum(
x70 * (x37 * (x35 * x65 + x63 * x64) + x43 * (x66 * x8 + x67))
)
result[0, 0, 4] = numpy.sum(x75 * (x37 * x72 * (x33 + x35) + x43 * (x66 * x73 + x74)))
result[0, 0, 5] = numpy.sum(x70 * (x37 * x76 * (x33 + x35) + x43 * (x11 * x66 + x77)))
result[0, 0, 6] = numpy.sum(x59 * (x35 * x81 + x78 * x80))
result[0, 0, 7] = numpy.sum(x75 * (x10 * x64 * x79 + x35 * x83))
result[0, 0, 8] = numpy.sum(x75 * (x35 * x85 + x80 * x84))
result[0, 0, 9] = numpy.sum(x59 * (x35 * x87 + x80 * x86))
result[0, 0, 10] = numpy.sum(x91 * x92)
result[0, 0, 11] = numpy.sum(x10 * x32 * x95)
result[0, 0, 12] = numpy.sum(x32 * x8 * x96)
result[0, 0, 13] = numpy.sum(x32 * x7 * x97)
result[0, 0, 14] = numpy.sum(x92 * x98)
result[1, 0, 0] = numpy.sum(
x109 * (x106 * x107 + x37 * (x101 * x105 + x37**2 * (2.0 * x101 + x104)))
)
result[1, 0, 1] = numpy.sum(
x120 * (x116 * x118 + x37 * (x116 * x117 + x37 * (x113 + x115 * x37)))
)
result[1, 0, 2] = numpy.sum(
x120 * (x10 * x107 * x5 + x37 * (x10 * x101 * x117 + x37 * (x104 * x60 + x121)))
)
result[1, 0, 3] = numpy.sum(x75 * (x122 * x125 + x37 * (x123 + x124 * x37)))
result[1, 0, 4] = numpy.sum(x130 * (x125 * x126 + x37 * (x127 + x129 * x37)))
result[1, 0, 5] = numpy.sum(x75 * (x107 * x11 * x3 + x37 * (x104 * x76 + x131)))
result[1, 0, 6] = numpy.sum(x120 * (x132 + x133 * x37))
result[1, 0, 7] = numpy.sum(x130 * (x134 + x135 * x37))
result[1, 0, 8] = numpy.sum(x130 * (x136 + x138 * x37))
result[1, 0, 9] = numpy.sum(x120 * (x104 * x87 + x139))
result[1, 0, 10] = numpy.sum(x109 * (x133 * x53 + x34 * x81))
result[1, 0, 11] = numpy.sum(x120 * (x135 * x53 + x34 * x83))
result[1, 0, 12] = numpy.sum(x75 * (x138 * x53 + x34 * x85))
result[1, 0, 13] = numpy.sum(x120 * (x114 * x87 + x140))
result[1, 0, 14] = numpy.sum(x103 * x108 * x98)
result[2, 0, 0] = numpy.sum(
x109 * (x106 * x147 + x37 * (x105 * x143 + x37**2 * (2.0 * x143 + x146)))
)
result[2, 0, 1] = numpy.sum(
x120 * (x118 * x143 * x7 + x37 * (x143 * x149 + x37 * (x146 * x53 + x148)))
)
result[2, 0, 2] = numpy.sum(
x120 * (x118 * x153 + x37 * (x125 * x150 + x37 * (x151 + x152 * x37)))
)
result[2, 0, 3] = numpy.sum(x75 * (x147 * x155 + x37 * (x146 * x65 + x154)))
result[2, 0, 4] = numpy.sum(x130 * (x153 * x157 + x37 * (x149 * x152 + x156)))
result[2, 0, 5] = numpy.sum(x75 * (x125 * x158 + x37 * (x159 + x160 * x37)))
result[2, 0, 6] = numpy.sum(x120 * (x146 * x81 + x161))
result[2, 0, 7] = numpy.sum(x130 * (x152 * x3 * x82 + x162))
result[2, 0, 8] = numpy.sum(x130 * (x149 * x160 + x163))
result[2, 0, 9] = numpy.sum(x120 * (x164 + x165 * x37))
result[2, 0, 10] = numpy.sum(x108 * x145 * x91)
result[2, 0, 11] = numpy.sum(x152 * x167 * x78)
result[2, 0, 12] = numpy.sum(x160 * x168 * x82)
result[2, 0, 13] = numpy.sum(x165 * x169 * x71)
result[2, 0, 14] = numpy.sum(x109 * (x140 + x165 * x60))
result[3, 0, 0] = numpy.sum(x172 * x173)
result[3, 0, 1] = numpy.sum(x176 * x177)
result[3, 0, 2] = numpy.sum(x10 * x171 * x177)
result[3, 0, 3] = numpy.sum(x178 * x180)
result[3, 0, 4] = numpy.sum(x181 * x182)
result[3, 0, 5] = numpy.sum(x171 * x5 * x96)
result[3, 0, 6] = numpy.sum(x183 * x185)
result[3, 0, 7] = numpy.sum(x186 * x187)
result[3, 0, 8] = numpy.sum(x187 * x188)
result[3, 0, 9] = numpy.sum(x171 * x3 * x97)
result[3, 0, 10] = numpy.sum(x52 * (2.0 * x132 + x183 * x53))
result[3, 0, 11] = numpy.sum(x59 * (2.0 * x134 + x186 * x53))
result[3, 0, 12] = numpy.sum(x70 * (2.0 * x136 + x188 * x53))
result[3, 0, 13] = numpy.sum(x59 * x87 * (x174 + x175))
result[3, 0, 14] = numpy.sum(x172 * x98)
result[4, 0, 0] = numpy.sum(x108 * x173 * x189)
result[4, 0, 1] = numpy.sum(x190 * x191)
result[4, 0, 2] = numpy.sum(x191 * x192)
result[4, 0, 3] = numpy.sum(x182 * x193)
result[4, 0, 4] = numpy.sum(x182 * x194 * x68)
result[4, 0, 5] = numpy.sum(x182 * x195)
result[4, 0, 6] = numpy.sum(x196 * x197)
result[4, 0, 7] = numpy.sum(x198 * x199)
result[4, 0, 8] = numpy.sum(x199 * x200)
result[4, 0, 9] = numpy.sum(x197 * x201)
result[4, 0, 10] = numpy.sum(x109 * (x161 + x196 * x53))
result[4, 0, 11] = numpy.sum(x120 * (x162 + x198 * x53))
result[4, 0, 12] = numpy.sum(x75 * (x163 + x200 * x53))
result[4, 0, 13] = numpy.sum(x120 * (x164 + x201 * x53))
result[4, 0, 14] = numpy.sum(x109 * (x139 + x201 * x60))
result[5, 0, 0] = numpy.sum(x173 * x203)
result[5, 0, 1] = numpy.sum(x177 * x202 * x7)
result[5, 0, 2] = numpy.sum(x177 * x204)
result[5, 0, 3] = numpy.sum(x202 * x5 * x69 * x8 * x89)
result[5, 0, 4] = numpy.sum(x205 * x5 * x7)
result[5, 0, 5] = numpy.sum(x180 * x206)
result[5, 0, 6] = numpy.sum(x202 * x3 * x95)
result[5, 0, 7] = numpy.sum(x155 * x205)
result[5, 0, 8] = numpy.sum(x157 * x168 * x206)
result[5, 0, 9] = numpy.sum(x185 * x207)
result[5, 0, 10] = numpy.sum(x203 * x91)
result[5, 0, 11] = numpy.sum(x204 * x95)
result[5, 0, 12] = numpy.sum(x179 * x206 * x82)
result[5, 0, 13] = numpy.sum(x184 * x207 * x71)
result[5, 0, 14] = numpy.sum(x52 * (2.0 * x164 + x207 * x60))
return result
[docs]
def int3c2e3d_sph_210(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (dp|s) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 3, 1), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = cx + x1
x4 = x3 ** (-1.0)
x5 = -x2 * (ax * A[0] + bx * B[0])
x6 = x5 + C[0]
x7 = -x6
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = x8 + C[1]
x10 = -x9
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = x11 + C[2]
x13 = -x12
x14 = cx * x4
x15 = x1 * x14
x16 = x15 * (x10**2 + x13**2 + x7**2)
x17 = boys(1, x16)
x18 = x17 * x4
x19 = cx ** (-1.0)
x20 = x19 * boys(0, x16)
x21 = x2 * (x18 - x20)
x22 = x5 + A[0]
x23 = -x22
x24 = 2.0 * x22
x25 = boys(2, x16)
x26 = x25 * x4
x27 = x17 * x19
x28 = -x23 * x27 + x26 * x7
x29 = x14 * x28
x30 = x21 - x24 * (x18 * x7 - x20 * x23) + 2.0 * x29 * x6
x31 = x15 * (x12**2 + x6**2 + x9**2)
x32 = x4 * boys(1, x31)
x33 = boys(0, x31)
x34 = 2.0 * x2
x35 = x2 * (x26 - x27)
x36 = x4 * boys(3, x16)
x37 = x14 * x6
x38 = 2.0 * x37
x39 = A[1] - B[1]
x40 = A[2] - B[2]
x41 = (
17.49341832762486
* da
* db
* dc
* x3 ** (-0.5)
* numpy.exp(-ax * bx * x2 * (x0**2 + x39**2 + x40**2))
)
x42 = x2 * x41
x43 = 0.5773502691896258 * x42
x44 = -x30
x45 = x8 + A[1]
x46 = -x45
x47 = x10 * x26 - x17 * x19 * x46
x48 = -x47
x49 = x14 * x48
x50 = x10 * x18 - x20 * x46
x51 = x23 * x50 + x49 * x7
x52 = x10 * x36 - x19 * x25 * x46
x53 = x14 * x7
x54 = x2 * (x49 + x50) - x24 * x51 - x38 * (x23 * x48 + x52 * x53)
x55 = x11 + A[2]
x56 = -x55
x57 = x13 * x26 - x17 * x19 * x56
x58 = -x57
x59 = x14 * x58
x60 = x13 * x18 - x20 * x56
x61 = x2 * (x59 + x60)
x62 = -x60
x63 = -x23 * x62 + x59 * x7
x64 = x13 * x36 - x19 * x25 * x56
x65 = -x64
x66 = -x24 * x63 - x38 * (x23 * x58 - x53 * x65) + x61
x67 = 2.0 * x51
x68 = x14 * x47
x69 = x21 - 2.0 * x45 * x50 + 2.0 * x68 * x9
x70 = -x69
x71 = x14 * x9
x72 = 2.0 * x71
x73 = x35 - 2.0 * x45 * x47 + x52 * x72
x74 = x10 * x59 - x46 * x62
x75 = x10 * x14 * x65 - x46 * x58
x76 = -x22 * x74 + x37 * x75
x77 = x34 * x41
x78 = 2.0 * x63
x79 = x14 * x57
x80 = 2.0 * x12 * x79 + x21 - 2.0 * x55 * x60
x81 = -x80
x82 = x12 * x14
x83 = x35 - 2.0 * x55 * x57 + 2.0 * x64 * x82
x84 = -x83
x85 = -2.0 * x45 * x74 + x61 + x72 * x75
x86 = 2.0 * x74
# 18 item(s)
result[0, 0, 0] = numpy.sum(
x43
* (
-x0 * x30
+ x22 * x30
+ x34 * (-x19 * x22 * x33 + x29 + x32 * x6)
+ x37 * (x24 * x28 - x35 + x38 * (x19 * x23 * x25 - x36 * x7))
)
)
result[0, 1, 0] = numpy.sum(x43 * (x39 * x44 - x54))
result[0, 2, 0] = numpy.sum(x43 * (x40 * x44 - x66))
result[1, 0, 0] = numpy.sum(-x42 * (x0 * x67 + x54))
result[1, 1, 0] = numpy.sum(-x42 * (x22 * x70 + x37 * x73 + x39 * x67))
result[1, 2, 0] = numpy.sum(-x77 * (x40 * x51 + x76))
result[2, 0, 0] = numpy.sum(-x42 * (x0 * x78 + x66))
result[2, 1, 0] = numpy.sum(-x77 * (x39 * x63 + x76))
result[2, 2, 0] = numpy.sum(x42 * (-x22 * x81 + x37 * x84 - x40 * x78))
result[3, 0, 0] = numpy.sum(x43 * (-x0 * x69 + x22 * x69 - x37 * x73))
result[3, 1, 0] = numpy.sum(
x43
* (x34 * (-x19 * x33 * x45 + x32 * x9 + x68) - x39 * x69 + x45 * x69 - x71 * x73)
)
result[3, 2, 0] = numpy.sum(x43 * (x40 * x70 - x85))
result[4, 0, 0] = numpy.sum(-x77 * (x0 * x74 + x76))
result[4, 1, 0] = numpy.sum(-x42 * (x39 * x86 + x85))
result[4, 2, 0] = numpy.sum(x42 * (-x40 * x86 - x45 * x81 + x71 * x84))
result[5, 0, 0] = numpy.sum(x43 * (-x0 * x80 + x22 * x80 - x37 * x83))
result[5, 1, 0] = numpy.sum(x43 * (-x39 * x80 + x45 * x80 - x71 * x83))
result[5, 2, 0] = numpy.sum(
x43
* (x34 * (x12 * x32 - x19 * x33 * x55 + x79) - x40 * x80 + x55 * x80 - x82 * x83)
)
return result
[docs]
def int3c2e3d_sph_211(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (dp|p) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 3, 3), dtype=float)
x0 = A[0] - B[0]
x1 = ax + bx
x2 = x1 ** (-1.0)
x3 = -x2 * (ax * A[0] + bx * B[0])
x4 = x3 + C[0]
x5 = cx + x1
x6 = x5 ** (-1.0)
x7 = -x4
x8 = -x2 * (ax * A[1] + bx * B[1])
x9 = x8 + C[1]
x10 = -x9
x11 = -x2 * (ax * A[2] + bx * B[2])
x12 = x11 + C[2]
x13 = -x12
x14 = cx * x6
x15 = x1 * x14
x16 = x15 * (x10**2 + x13**2 + x7**2)
x17 = boys(2, x16)
x18 = x17 * x6
x19 = cx ** (-1.0)
x20 = x19 * boys(1, x16)
x21 = x18 - x20
x22 = x2 * x21
x23 = x3 + A[0]
x24 = -x23
x25 = x18 * x7 - x20 * x24
x26 = boys(3, x16)
x27 = x26 * x6
x28 = x17 * x19
x29 = -x24 * x28 + x27 * x7
x30 = x14 * x4
x31 = 2.0 * x30
x32 = -x22 + 2.0 * x23 * x25 - x29 * x31
x33 = 2.0 * x2 * x25 + x32 * x4
x34 = x23 * x32
x35 = 2.0 * x2
x36 = x35 * (-x14 * x29 + x25)
x37 = x27 - x28
x38 = x2 * x37
x39 = x6 * boys(4, x16)
x40 = 2.0 * x23 * x29 + x31 * (x19 * x24 * x26 - x39 * x7) - x38
x41 = x2 * x32
x42 = A[1] - B[1]
x43 = A[2] - B[2]
x44 = (
17.49341832762486
* da
* db
* dc
* x5 ** (-1.5)
* numpy.exp(-ax * bx * x2 * (x0**2 + x42**2 + x43**2))
)
x45 = 0.5773502691896258
x46 = x44 * x45
x47 = x44 * x9
x48 = x45 * (x0 * x32 + x30 * x40 - x34 - x36)
x49 = x12 * x44
x50 = x8 + A[1]
x51 = -x50
x52 = x10 * x27 - x17 * x19 * x51
x53 = -x52
x54 = x14 * x53
x55 = x10 * x18 - x20 * x51
x56 = x2 * (x54 + x55)
x57 = -x55
x58 = -x24 * x57 + x54 * x7
x59 = 2.0 * x23
x60 = x10 * x39 - x19 * x26 * x51
x61 = -x60
x62 = x14 * x7
x63 = -x31 * (x24 * x53 - x61 * x62) + x56 - x58 * x59
x64 = -x63
x65 = x35 * x58 + x4 * x64
x66 = x64 * x9
x67 = 0.5 * x41
x68 = -x67
x69 = x45 * x49
x70 = x11 + A[2]
x71 = -x70
x72 = x13 * x27 - x17 * x19 * x71
x73 = -x72
x74 = x14 * x73
x75 = x13 * x18 - x20 * x71
x76 = x2 * (x74 + x75)
x77 = -x75
x78 = -x24 * x77 + x7 * x74
x79 = x13 * x39 - x19 * x26 * x71
x80 = -x79
x81 = -x31 * (x24 * x73 - x62 * x80) - x59 * x78 + x76
x82 = -x81
x83 = x35 * x78 + x4 * x82
x84 = x45 * x47
x85 = x12 * x82
x86 = x15 * (x12**2 + x4**2 + x9**2)
x87 = x6 * boys(2, x86)
x88 = boys(1, x86)
x89 = x2 * (-x19 * x50 * x88 + x87 * x9)
x90 = -x23 * x55 + x30 * x52
x91 = 2.0 * x90
x92 = x4 * x91 + x89
x93 = x2 * (-x19 * x23 * x88 + x4 * x87)
x94 = x9 * x91 + x93
x95 = x14 * x9
x96 = 2.0 * x95
x97 = x22 - 2.0 * x50 * x55 + x52 * x96
x98 = -x97
x99 = -x38 + 2.0 * x50 * x52 - x60 * x96
x100 = x30 * x99
x101 = -x100 + x23 * x98
x102 = 0.5 * x2
x103 = x2 * x90
x104 = 2.0 * x103
x105 = -x50 * x75 + x72 * x95
x106 = x105 * x2
x107 = x10 * x74 - x51 * x77
x108 = x10 * x14
x109 = x108 * x80 - x51 * x73
x110 = -2.0 * x107 * x23 + 2.0 * x109 * x30
x111 = -x106 + x110 * x4
x112 = -x23 * x75 + x30 * x72
x113 = x112 * x2
x114 = x110 * x9 - x113
x115 = -x103 + x110 * x12
x116 = x2 * (x12 * x87 - x19 * x70 * x88)
x117 = 2.0 * x112
x118 = x116 + x117 * x4
x119 = x117 * x12 + x93
x120 = x12 * x14
x121 = 2.0 * x120
x122 = x121 * x72 + x22 - 2.0 * x70 * x75
x123 = -x122
x124 = -x121 * x79 - x38 + 2.0 * x70 * x72
x125 = x124 * x30
x126 = x123 * x23 - x125
x127 = -x102 * x122
x128 = 2.0 * x113
x129 = -x2 * x21
x130 = 2.0 * x51
x131 = x24 * (-2.0 * x10 * x54 + x129 + x130 * x57)
x132 = -x2 * x37
x133 = x62 * (-2.0 * x108 * x61 + x130 * x53 + x132)
x134 = x102 * x98
x135 = x35 * x55 + x9 * x98
x136 = x50 * x98
x137 = 2.0 * x56
x138 = -x136 - x137 + x42 * x98 + x95 * x99
x139 = x4 * x44
x140 = x139 * x45
x141 = 1.5 * x2
x142 = -2.0 * x107 * x50 + x109 * x96 + x76
x143 = -x142
x144 = x107 * x35 + x143 * x9
x145 = x12 * x143
x146 = 2.0 * x105
x147 = x116 + x146 * x9
x148 = x12 * x146 + x89
x149 = x124 * x95
x150 = x123 * x50 - x149
x151 = 2.0 * x106
x152 = 2.0 * x71
x153 = 2.0 * x13
x154 = x129 + x152 * x77 - x153 * x74
x155 = x154 * x24
x156 = x132 - x14 * x153 * x80 + x152 * x73
x157 = x156 * x62
x158 = x102 * x123
x159 = x12 * x123 + x35 * x75
x160 = x154 * x51
x161 = x108 * x156
x162 = x123 * x70
x163 = 2.0 * x76
x164 = x120 * x124 + x123 * x43 - x162 - x163
# 54 item(s)
result[0, 0, 0] = numpy.sum(
0.5
* x46
* (-2.0 * x0 * x33 + 2.0 * x4 * (-cx * x4 * x40 * x6 + x34 + x36) + 3.0 * x41)
)
result[0, 0, 1] = numpy.sum(-x47 * x48)
result[0, 0, 2] = numpy.sum(-x48 * x49)
result[0, 1, 0] = numpy.sum(-x46 * (x33 * x42 + x65))
result[0, 1, 1] = numpy.sum(-x46 * (x32 * x42 * x9 + x66 + x68))
result[0, 1, 2] = numpy.sum(x69 * (-x32 * x42 + x63))
result[0, 2, 0] = numpy.sum(-x46 * (x33 * x43 + x83))
result[0, 2, 1] = numpy.sum(x84 * (-x32 * x43 + x81))
result[0, 2, 2] = numpy.sum(-x46 * (x12 * x32 * x43 + x68 + x85))
result[1, 0, 0] = numpy.sum(x44 * (x0 * x92 - x65))
result[1, 0, 1] = numpy.sum(x44 * (x0 * x94 - x66 + x67))
result[1, 0, 2] = numpy.sum(x49 * (x0 * x91 + x63))
result[1, 1, 0] = numpy.sum(x44 * (x101 * x4 - x102 * x97 + x42 * x92))
result[1, 1, 1] = numpy.sum(x44 * (x101 * x9 - x104 + x42 * x94))
result[1, 1, 2] = numpy.sum(x49 * (-x100 + x23 * x98 + x42 * x91))
result[1, 2, 0] = numpy.sum(x44 * (x111 + x43 * x92))
result[1, 2, 1] = numpy.sum(x44 * (x114 + x43 * x94))
result[1, 2, 2] = numpy.sum(x44 * (x115 + x12 * x43 * x91))
result[2, 0, 0] = numpy.sum(x44 * (x0 * x118 - x83))
result[2, 0, 1] = numpy.sum(x47 * (x0 * x117 + x81))
result[2, 0, 2] = numpy.sum(x44 * (x0 * x119 + x67 - x85))
result[2, 1, 0] = numpy.sum(x44 * (x111 + x118 * x42))
result[2, 1, 1] = numpy.sum(x44 * (x114 + x117 * x42 * x9))
result[2, 1, 2] = numpy.sum(x44 * (x115 + x119 * x42))
result[2, 2, 0] = numpy.sum(x44 * (x118 * x43 + x126 * x4 + x127))
result[2, 2, 1] = numpy.sum(x47 * (x117 * x43 + x123 * x23 - x125))
result[2, 2, 2] = numpy.sum(x44 * (x119 * x43 + x12 * x126 - x128))
result[3, 0, 0] = numpy.sum(x46 * (-x0 * x4 * x98 + x134 - x4 * (x131 - x133)))
result[3, 0, 1] = numpy.sum(x46 * (-x0 * x135 + x101 * x9 - x104))
result[3, 0, 2] = numpy.sum(x69 * (-x0 * x98 - x131 + x133))
result[3, 1, 0] = numpy.sum(-x138 * x140)
result[3, 1, 1] = numpy.sum(
x46 * (-x135 * x42 + x141 * x98 + x9 * (-cx * x6 * x9 * x99 + x136 + x137))
)
result[3, 1, 2] = numpy.sum(-x138 * x69)
result[3, 2, 0] = numpy.sum(x140 * (x142 - x43 * x98))
result[3, 2, 1] = numpy.sum(-x46 * (x135 * x43 + x144))
result[3, 2, 2] = numpy.sum(x46 * (-x12 * x43 * x98 + x134 - x145))
result[4, 0, 0] = numpy.sum(x44 * (x0 * x146 * x4 + x111))
result[4, 0, 1] = numpy.sum(x44 * (x0 * x147 + x114))
result[4, 0, 2] = numpy.sum(x44 * (x0 * x148 + x115))
result[4, 1, 0] = numpy.sum(x139 * (x142 + x146 * x42))
result[4, 1, 1] = numpy.sum(x44 * (-x144 + x147 * x42))
result[4, 1, 2] = numpy.sum(x44 * (x134 - x145 + x148 * x42))
result[4, 2, 0] = numpy.sum(x139 * (x123 * x50 + x146 * x43 - x149))
result[4, 2, 1] = numpy.sum(x44 * (x127 + x147 * x43 + x150 * x9))
result[4, 2, 2] = numpy.sum(x44 * (x12 * x150 + x148 * x43 - x151))
result[5, 0, 0] = numpy.sum(x46 * (-x0 * x123 * x4 + x158 - x4 * (x155 - x157)))
result[5, 0, 1] = numpy.sum(x84 * (-x0 * x123 - x155 + x157))
result[5, 0, 2] = numpy.sum(x46 * (-x0 * x159 + x12 * x126 - x128))
result[5, 1, 0] = numpy.sum(x140 * (-x123 * x42 - x160 + x161))
result[5, 1, 1] = numpy.sum(x46 * (-x123 * x42 * x9 + x158 - x9 * (x160 - x161)))
result[5, 1, 2] = numpy.sum(x46 * (x12 * x150 - x151 - x159 * x42))
result[5, 2, 0] = numpy.sum(-x140 * x164)
result[5, 2, 1] = numpy.sum(-x164 * x84)
result[5, 2, 2] = numpy.sum(
x46 * (x12 * (-cx * x12 * x124 * x6 + x162 + x163) + x123 * x141 - x159 * x43)
)
return result
[docs]
def int3c2e3d_sph_212(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (dp|d) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 3, 6), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = cx + x0
x3 = x2 ** (-1.0)
x4 = -x1 * (ax * A[0] + bx * B[0])
x5 = x4 + C[0]
x6 = -x5
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = x7 + C[1]
x9 = -x8
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = x10 + C[2]
x12 = -x11
x13 = cx * x3
x14 = x0 * x13
x15 = x14 * (x12**2 + x6**2 + x9**2)
x16 = boys(3, x15)
x17 = x16 * x3
x18 = cx ** (-1.0)
x19 = x18 * boys(2, x15)
x20 = x17 - x19
x21 = x1 * x20
x22 = x4 + A[0]
x23 = -x22
x24 = x17 * x6 - x19 * x23
x25 = boys(4, x15)
x26 = x25 * x3
x27 = x16 * x18
x28 = -x23 * x27 + x26 * x6
x29 = 2.0 * x5
x30 = x13 * x29
x31 = x21 - 2.0 * x22 * x24 + x28 * x30
x32 = -x31
x33 = 2.0 * x1
x34 = x26 - x27
x35 = x1 * x34
x36 = x3 * boys(5, x15)
x37 = x13 * x5
x38 = (
x22 * x32
- x33 * (x13 * x28 - x24)
- x37 * (2.0 * x22 * x28 + x30 * (x18 * x23 * x25 - x36 * x6) - x35)
)
x39 = 0.5 * x5
x40 = A[0] - B[0]
x41 = x5**2
x42 = x8**2
x43 = x11**2
x44 = x14 * (x41 + x42 + x43)
x45 = boys(2, x44)
x46 = x1 * x18 * x45
x47 = x1 * x24
x48 = x32 * x5 + 2.0 * x47
x49 = x1 * (2.0 * x24 * x5 + x46) + x48 * x5
x50 = 1.5 * x1
x51 = A[1] - B[1]
x52 = A[2] - B[2]
x53 = (
17.49341832762486
* da
* db
* dc
* x0
* x2 ** (-2.5)
* numpy.exp(-ax * bx * x1 * (x40**2 + x51**2 + x52**2))
)
x54 = 0.3333333333333333 * x53
x55 = x3 * boys(3, x44)
x56 = 2.0 * x1 * (x18 * x22 * x45 - x5 * x55) - x31 * x5
x57 = 1.732050807568877
x58 = x54 * x57
x59 = x58 * (x31 * x50 - x38 * x5 + x40 * x56)
x60 = x54 * (x31 * x40 + x38)
x61 = x7 + A[1]
x62 = -x61
x63 = x17 * x9 - x19 * x62
x64 = x1 * x63
x65 = -x64
x66 = -x63
x67 = -x16 * x18 * x62 + x26 * x9
x68 = -x67
x69 = x13 * x68
x70 = -x23 * x66 + x6 * x69
x71 = x5 * x70
x72 = x65 + 2.0 * x71
x73 = x1 * (x63 + x69)
x74 = 2.0 * x22
x75 = -x18 * x25 * x62 + x36 * x9
x76 = -x75
x77 = x13 * x6
x78 = -x30 * (x23 * x68 - x76 * x77) - x70 * x74 + x73
x79 = -x78
x80 = x1 * x70
x81 = 2.0 * x80
x82 = x1 * x72 + x5 * (x5 * x79 + x81)
x83 = -x47
x84 = x70 * x8
x85 = x83 + 2.0 * x84
x86 = x1 * x85
x87 = -x1 * x32
x88 = x79 * x8
x89 = -x39 * (x87 + 2.0 * x88)
x90 = x51 * x56
x91 = x5 * x78
x92 = -x22 * x63 + x37 * x67
x93 = x11 * x58
x94 = x31 * x51
x95 = x8 * x94
x96 = x1 * x32
x97 = -x88 + x96
x98 = x54 * x8
x99 = -0.5 * x1 * x31 + x78 * x8
x100 = x43 * x54
x101 = x10 + A[2]
x102 = -x101
x103 = -x102 * x19 + x12 * x17
x104 = x1 * x103
x105 = -x104
x106 = -x103
x107 = -x102 * x16 * x18 + x12 * x26
x108 = -x107
x109 = x108 * x13
x110 = -x106 * x23 + x109 * x6
x111 = x110 * x5
x112 = x105 + 2.0 * x111
x113 = x1 * (x103 + x109)
x114 = -x102 * x18 * x25 + x12 * x36
x115 = -x114
x116 = -x110 * x74 + x113 - x30 * (x108 * x23 - x115 * x77)
x117 = -x116
x118 = x1 * x110
x119 = 2.0 * x118
x120 = x1 * x112 + x5 * (x117 * x5 + x119)
x121 = x52 * x56
x122 = x116 * x5
x123 = -x103 * x22 + x107 * x37
x124 = x58 * x8
x125 = x11 * x110
x126 = 2.0 * x125 + x83
x127 = x1 * x126
x128 = x11 * x117
x129 = -x39 * (2.0 * x128 + x87)
x130 = x31 * x52
x131 = x42 * x54
x132 = 0.5 * x96
x133 = -x128
x134 = x11 * x130 + x133
x135 = x11 * x54
x136 = x65 + x71
x137 = x29 * x40
x138 = x1 * (x46 + 2.0 * x63 * x8)
x139 = -0.5 * x138 + 0.5 * x29 * x85
x140 = -x86
x141 = x11 * x53
x142 = x83 + x84
x143 = 2.0 * x40
x144 = x43 * x58
x145 = 2.0 * x51
x146 = 2.0 * x8
x147 = x13 * x146
x148 = x147 * x67 + x21 - 2.0 * x61 * x63
x149 = -x148
x150 = x1 * x149
x151 = -x1 * x20
x152 = 2.0 * x62
x153 = -x1 * x34
x154 = x13 * x9
x155 = -x23 * (x151 + x152 * x66 - 2.0 * x69 * x9) + x77 * (
x152 * x68 + x153 - 2.0 * x154 * x76
)
x156 = x155 * x5
x157 = x150 + x156
x158 = x5 * x58
x159 = x155 * x8
x160 = x159 - x81
x161 = x149 * x8 + 2.0 * x64
x162 = 0.5 * x1
x163 = x160 * x5 + x161 * x162
x164 = 0.5 * x150
x165 = x156 + x164
x166 = x160 * x8
x167 = x145 * x8
x168 = -x106 * x62 + x109 * x9
x169 = -x108 * x62 + x115 * x154
x170 = x168 * x23 - x169 * x77
x171 = x1 * x168
x172 = x170 * x5 - x171
x173 = x5 * x53
x174 = 0.6666666666666667 * x57
x175 = x173 * x174
x176 = -x118
x177 = x170 * x8
x178 = x168 * x8
x179 = x105 + 2.0 * x178
x180 = x1 * x179
x181 = -0.5 * x180 + x5 * (x176 + 2.0 * x177)
x182 = x11 * x52
x183 = -x80
x184 = x11 * x170
x185 = x183 + 2.0 * x184
x186 = x11 * x168
x187 = 2.0 * x186 + x65
x188 = x1 * x187
x189 = x185 * x5 - 0.5 * x188
x190 = x176 + x177
x191 = x53 * x8
x192 = x174 * x191
x193 = -0.5 * x127 + x185 * x8
x194 = x183 + x184
x195 = x141 * x174
x196 = x105 + x111
x197 = x1 * (2.0 * x103 * x11 + x46)
x198 = -x197
x199 = 0.5 * x126 * x29 + 0.5 * x198
x200 = -x127
x201 = x42 * x58
x202 = x125 + x83
x203 = x51 * x8
x204 = 2.0 * x52
x205 = x11 * x13
x206 = -2.0 * x101 * x103 + 2.0 * x107 * x205 + x21
x207 = -x206
x208 = x1 * x207
x209 = 2.0 * x102
x210 = 2.0 * x12
x211 = x106 * x209 - x109 * x210 + x151
x212 = x108 * x209 - x115 * x13 * x210 + x153
x213 = -x211 * x23 + x212 * x77
x214 = x213 * x5
x215 = x208 + x214
x216 = 0.5 * x208
x217 = x214 + x216
x218 = x11 * x213 - x119
x219 = 2.0 * x104 + x11 * x207
x220 = x162 * x219
x221 = x218 * x5 + x220
x222 = x11 * x218
x223 = 2.0 * x182
x224 = x148 * x40
x225 = x224 * x5
x226 = x5 * x54
x227 = x40 * x5
x228 = x138 + x161 * x8
x229 = 2.0 * x1 * (x18 * x45 * x61 - x55 * x8) - x148 * x8
x230 = -x147 * x75 - x35 + 2.0 * x61 * x67
x231 = x13 * x8
x232 = x149 * x61 - x230 * x231 + 2.0 * x73
x233 = x148 * x51 + x232
x234 = x41 * x54
x235 = -x232 * x8
x236 = 0.5 * x8
x237 = x148 * x52
x238 = x113 + x147 * x169 - 2.0 * x168 * x61
x239 = -x238
x240 = 2.0 * x171
x241 = x239 * x8 + x240
x242 = x11 * x239
x243 = -x242
x244 = x11 * x237 + x243
x245 = x180 + x241 * x8
x246 = x236 * (x1 * x149 - 2.0 * x242)
x247 = x105 + x178
x248 = 0.5 * x146 * x187 + 0.5 * x198
x249 = x186 + x65
x250 = x41 * x58
x251 = -x188
x252 = x154 * x212 - x211 * x62
x253 = x252 * x8
x254 = x11 * x252 - x240
x255 = x208 + x253
x256 = x220 + x254 * x8
x257 = x11 * x254
x258 = x206 * x40
x259 = x258 * x5
x260 = x219 * x40
x261 = 2.0 * x101 * x107 - 2.0 * x114 * x205 - x35
x262 = x11 * x219 + x197
x263 = x206 * x51
x264 = x231 * x261
x265 = x263 * x8
x266 = x219 * x51
x267 = x101 * x207 + 2.0 * x113 - x205 * x261
x268 = x206 * x52 + x267
x269 = -x11 * x267
x270 = 1.5 * x1 * x207 - x219 * x52 - x269
# 108 item(s)
result[0, 0, 0] = numpy.sum(
-x54 * (x39 * (3.0 * x1 * x32 + x29 * x38) - x40 * x49 + x48 * x50)
)
result[0, 0, 1] = numpy.sum(x59 * x8)
result[0, 0, 2] = numpy.sum(x11 * x59)
result[0, 0, 3] = numpy.sum(-x42 * x60)
result[0, 0, 4] = numpy.sum(-x11 * x57 * x60 * x8)
result[0, 0, 5] = numpy.sum(-x43 * x60)
result[0, 1, 0] = numpy.sum(x54 * (x49 * x51 + x82))
result[0, 1, 1] = numpy.sum(x58 * (x8 * x90 + x86 - x89))
result[0, 1, 2] = numpy.sum(x93 * (x33 * x92 + x90 - x91))
result[0, 1, 3] = numpy.sum(-x98 * (x95 + x97))
result[0, 1, 4] = numpy.sum(-x93 * (x95 + x99))
result[0, 1, 5] = numpy.sum(-x100 * (x78 + x94))
result[0, 2, 0] = numpy.sum(x54 * (x120 + x49 * x52))
result[0, 2, 1] = numpy.sum(x124 * (x121 - x122 + x123 * x33))
result[0, 2, 2] = numpy.sum(x58 * (x11 * x121 + x127 - x129))
result[0, 2, 3] = numpy.sum(-x131 * (x116 + x130))
result[0, 2, 4] = numpy.sum(-x124 * (x132 + x134))
result[0, 2, 5] = numpy.sum(-x135 * (x134 + x96))
result[1, 0, 0] = numpy.sum(x58 * (-x136 * x137 + x82))
result[1, 0, 1] = numpy.sum(-x53 * (x139 * x40 + x140 + x89))
result[1, 0, 2] = numpy.sum(x141 * (2.0 * x1 * x92 - x40 * x72 - x91))
result[1, 0, 3] = numpy.sum(-x124 * (x142 * x143 + x97))
result[1, 0, 4] = numpy.sum(-x141 * (x40 * x85 + x99))
result[1, 0, 5] = numpy.sum(-x144 * (x143 * x70 + x78))
result[1, 1, 0] = numpy.sum(-x158 * (x136 * x145 + x157))
result[1, 1, 1] = numpy.sum(-x53 * (x139 * x51 + x163))
result[1, 1, 2] = numpy.sum(-x141 * (x165 + x51 * x72))
result[1, 1, 3] = numpy.sum(-x58 * (x140 + x142 * x167 + x166))
result[1, 1, 4] = numpy.sum(-x141 * (x160 + x51 * x85))
result[1, 1, 5] = numpy.sum(-x144 * (x145 * x70 + x155))
result[1, 2, 0] = numpy.sum(-x175 * (x136 * x52 + x172))
result[1, 2, 1] = numpy.sum(-x53 * (x139 * x52 + x181))
result[1, 2, 2] = numpy.sum(-x53 * (x182 * x72 + x189))
result[1, 2, 3] = numpy.sum(-x192 * (x142 * x52 + x190))
result[1, 2, 4] = numpy.sum(-x53 * (x182 * x85 + x193))
result[1, 2, 5] = numpy.sum(-x195 * (x182 * x70 + x194))
result[2, 0, 0] = numpy.sum(x58 * (x120 - x137 * x196))
result[2, 0, 1] = numpy.sum(x191 * (2.0 * x1 * x123 - x112 * x40 - x122))
result[2, 0, 2] = numpy.sum(-x53 * (x129 + x199 * x40 + x200))
result[2, 0, 3] = numpy.sum(-x201 * (x110 * x143 + x116))
result[2, 0, 4] = numpy.sum(-x191 * (x126 * x40 + x132 + x133))
result[2, 0, 5] = numpy.sum(-x93 * (x133 + x143 * x202 + x96))
result[2, 1, 0] = numpy.sum(-x175 * (x172 + x196 * x51))
result[2, 1, 1] = numpy.sum(-x53 * (x112 * x203 + x181))
result[2, 1, 2] = numpy.sum(-x53 * (x189 + x199 * x51))
result[2, 1, 3] = numpy.sum(-x192 * (x110 * x203 + x190))
result[2, 1, 4] = numpy.sum(-x53 * (x126 * x203 + x193))
result[2, 1, 5] = numpy.sum(-x195 * (x194 + x202 * x51))
result[2, 2, 0] = numpy.sum(-x158 * (x196 * x204 + x215))
result[2, 2, 1] = numpy.sum(-x191 * (x112 * x52 + x217))
result[2, 2, 2] = numpy.sum(-x53 * (x199 * x52 + x221))
result[2, 2, 3] = numpy.sum(-x201 * (x110 * x204 + x213))
result[2, 2, 4] = numpy.sum(-x191 * (x126 * x52 + x218))
result[2, 2, 5] = numpy.sum(-x58 * (x200 + x202 * x223 + x222))
result[3, 0, 0] = numpy.sum(-x226 * (x157 + x225))
result[3, 0, 1] = numpy.sum(x58 * (x161 * x227 - x163))
result[3, 0, 2] = numpy.sum(-x93 * (x165 + x225))
result[3, 0, 3] = numpy.sum(x54 * (-x166 + x228 * x40 + x86))
result[3, 0, 4] = numpy.sum(x93 * (-x159 + x229 * x40 + x81))
result[3, 0, 5] = numpy.sum(x100 * (-x149 * x22 - x224 + x230 * x37))
result[3, 1, 0] = numpy.sum(-x233 * x234)
result[3, 1, 1] = numpy.sum(
0.5 * x158 * (-3.0 * x1 * x149 + 2.0 * x161 * x51 + 2.0 * x235)
)
result[3, 1, 2] = numpy.sum(-x233 * x5 * x93)
result[3, 1, 3] = numpy.sum(
-x54 * (x161 * x50 - x228 * x51 + x236 * (3.0 * x1 * x149 - 2.0 * x235))
)
result[3, 1, 4] = numpy.sum(x93 * (x148 * x50 + x229 * x51 - x232 * x8))
result[3, 1, 5] = numpy.sum(-x100 * x233)
result[3, 2, 0] = numpy.sum(-x234 * (x237 + x238))
result[3, 2, 1] = numpy.sum(x158 * (x161 * x52 + x241))
result[3, 2, 2] = numpy.sum(-x158 * (x164 + x244))
result[3, 2, 3] = numpy.sum(x54 * (x228 * x52 + x245))
result[3, 2, 4] = numpy.sum(x58 * (x182 * x229 + x188 - x246))
result[3, 2, 5] = numpy.sum(-x135 * (x150 + x244))
result[4, 0, 0] = numpy.sum(-x175 * (x168 * x227 + x172))
result[4, 0, 1] = numpy.sum(-x53 * (x179 * x227 + x181))
result[4, 0, 2] = numpy.sum(-x53 * (x187 * x227 + x189))
result[4, 0, 3] = numpy.sum(-x192 * (x190 + x247 * x40))
result[4, 0, 4] = numpy.sum(-x53 * (x193 + x248 * x40))
result[4, 0, 5] = numpy.sum(-x195 * (x194 + x249 * x40))
result[4, 1, 0] = numpy.sum(-x250 * (x145 * x168 + x238))
result[4, 1, 1] = numpy.sum(x173 * (-x179 * x51 + x241))
result[4, 1, 2] = numpy.sum(-x173 * (x164 + x187 * x51 + x243))
result[4, 1, 3] = numpy.sum(x58 * (-x167 * x247 + x245))
result[4, 1, 4] = numpy.sum(-x53 * (x246 + x248 * x51 + x251))
result[4, 1, 5] = numpy.sum(-x93 * (x145 * x249 + x150 + x243))
result[4, 2, 0] = numpy.sum(-x250 * (x168 * x204 + x252))
result[4, 2, 1] = numpy.sum(-x173 * (x179 * x52 + x216 + x253))
result[4, 2, 2] = numpy.sum(-x173 * (x187 * x52 + x254))
result[4, 2, 3] = numpy.sum(-x124 * (x204 * x247 + x255))
result[4, 2, 4] = numpy.sum(-x53 * (x248 * x52 + x256))
result[4, 2, 5] = numpy.sum(-x58 * (x223 * x249 + x251 + x257))
result[5, 0, 0] = numpy.sum(-x226 * (x215 + x259))
result[5, 0, 1] = numpy.sum(-x124 * (x217 + x259))
result[5, 0, 2] = numpy.sum(x58 * (-x221 + x260 * x5))
result[5, 0, 3] = numpy.sum(x131 * (-x207 * x22 - x258 + x261 * x37))
result[5, 0, 4] = numpy.sum(x124 * (-x11 * x213 + x119 + x260))
result[5, 0, 5] = numpy.sum(x54 * (x127 - x222 + x262 * x40))
result[5, 1, 0] = numpy.sum(x234 * (-x207 * x61 - x263 + x264))
result[5, 1, 1] = numpy.sum(-x158 * (-x162 * x206 + x265 + x8 * (x207 * x61 - x264)))
result[5, 1, 2] = numpy.sum(x158 * (-x11 * x252 + x240 + x266))
result[5, 1, 3] = numpy.sum(-x98 * (x255 + x265))
result[5, 1, 4] = numpy.sum(x58 * (-x256 + x266 * x8))
result[5, 1, 5] = numpy.sum(x54 * (x188 - x257 + x262 * x51))
result[5, 2, 0] = numpy.sum(-x234 * x268)
result[5, 2, 1] = numpy.sum(-x124 * x268 * x5)
result[5, 2, 2] = numpy.sum(-x158 * x270)
result[5, 2, 3] = numpy.sum(-x131 * x268)
result[5, 2, 4] = numpy.sum(-x124 * x270)
result[5, 2, 5] = numpy.sum(
-0.5
* x54
* (x11 * (3.0 * x1 * x207 - 2.0 * x269) + 2.0 * x219 * x50 - 2.0 * x262 * x52)
)
return result
[docs]
def int3c2e3d_sph_213(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (dp|f) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 3, 10), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = -x2 - A[0]
x5 = 0.5 / (ax + bx)
x6 = x3**2
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = x8**2
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = -x10 - C[2]
x12 = x11**2
x13 = cx + x0
x14 = x13 ** (-1.0)
x15 = cx * x14
x16 = x0 * x15 * (x12 + x6 + x9)
x17 = boys(4, x16)
x18 = x13 ** (-1.5)
x19 = 17.49341832762486
x20 = A[0] - B[0]
x21 = A[1] - B[1]
x22 = A[2] - B[2]
x23 = numpy.exp(-ax * bx * x1 * (x20**2 + x21**2 + x22**2))
x24 = x1 * x19 * x23
x25 = 2.0 * x18 * x24
x26 = x17 * x25
x27 = cx ** (-1.0)
x28 = x13 ** (-0.5)
x29 = boys(3, x16)
x30 = x5 * (2.0 * x1 * x19 * x23 * x27 * x28 * x29 - x26)
x31 = -2.0 * x1 * x19 * x23 * x27 * x28 * x29 * x4 + x26 * x3
x32 = -x31
x33 = boys(5, x16)
x34 = x25 * x33
x35 = 2.0 * x1 * x17 * x19 * x23 * x27 * x28 * x4 - x3 * x34
x36 = x15 * x35
x37 = -x3 * x36 + x30 + x32 * x4
x38 = 2.0 * x5
x39 = x5 * (2.0 * x1 * x17 * x19 * x23 * x27 * x28 - x34)
x40 = x25 * boys(6, x16)
x41 = x15 * x3
x42 = (
x37 * x4
- x38 * (x31 + x36)
- x41
* (
x35 * x4
+ x39
- x41 * (2.0 * x1 * x19 * x23 * x27 * x28 * x33 * x4 - x3 * x40)
)
)
x43 = x3 * x42
x44 = x37 * x5
x45 = 3.0 * x44
x46 = x0 * x14
x47 = x3 * x46
x48 = x3 * x37
x49 = x32 * x5
x50 = 2.0 * x49
x51 = x48 + x50
x52 = x46 * x5
x53 = 3.0 * x52
x54 = x3 * x32
x55 = x27 * x29 * x38
x56 = x24 * x28 * x55
x57 = x54 + x56
x58 = x38 * x46
x59 = x47 * x51 + x57 * x58
x60 = x18 * x19 * x23 * x55
x61 = x47 * x59 + x58 * (x3 * x60 + x47 * x57)
x62 = x20 * x46
x63 = da * db * dc
x64 = 0.06666666666666667 * x63
x65 = 2.23606797749979 * x64
x66 = x46 * x8
x67 = x66 * (x48 + x50)
x68 = x60 * x8
x69 = x47 * x67 + x58 * (x54 * x66 + x68)
x70 = 0.3333333333333333 * x63
x71 = x11 * x46
x72 = x71 * (x48 + x50)
x73 = x11 * x60
x74 = x47 * x72 + x58 * (x54 * x71 + x73)
x75 = x0**2 / x13**2
x76 = x75 * x9
x77 = x76 * (x48 + x50)
x78 = x75 * x8
x79 = x11 * x78
x80 = x79 * (x48 + x50)
x81 = 1.732050807568877 * x70
x82 = x12 * x75
x83 = x82 * (x48 + x50)
x84 = x8**3
x85 = x0**3 / x13**3
x86 = x42 * x85
x87 = x84 * x85
x88 = x20 * x37
x89 = x85 * x9
x90 = x11 * x89
x91 = x12 * x8
x92 = x85 * x91
x93 = x11**3
x94 = x85 * x93
x95 = -x7 - A[1]
x96 = 2.0 * x1 * x17 * x19 * x23 * x27 * x28 * x95 - x34 * x8
x97 = x15 * x96
x98 = -2.0 * x1 * x19 * x23 * x27 * x28 * x29 * x95 + x26 * x8
x99 = -x5 * (x97 + x98)
x100 = -x98
x101 = x100 * x4 - x3 * x97
x102 = 2.0 * x1 * x19 * x23 * x27 * x28 * x33 * x95 - x40 * x8
x103 = x101 * x4 + x41 * (x102 * x41 - x4 * x96) + x99
x104 = x103 * x3
x105 = x101 * x5
x106 = 2.0 * x105
x107 = x100 * x5
x108 = x101 * x3
x109 = x107 + x108
x110 = x47 * (x107 + x109)
x111 = x46 * (x110 * x58 + x47 * (x109 * x58 + x47 * (x104 + x106)))
x112 = x21 * x46
x113 = x103 * x8
x114 = x113 + x44
x115 = x101 * x8
x116 = x115 + x49
x117 = x116 * x58
x118 = x100 * x8
x119 = x118 + x56
x120 = x116 * x47 + x119 * x52
x121 = x46 * (x120 * x58 + x47 * (x114 * x47 + x117))
x122 = x106 * x71
x123 = x107 * x71
x124 = x108 * x71 + x123
x125 = x46 * (x124 * x58 + x47 * (x104 * x71 + x122))
x126 = x66 * (x114 + x44)
x127 = x66 * (x116 + x49)
x128 = x127 * x58
x129 = x46 * (x126 * x47 + x128)
x130 = x44 * x71
x131 = x113 * x71 + x130
x132 = x49 * x71
x133 = x115 * x71 + x132
x134 = x133 * x58
x135 = x46 * (x131 * x47 + x134)
x136 = x106 * x82
x137 = x46 * (x104 * x82 + x136)
x138 = x46 * (x126 * x66 + x44 * x76)
x139 = x21 * x37
x140 = x46 * (x131 * x66 + x44 * x79)
x141 = x44 * x82
x142 = x46 * (x113 * x82 + x141)
x143 = x103 * x94
x144 = -x10 - A[2]
x145 = 2.0 * x1 * x144 * x17 * x19 * x23 * x27 * x28 - x11 * x34
x146 = x145 * x15
x147 = -2.0 * x1 * x144 * x19 * x23 * x27 * x28 * x29 + x11 * x26
x148 = -x5 * (x146 + x147)
x149 = -x147
x150 = -x146 * x3 + x149 * x4
x151 = 2.0 * x1 * x144 * x19 * x23 * x27 * x28 * x33 - x11 * x40
x152 = x148 + x150 * x4 - x41 * (x145 * x4 - x151 * x41)
x153 = x152 * x3
x154 = x150 * x5
x155 = 2.0 * x154
x156 = x149 * x5
x157 = x150 * x3
x158 = x156 + x157
x159 = x47 * (x156 + x158)
x160 = x46 * (x159 * x58 + x47 * (x158 * x58 + x47 * (x153 + x155)))
x161 = x22 * x46
x162 = x156 * x66
x163 = x157 * x66 + x162
x164 = x46 * (x163 * x58 + x47 * x66 * (x153 + x155))
x165 = x11 * x152 + x44
x166 = x11 * x150 + x49
x167 = x166 * x58
x168 = x11 * x149 + x56
x169 = x168 * x52
x170 = x166 * x47 + x169
x171 = x46 * (x170 * x58 + x47 * (x165 * x47 + x167))
x172 = x46 * x76 * (x153 + x155)
x173 = x3 * x78
x174 = x46 * (x165 * x173 + x166 * x38 * x78)
x175 = x130 + x165 * x71
x176 = x132 + x166 * x71
x177 = x176 * x58
x178 = x46 * (x175 * x47 + x177)
x179 = x152 * x87
x180 = x22 * x37
x181 = x165 * x89
x182 = x175 * x78
x183 = x46 * (x141 + x175 * x71)
x184 = x6 * x75
x185 = x107 * x184 + x110 * x47
x186 = 3.872983346207417 * x64
x187 = x3 * x75
x188 = x187 * x5
x189 = x119 * x188 + x120 * x47
x190 = x11 * x187
x191 = x107 * x190 + x124 * x47
x192 = x119 * x66 + x68
x193 = x127 * x47 + x192 * x52
x194 = x118 * x71 + x73
x195 = x133 * x47 + x194 * x52
x196 = x107 * x82
x197 = x108 * x82 + x196
x198 = x127 * x66 + x49 * x76
x199 = x133 * x66 + x49 * x79
x200 = x49 * x82
x201 = x115 * x82 + x200
x202 = x101 * x94
x203 = x100 * x95 + x30 - x8 * x97
x204 = x203 * x5
x205 = x15 * x8
x206 = -x102 * x205 + x39 + x95 * x96
x207 = x203 * x4 - x206 * x41
x208 = x207 * x3
x209 = x46 * (x184 * x204 + x47**2 * (2.0 * x204 + x208))
x210 = x203 * x8
x211 = 2.0 * x107
x212 = x210 + x211
x213 = x212 * x52
x214 = x207 * x8
x215 = x106 + x214
x216 = x46 * (x188 * x212 + x47 * (x213 + x215 * x47))
x217 = x204 * x71
x218 = x46 * (x190 * x204 + x47 * (x208 * x71 + x217))
x219 = x119 * x58 + x212 * x66
x220 = x219 * x52
x221 = x117 + x215 * x66
x222 = x46 * (x220 + x221 * x47)
x223 = x71 * (x210 + x211)
x224 = x223 * x52
x225 = x122 + x214 * x71
x226 = x46 * (x224 + x225 * x47)
x227 = x204 * x82
x228 = x46 * (x208 * x82 + x227)
x229 = x46 * (x128 + x221 * x66)
x230 = x46 * (x134 + x225 * x66)
x231 = x46 * (x136 + x214 * x82)
x232 = x207 * x94
x233 = -x146 * x8 + x149 * x95
x234 = x233 * x5
x235 = x145 * x95 - x151 * x205
x236 = x233 * x4 - x235 * x41
x237 = x46 * (x184 * x234 + x47**2 * (2.0 * x234 + x236 * x3))
x238 = x156 + x233 * x8
x239 = x154 + x236 * x8
x240 = x46 * (x188 * x238 + x47 * (x238 * x52 + x239 * x47))
x241 = x107 + x11 * x233
x242 = x105 + x11 * x236
x243 = x46 * (x188 * x241 + x47 * (x241 * x52 + x242 * x47))
x244 = x162 + x238 * x66
x245 = x66 * (x154 + x239)
x246 = x46 * (x244 * x52 + x245 * x47)
x247 = x169 + x241 * x66
x248 = x166 * x52 + x242 * x66
x249 = x46 * (x247 * x52 + x248 * x47)
x250 = x123 + x241 * x71
x251 = x71 * (x105 + x242)
x252 = x46 * (x250 * x52 + x251 * x47)
x253 = x46 * (x154 * x76 + x245 * x66)
x254 = x5 * x78
x255 = x46 * (x166 * x254 + x248 * x66)
x256 = x46 * (x176 * x52 + x251 * x66)
x257 = x46 * (x105 * x82 + x251 * x71)
x258 = x156 * x184 + x159 * x47
x259 = x156 * x173 + x163 * x47
x260 = x168 * x188 + x170 * x47
x261 = x156 * x76
x262 = x157 * x76 + x261
x263 = x168 * x254
x264 = x166 * x173 + x263
x265 = x168 * x71 + x73
x266 = x265 * x52
x267 = x176 * x47 + x266
x268 = x150 * x87
x269 = x166 * x89
x270 = x176 * x78
x271 = x176 * x71 + x200
x272 = -x11 * x146 + x144 * x149 + x30
x273 = x272 * x5
x274 = x11 * x15
x275 = x144 * x145 - x151 * x274 + x39
x276 = x272 * x4 - x275 * x41
x277 = x276 * x3
x278 = x46 * (x184 * x273 + x47**2 * (2.0 * x273 + x277))
x279 = x273 * x66
x280 = x46 * (x173 * x273 + x47 * (x277 * x66 + x279))
x281 = x11 * x272 + 2.0 * x156
x282 = x281 * x52
x283 = x11 * x276 + x155
x284 = x46 * (x188 * x281 + x47 * (x282 + x283 * x47))
x285 = x273 * x76
x286 = x46 * (x277 * x76 + x285)
x287 = x254 * x281
x288 = x46 * (x173 * x283 + x287)
x289 = x168 * x58 + x281 * x71
x290 = x289 * x52
x291 = x167 + x283 * x71
x292 = x46 * (x290 + x291 * x47)
x293 = x276 * x87
x294 = x283 * x89
x295 = x291 * x78
x296 = x46 * (x177 + x291 * x71)
x297 = x3**3 * x85
x298 = x20 * x203
x299 = x6 * x85
x300 = x212 * x299
x301 = x11 * x299
x302 = x187 * x20
x303 = x3 * x85
x304 = x12 * x303
x305 = x192 * x58 + x219 * x66
x306 = x194 * x58 + x223 * x66
x307 = x82 * (x210 + x211)
x308 = x203 * x95 - x205 * x206 + 2.0 * x99
x309 = x203 * x21
x310 = x308 * x8
x311 = 3.0 * x204
x312 = x310 + x311
x313 = 3.0 * x213 + x312 * x66
x314 = x187 * x21
x315 = x71 * (x310 + x311)
x316 = x148 - x205 * x235 + x233 * x95
x317 = x297 * x316
x318 = x203 * x22
x319 = 2.0 * x234
x320 = x316 * x8 + x319
x321 = x299 * x320
x322 = x11 * x316 + x204
x323 = x299 * x322
x324 = x238 * x58 + x320 * x66
x325 = x187 * x324
x326 = x187 * x22
x327 = x241 * x58
x328 = x322 * x66 + x327
x329 = x187 * x328
x330 = x217 + x322 * x71
x331 = x187 * x330
x332 = x46 * (x244 * x58 + x324 * x66)
x333 = x46 * (x247 * x58 + x328 * x66)
x334 = x250 * x58
x335 = x46 * (x330 * x66 + x334)
x336 = x46 * (x227 + x330 * x71)
x337 = x233 * x297
x338 = x20 * x299
x339 = x244 * x66 + x261
x340 = x247 * x66 + x263
x341 = x250 * x66 + x266
x342 = x196 + x250 * x71
x343 = x21 * x299
x344 = -x205 * x275 + x272 * x95
x345 = x297 * x344
x346 = x273 + x344 * x8
x347 = x299 * x346
x348 = x22 * x299
x349 = x11 * x344 + x319
x350 = x299 * x349
x351 = x279 + x346 * x66
x352 = x187 * x351
x353 = x282 + x349 * x66
x354 = x187 * x353
x355 = x327 + x349 * x71
x356 = x187 * x355
x357 = x46 * (x285 + x351 * x66)
x358 = x46 * (x287 + x353 * x66)
x359 = x46 * (x290 + x355 * x66)
x360 = x46 * (x334 + x355 * x71)
x361 = x20 * x272
x362 = x272 * x8
x363 = x3 * x89
x364 = x303 * x8
x365 = x281 * x364
x366 = x281 * x89
x367 = x289 * x78
x368 = x265 * x58 + x289 * x71
x369 = x21 * x272
x370 = x144 * x272 + 2.0 * x148 - x274 * x275
x371 = x22 * x272
x372 = x11 * x370 + 3.0 * x273
x373 = 3.0 * x282 + x372 * x71
# 180 item(s)
result[0, 0, 0] = numpy.sum(
x65 * (x46 * (x47 * (x47 * (x43 + x45) + x51 * x53) + x53 * x59) + x61 * x62)
)
result[0, 0, 1] = numpy.sum(
x70 * (x46 * (x47 * x66 * (x43 + x45) + x53 * x67) + x62 * x69)
)
result[0, 0, 2] = numpy.sum(
x70 * (x46 * (x47 * x71 * (x43 + x45) + x53 * x72) + x62 * x74)
)
result[0, 0, 3] = numpy.sum(x70 * (x46 * x76 * (x43 + x45) + x62 * x77))
result[0, 0, 4] = numpy.sum(x81 * (x46 * x79 * (x43 + x45) + x62 * x80))
result[0, 0, 5] = numpy.sum(x70 * (x46 * x82 * (x43 + x45) + x62 * x83))
result[0, 0, 6] = numpy.sum(x65 * (x84 * x86 + x87 * x88))
result[0, 0, 7] = numpy.sum(x70 * (x11 * x86 * x9 + x88 * x90))
result[0, 0, 8] = numpy.sum(x70 * (x86 * x91 + x88 * x92))
result[0, 0, 9] = numpy.sum(x65 * (x86 * x93 + x88 * x94))
result[0, 1, 0] = numpy.sum(x65 * (x111 + x112 * x61))
result[0, 1, 1] = numpy.sum(x70 * (x112 * x69 + x121))
result[0, 1, 2] = numpy.sum(x70 * (x112 * x74 + x125))
result[0, 1, 3] = numpy.sum(x70 * (x112 * x77 + x129))
result[0, 1, 4] = numpy.sum(x81 * (x112 * x80 + x135))
result[0, 1, 5] = numpy.sum(x70 * (x112 * x83 + x137))
result[0, 1, 6] = numpy.sum(x65 * (x138 + x139 * x87))
result[0, 1, 7] = numpy.sum(x70 * (x139 * x90 + x140))
result[0, 1, 8] = numpy.sum(x70 * (x139 * x92 + x142))
result[0, 1, 9] = numpy.sum(x65 * (x139 * x94 + x143))
result[0, 2, 0] = numpy.sum(x65 * (x160 + x161 * x61))
result[0, 2, 1] = numpy.sum(x70 * (x161 * x69 + x164))
result[0, 2, 2] = numpy.sum(x70 * (x161 * x74 + x171))
result[0, 2, 3] = numpy.sum(x70 * (x161 * x77 + x172))
result[0, 2, 4] = numpy.sum(x81 * (x161 * x80 + x174))
result[0, 2, 5] = numpy.sum(x70 * (x161 * x83 + x178))
result[0, 2, 6] = numpy.sum(x65 * (x179 + x180 * x87))
result[0, 2, 7] = numpy.sum(x70 * (x180 * x90 + x181))
result[0, 2, 8] = numpy.sum(x70 * (x180 * x92 + x182))
result[0, 2, 9] = numpy.sum(x65 * (x180 * x94 + x183))
result[1, 0, 0] = numpy.sum(x186 * (x111 + x185 * x62))
result[1, 0, 1] = numpy.sum(x81 * (x121 + x189 * x62))
result[1, 0, 2] = numpy.sum(x81 * (x125 + x191 * x62))
result[1, 0, 3] = numpy.sum(x81 * (x129 + x193 * x62))
result[1, 0, 4] = numpy.sum(x63 * (x135 + x195 * x62))
result[1, 0, 5] = numpy.sum(x81 * (x137 + x197 * x62))
result[1, 0, 6] = numpy.sum(x186 * (x138 + x198 * x62))
result[1, 0, 7] = numpy.sum(x81 * (x140 + x199 * x62))
result[1, 0, 8] = numpy.sum(x81 * (x142 + x201 * x62))
result[1, 0, 9] = numpy.sum(x186 * (x143 + x20 * x202))
result[1, 1, 0] = numpy.sum(x186 * (x112 * x185 + x209))
result[1, 1, 1] = numpy.sum(x81 * (x112 * x189 + x216))
result[1, 1, 2] = numpy.sum(x81 * (x112 * x191 + x218))
result[1, 1, 3] = numpy.sum(x81 * (x112 * x193 + x222))
result[1, 1, 4] = numpy.sum(x63 * (x112 * x195 + x226))
result[1, 1, 5] = numpy.sum(x81 * (x112 * x197 + x228))
result[1, 1, 6] = numpy.sum(x186 * (x112 * x198 + x229))
result[1, 1, 7] = numpy.sum(x81 * (x112 * x199 + x230))
result[1, 1, 8] = numpy.sum(x81 * (x112 * x201 + x231))
result[1, 1, 9] = numpy.sum(x186 * (x202 * x21 + x232))
result[1, 2, 0] = numpy.sum(x186 * (x161 * x185 + x237))
result[1, 2, 1] = numpy.sum(x81 * (x161 * x189 + x240))
result[1, 2, 2] = numpy.sum(x81 * (x161 * x191 + x243))
result[1, 2, 3] = numpy.sum(x81 * (x161 * x193 + x246))
result[1, 2, 4] = numpy.sum(x63 * (x161 * x195 + x249))
result[1, 2, 5] = numpy.sum(x81 * (x161 * x197 + x252))
result[1, 2, 6] = numpy.sum(x186 * (x161 * x198 + x253))
result[1, 2, 7] = numpy.sum(x81 * (x161 * x199 + x255))
result[1, 2, 8] = numpy.sum(x81 * (x161 * x201 + x256))
result[1, 2, 9] = numpy.sum(x186 * (x202 * x22 + x257))
result[2, 0, 0] = numpy.sum(x186 * (x160 + x258 * x62))
result[2, 0, 1] = numpy.sum(x81 * (x164 + x259 * x62))
result[2, 0, 2] = numpy.sum(x81 * (x171 + x260 * x62))
result[2, 0, 3] = numpy.sum(x81 * (x172 + x262 * x62))
result[2, 0, 4] = numpy.sum(x63 * (x174 + x264 * x62))
result[2, 0, 5] = numpy.sum(x81 * (x178 + x267 * x62))
result[2, 0, 6] = numpy.sum(x186 * (x179 + x20 * x268))
result[2, 0, 7] = numpy.sum(x81 * (x181 + x20 * x269))
result[2, 0, 8] = numpy.sum(x81 * (x182 + x20 * x270))
result[2, 0, 9] = numpy.sum(x186 * (x183 + x271 * x62))
result[2, 1, 0] = numpy.sum(x186 * (x112 * x258 + x237))
result[2, 1, 1] = numpy.sum(x81 * (x112 * x259 + x240))
result[2, 1, 2] = numpy.sum(x81 * (x112 * x260 + x243))
result[2, 1, 3] = numpy.sum(x81 * (x112 * x262 + x246))
result[2, 1, 4] = numpy.sum(x63 * (x112 * x264 + x249))
result[2, 1, 5] = numpy.sum(x81 * (x112 * x267 + x252))
result[2, 1, 6] = numpy.sum(x186 * (x21 * x268 + x253))
result[2, 1, 7] = numpy.sum(x81 * (x21 * x269 + x255))
result[2, 1, 8] = numpy.sum(x81 * (x21 * x270 + x256))
result[2, 1, 9] = numpy.sum(x186 * (x112 * x271 + x257))
result[2, 2, 0] = numpy.sum(x186 * (x161 * x258 + x278))
result[2, 2, 1] = numpy.sum(x81 * (x161 * x259 + x280))
result[2, 2, 2] = numpy.sum(x81 * (x161 * x260 + x284))
result[2, 2, 3] = numpy.sum(x81 * (x161 * x262 + x286))
result[2, 2, 4] = numpy.sum(x63 * (x161 * x264 + x288))
result[2, 2, 5] = numpy.sum(x81 * (x161 * x267 + x292))
result[2, 2, 6] = numpy.sum(x186 * (x22 * x268 + x293))
result[2, 2, 7] = numpy.sum(x81 * (x22 * x269 + x294))
result[2, 2, 8] = numpy.sum(x81 * (x22 * x270 + x295))
result[2, 2, 9] = numpy.sum(x186 * (x161 * x271 + x296))
result[3, 0, 0] = numpy.sum(x65 * (x209 + x297 * x298))
result[3, 0, 1] = numpy.sum(x70 * (x20 * x300 + x216))
result[3, 0, 2] = numpy.sum(x70 * (x218 + x298 * x301))
result[3, 0, 3] = numpy.sum(x70 * (x219 * x302 + x222))
result[3, 0, 4] = numpy.sum(x81 * (x223 * x302 + x226))
result[3, 0, 5] = numpy.sum(x70 * (x228 + x298 * x304))
result[3, 0, 6] = numpy.sum(x65 * (x229 + x305 * x62))
result[3, 0, 7] = numpy.sum(x70 * (x230 + x306 * x62))
result[3, 0, 8] = numpy.sum(x70 * (x231 + x307 * x62))
result[3, 0, 9] = numpy.sum(x65 * (x232 + x298 * x94))
result[3, 1, 0] = numpy.sum(x297 * x65 * (x308 + x309))
result[3, 1, 1] = numpy.sum(x70 * (x21 * x300 + x299 * x312))
result[3, 1, 2] = numpy.sum(x301 * x70 * (x308 + x309))
result[3, 1, 3] = numpy.sum(x70 * (x187 * x313 + x219 * x314))
result[3, 1, 4] = numpy.sum(x81 * (x187 * x315 + x223 * x314))
result[3, 1, 5] = numpy.sum(x304 * x70 * (x308 + x309))
result[3, 1, 6] = numpy.sum(x65 * (x112 * x305 + x46 * (3.0 * x220 + x313 * x66)))
result[3, 1, 7] = numpy.sum(x70 * (x112 * x306 + x46 * (3.0 * x224 + x315 * x66)))
result[3, 1, 8] = numpy.sum(x70 * (x112 * x307 + x46 * x82 * (x310 + x311)))
result[3, 1, 9] = numpy.sum(x65 * x94 * (x308 + x309))
result[3, 2, 0] = numpy.sum(x65 * (x297 * x318 + x317))
result[3, 2, 1] = numpy.sum(x70 * (x22 * x300 + x321))
result[3, 2, 2] = numpy.sum(x70 * (x301 * x318 + x323))
result[3, 2, 3] = numpy.sum(x70 * (x219 * x326 + x325))
result[3, 2, 4] = numpy.sum(x81 * (x223 * x326 + x329))
result[3, 2, 5] = numpy.sum(x70 * (x304 * x318 + x331))
result[3, 2, 6] = numpy.sum(x65 * (x161 * x305 + x332))
result[3, 2, 7] = numpy.sum(x70 * (x161 * x306 + x333))
result[3, 2, 8] = numpy.sum(x70 * (x161 * x307 + x335))
result[3, 2, 9] = numpy.sum(x65 * (x318 * x94 + x336))
result[4, 0, 0] = numpy.sum(x186 * (x20 * x337 + x237))
result[4, 0, 1] = numpy.sum(x81 * (x238 * x338 + x240))
result[4, 0, 2] = numpy.sum(x81 * (x241 * x338 + x243))
result[4, 0, 3] = numpy.sum(x81 * (x244 * x302 + x246))
result[4, 0, 4] = numpy.sum(x63 * (x247 * x302 + x249))
result[4, 0, 5] = numpy.sum(x81 * (x250 * x302 + x252))
result[4, 0, 6] = numpy.sum(x186 * (x253 + x339 * x62))
result[4, 0, 7] = numpy.sum(x81 * (x255 + x340 * x62))
result[4, 0, 8] = numpy.sum(x81 * (x256 + x341 * x62))
result[4, 0, 9] = numpy.sum(x186 * (x257 + x342 * x62))
result[4, 1, 0] = numpy.sum(x186 * (x21 * x337 + x317))
result[4, 1, 1] = numpy.sum(x81 * (x238 * x343 + x321))
result[4, 1, 2] = numpy.sum(x81 * (x241 * x343 + x323))
result[4, 1, 3] = numpy.sum(x81 * (x244 * x314 + x325))
result[4, 1, 4] = numpy.sum(x63 * (x247 * x314 + x329))
result[4, 1, 5] = numpy.sum(x81 * (x250 * x314 + x331))
result[4, 1, 6] = numpy.sum(x186 * (x112 * x339 + x332))
result[4, 1, 7] = numpy.sum(x81 * (x112 * x340 + x333))
result[4, 1, 8] = numpy.sum(x81 * (x112 * x341 + x335))
result[4, 1, 9] = numpy.sum(x186 * (x112 * x342 + x336))
result[4, 2, 0] = numpy.sum(x186 * (x22 * x337 + x345))
result[4, 2, 1] = numpy.sum(x81 * (x238 * x348 + x347))
result[4, 2, 2] = numpy.sum(x81 * (x241 * x348 + x350))
result[4, 2, 3] = numpy.sum(x81 * (x244 * x326 + x352))
result[4, 2, 4] = numpy.sum(x63 * (x247 * x326 + x354))
result[4, 2, 5] = numpy.sum(x81 * (x250 * x326 + x356))
result[4, 2, 6] = numpy.sum(x186 * (x161 * x339 + x357))
result[4, 2, 7] = numpy.sum(x81 * (x161 * x340 + x358))
result[4, 2, 8] = numpy.sum(x81 * (x161 * x341 + x359))
result[4, 2, 9] = numpy.sum(x186 * (x161 * x342 + x360))
result[5, 0, 0] = numpy.sum(x65 * (x278 + x297 * x361))
result[5, 0, 1] = numpy.sum(x70 * (x280 + x338 * x362))
result[5, 0, 2] = numpy.sum(x70 * (x281 * x338 + x284))
result[5, 0, 3] = numpy.sum(x70 * (x286 + x361 * x363))
result[5, 0, 4] = numpy.sum(x81 * (x20 * x365 + x288))
result[5, 0, 5] = numpy.sum(x70 * (x289 * x302 + x292))
result[5, 0, 6] = numpy.sum(x65 * (x293 + x361 * x87))
result[5, 0, 7] = numpy.sum(x70 * (x20 * x366 + x294))
result[5, 0, 8] = numpy.sum(x70 * (x20 * x367 + x295))
result[5, 0, 9] = numpy.sum(x65 * (x296 + x368 * x62))
result[5, 1, 0] = numpy.sum(x65 * (x297 * x369 + x345))
result[5, 1, 1] = numpy.sum(x70 * (x343 * x362 + x347))
result[5, 1, 2] = numpy.sum(x70 * (x281 * x343 + x350))
result[5, 1, 3] = numpy.sum(x70 * (x352 + x363 * x369))
result[5, 1, 4] = numpy.sum(x81 * (x21 * x365 + x354))
result[5, 1, 5] = numpy.sum(x70 * (x289 * x314 + x356))
result[5, 1, 6] = numpy.sum(x65 * (x357 + x369 * x87))
result[5, 1, 7] = numpy.sum(x70 * (x21 * x366 + x358))
result[5, 1, 8] = numpy.sum(x70 * (x21 * x367 + x359))
result[5, 1, 9] = numpy.sum(x65 * (x112 * x368 + x360))
result[5, 2, 0] = numpy.sum(x297 * x65 * (x370 + x371))
result[5, 2, 1] = numpy.sum(x70 * (x299 * x370 * x8 + x348 * x362))
result[5, 2, 2] = numpy.sum(x70 * (x281 * x348 + x299 * x372))
result[5, 2, 3] = numpy.sum(x363 * x70 * (x370 + x371))
result[5, 2, 4] = numpy.sum(x81 * (x22 * x365 + x364 * x372))
result[5, 2, 5] = numpy.sum(x70 * (x187 * x373 + x289 * x326))
result[5, 2, 6] = numpy.sum(x65 * x87 * (x370 + x371))
result[5, 2, 7] = numpy.sum(x70 * (x22 * x366 + x372 * x89))
result[5, 2, 8] = numpy.sum(x70 * (x22 * x367 + x373 * x78))
result[5, 2, 9] = numpy.sum(x65 * (x161 * x368 + x46 * (3.0 * x290 + x373 * x71)))
return result
[docs]
def int3c2e3d_sph_214(ax, da, A, bx, db, B, cx, dc, C):
"""Cartesian (dp|g) three-center two-electron repulsion integral.
These integrals MUST BE converted to spherical harmonics!
Integral generation utilized Ahlrichs (truncated) vertical recursion relation.
There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6, 3, 15), dtype=float)
x0 = ax + bx
x1 = x0 ** (-1.0)
x2 = -x1 * (ax * A[0] + bx * B[0])
x3 = -x2 - C[0]
x4 = -x2 - A[0]
x5 = 0.5 / (ax + bx)
x6 = x3**2
x7 = -x1 * (ax * A[1] + bx * B[1])
x8 = -x7 - C[1]
x9 = x8**2
x10 = -x1 * (ax * A[2] + bx * B[2])
x11 = -x10 - C[2]
x12 = x11**2
x13 = cx + x0
x14 = x13 ** (-1.0)
x15 = cx * x14
x16 = x0 * x15 * (x12 + x6 + x9)
x17 = boys(5, x16)
x18 = x13 ** (-1.5)
x19 = 17.49341832762486
x20 = A[0] - B[0]
x21 = A[1] - B[1]
x22 = A[2] - B[2]
x23 = numpy.exp(-ax * bx * x1 * (x20**2 + x21**2 + x22**2))
x24 = x19 * x23
x25 = x1 * x24
x26 = 2.0 * x18 * x25
x27 = x17 * x26
x28 = cx ** (-1.0)
x29 = x13 ** (-0.5)
x30 = boys(4, x16)
x31 = x5 * (2.0 * x1 * x19 * x23 * x28 * x29 * x30 - x27)
x32 = -2.0 * x1 * x19 * x23 * x28 * x29 * x30 * x4 + x27 * x3
x33 = -x32
x34 = boys(6, x16)
x35 = x26 * x34
x36 = 2.0 * x1 * x17 * x19 * x23 * x28 * x29 * x4 - x3 * x35
x37 = x15 * x36
x38 = -x3 * x37 + x31 + x33 * x4
x39 = 2.0 * x5
x40 = x5 * (2.0 * x1 * x17 * x19 * x23 * x28 * x29 - x35)
x41 = x26 * boys(7, x16)
x42 = x15 * x3
x43 = (
x38 * x4
- x39 * (x32 + x37)
- x42
* (
x36 * x4
+ x40
- x42 * (2.0 * x1 * x19 * x23 * x28 * x29 * x34 * x4 - x3 * x41)
)
)
x44 = x3 * x43
x45 = x38 * x5
x46 = 3.0 * x45
x47 = x0 * x14
x48 = x3 * x47
x49 = x3 * x38
x50 = x33 * x5
x51 = 2.0 * x50
x52 = x49 + x51
x53 = x47 * x5
x54 = 3.0 * x53
x55 = x3 * x33
x56 = x28 * x30 * x39
x57 = x25 * x29 * x56
x58 = x55 + x57
x59 = x39 * x47
x60 = x48 * x52 + x58 * x59
x61 = x24 * x56
x62 = x18 * x61
x63 = x3 * x62 + x48 * x58
x64 = x48 * x60 + x59 * x63
x65 = x0 * x13 ** (-2.5) * x61
x66 = x48 * x64 + x59 * (x48 * x63 + x6 * x65)
x67 = x20 * x47
x68 = da * db * dc
x69 = 0.009523809523809524 * x68
x70 = 5.916079783099616 * x69
x71 = x47 * x8
x72 = x71 * (x49 + x51)
x73 = x62 * x8
x74 = x55 * x71 + x73
x75 = x48 * x72 + x59 * x74
x76 = x3 * x65
x77 = x48 * x75 + x59 * (x48 * x74 + x76 * x8)
x78 = 0.06666666666666667 * x68
x79 = 2.23606797749979 * x78
x80 = x11 * x47
x81 = x80 * (x49 + x51)
x82 = x11 * x62
x83 = x55 * x80 + x82
x84 = x48 * x81 + x59 * x83
x85 = x48 * x84 + x59 * (x11 * x76 + x48 * x83)
x86 = x0**2 / x13**2
x87 = x86 * x9
x88 = x87 * (x49 + x51)
x89 = x65 * x9
x90 = x48 * x88 + x59 * (x55 * x87 + x89)
x91 = 1.732050807568877
x92 = 0.1111111111111111 * x68 * x91
x93 = x8 * x86
x94 = x11 * x93
x95 = x94 * (x49 + x51)
x96 = x11 * x65 * x8
x97 = x48 * x95 + x59 * (x55 * x94 + x96)
x98 = 0.3333333333333333 * x68
x99 = x12 * x86
x100 = x99 * (x49 + x51)
x101 = x12 * x65
x102 = x100 * x48 + x59 * (x101 + x55 * x99)
x103 = x8**3
x104 = x0**3 / x13**3
x105 = x103 * x104
x106 = x105 * (x49 + x51)
x107 = x104 * x9
x108 = x107 * x11
x109 = x108 * (x49 + x51)
x110 = x104 * x8
x111 = x110 * x12
x112 = x111 * (x49 + x51)
x113 = x11**3
x114 = x104 * x113
x115 = x114 * (x49 + x51)
x116 = x8**4
x117 = x0**4 / x13**4
x118 = x117 * x43
x119 = x116 * x117
x120 = x20 * x38
x121 = x103 * x117
x122 = x11 * x121
x123 = x12 * x9
x124 = x117 * x120
x125 = x113 * x8
x126 = x11**4
x127 = x117 * x126
x128 = -x7 - A[1]
x129 = 2.0 * x1 * x128 * x17 * x19 * x23 * x28 * x29 - x35 * x8
x130 = x129 * x15
x131 = -2.0 * x1 * x128 * x19 * x23 * x28 * x29 * x30 + x27 * x8
x132 = -x5 * (x130 + x131)
x133 = -x131
x134 = -x130 * x3 + x133 * x4
x135 = 2.0 * x1 * x128 * x19 * x23 * x28 * x29 * x34 - x41 * x8
x136 = x132 + x134 * x4 - x42 * (x129 * x4 - x135 * x42)
x137 = x136 * x3
x138 = x134 * x5
x139 = 2.0 * x138
x140 = x133 * x5
x141 = x134 * x3
x142 = x140 + x141
x143 = x48 * (x140 + x142)
x144 = x6 * x86
x145 = x140 * x144 + x143 * x48
x146 = x47 * (
x145 * x59 + x48 * (x143 * x59 + x48 * (x142 * x59 + x48 * (x137 + x139)))
)
x147 = x21 * x47
x148 = x136 * x8
x149 = x148 + x45
x150 = x134 * x8
x151 = x150 + x50
x152 = x151 * x59
x153 = x133 * x8
x154 = x153 + x57
x155 = x154 * x47
x156 = x151 * x48 + x155 * x5
x157 = x3 * x86
x158 = x157 * x5
x159 = x154 * x158 + x156 * x48
x160 = x47 * (x159 * x59 + x48 * (x156 * x59 + x48 * (x149 * x48 + x152)))
x161 = x139 * x80
x162 = x140 * x80
x163 = x141 * x80 + x162
x164 = x11 * x140
x165 = x157 * x164 + x163 * x48
x166 = x47 * (x165 * x59 + x48 * (x163 * x59 + x48 * (x137 * x80 + x161)))
x167 = x71 * (x149 + x45)
x168 = x71 * (x151 + x50)
x169 = x168 * x59
x170 = x155 * x8 + x73
x171 = x168 * x48 + x170 * x53
x172 = x47 * (x171 * x59 + x48 * (x167 * x48 + x169))
x173 = x45 * x80
x174 = x148 * x80 + x173
x175 = x50 * x80
x176 = x150 * x80 + x175
x177 = x176 * x59
x178 = x153 * x80 + x82
x179 = x176 * x48 + x178 * x53
x180 = x47 * (x179 * x59 + x48 * (x174 * x48 + x177))
x181 = x139 * x99
x182 = x140 * x99
x183 = x141 * x99 + x182
x184 = x47 * (x183 * x59 + x48 * (x137 * x99 + x181))
x185 = x167 * x71 + x45 * x87
x186 = x168 * x71 + x50 * x87
x187 = x186 * x59
x188 = x47 * (x185 * x48 + x187)
x189 = x174 * x71 + x45 * x94
x190 = x176 * x71 + x50 * x94
x191 = x190 * x59
x192 = x47 * (x189 * x48 + x191)
x193 = x45 * x99
x194 = x148 * x99 + x193
x195 = x50 * x99
x196 = x150 * x99 + x195
x197 = x196 * x59
x198 = x47 * (x194 * x48 + x197)
x199 = x114 * x139
x200 = x47 * (x114 * x137 + x199)
x201 = x47 * (x105 * x45 + x185 * x71)
x202 = x21 * x38
x203 = x47 * (x108 * x45 + x189 * x71)
x204 = x47 * (x111 * x45 + x194 * x71)
x205 = x117 * x202
x206 = x114 * x45
x207 = x47 * (x114 * x148 + x206)
x208 = x127 * x136
x209 = -x10 - A[2]
x210 = 2.0 * x1 * x17 * x19 * x209 * x23 * x28 * x29 - x11 * x35
x211 = x15 * x210
x212 = -2.0 * x1 * x19 * x209 * x23 * x28 * x29 * x30 + x11 * x27
x213 = -x5 * (x211 + x212)
x214 = -x212
x215 = -x211 * x3 + x214 * x4
x216 = 2.0 * x1 * x19 * x209 * x23 * x28 * x29 * x34 - x11 * x41
x217 = x213 + x215 * x4 - x42 * (x210 * x4 - x216 * x42)
x218 = x217 * x3
x219 = x215 * x5
x220 = 2.0 * x219
x221 = x214 * x5
x222 = x215 * x3
x223 = x221 + x222
x224 = x48 * (x221 + x223)
x225 = x144 * x221 + x224 * x48
x226 = x47 * (
x225 * x59 + x48 * (x224 * x59 + x48 * (x223 * x59 + x48 * (x218 + x220)))
)
x227 = x22 * x47
x228 = x221 * x71
x229 = x222 * x71 + x228
x230 = x3 * x93
x231 = x221 * x230 + x229 * x48
x232 = x47 * (x231 * x59 + x48 * (x229 * x59 + x48 * x71 * (x218 + x220)))
x233 = x11 * x217 + x45
x234 = x11 * x215 + x50
x235 = x234 * x59
x236 = x11 * x214 + x57
x237 = x236 * x53
x238 = x234 * x48 + x237
x239 = x158 * x236 + x238 * x48
x240 = x47 * (x239 * x59 + x48 * (x238 * x59 + x48 * (x233 * x48 + x235)))
x241 = x221 * x87
x242 = x222 * x87 + x241
x243 = x47 * (x242 * x59 + x48 * x87 * (x218 + x220))
x244 = x234 * x39
x245 = x5 * x93
x246 = x236 * x245
x247 = x230 * x234 + x246
x248 = x47 * (x247 * x59 + x48 * (x230 * x233 + x244 * x93))
x249 = x173 + x233 * x80
x250 = x175 + x234 * x80
x251 = x250 * x59
x252 = x236 * x80 + x82
x253 = x252 * x53
x254 = x250 * x48 + x253
x255 = x47 * (x254 * x59 + x48 * (x249 * x48 + x251))
x256 = x105 * x47 * (x218 + x220)
x257 = x107 * x3
x258 = x47 * (x107 * x244 + x233 * x257)
x259 = x47 * (x230 * x249 + x250 * x39 * x93)
x260 = x193 + x249 * x80
x261 = x195 + x250 * x80
x262 = x261 * x59
x263 = x47 * (x260 * x48 + x262)
x264 = x119 * x217
x265 = x22 * x38
x266 = x121 * x233
x267 = x107 * x249
x268 = x117 * x265
x269 = x260 * x93
x270 = x47 * (x206 + x260 * x80)
x271 = x3**3
x272 = x104 * x271
x273 = x140 * x272 + x145 * x48
x274 = 10.2469507659596 * x69
x275 = x104 * x6
x276 = x275 * x5
x277 = x154 * x276 + x159 * x48
x278 = 3.872983346207417 * x78
x279 = x164 * x275 + x165 * x48
x280 = x158 * x170 + x171 * x48
x281 = x158 * x178 + x179 * x48
x282 = x91 * x98
x283 = x104 * x12 * x3
x284 = x140 * x283 + x183 * x48
x285 = x170 * x71 + x89
x286 = x186 * x48 + x285 * x53
x287 = x178 * x71 + x96
x288 = x190 * x48 + x287 * x53
x289 = x101 + x153 * x99
x290 = x196 * x48 + x289 * x53
x291 = x114 * x140
x292 = x114 * x141 + x291
x293 = x105 * x50 + x186 * x71
x294 = x108 * x50 + x190 * x71
x295 = x111 * x50 + x196 * x71
x296 = x114 * x50
x297 = x114 * x150 + x296
x298 = x127 * x134
x299 = x128 * x133 - x130 * x8 + x31
x300 = x299 * x5
x301 = x15 * x8
x302 = x128 * x129 - x135 * x301 + x40
x303 = x299 * x4 - x302 * x42
x304 = x3 * x303
x305 = x47 * (x272 * x300 + x48 * (x144 * x300 + x48**2 * (2.0 * x300 + x304)))
x306 = x299 * x8
x307 = 2.0 * x140
x308 = x306 + x307
x309 = x308 * x53
x310 = x303 * x8
x311 = x139 + x310
x312 = x47 * (x276 * x308 + x48 * (x158 * x308 + x48 * (x309 + x311 * x48)))
x313 = x300 * x80
x314 = x11 * x300
x315 = x47 * (x275 * x314 + x48 * (x157 * x314 + x48 * (x304 * x80 + x313)))
x316 = x155 * x39 + x308 * x71
x317 = x316 * x53
x318 = x152 + x311 * x71
x319 = x47 * (x158 * x316 + x48 * (x317 + x318 * x48))
x320 = x80 * (x306 + x307)
x321 = x320 * x53
x322 = x161 + x310 * x80
x323 = x47 * (x158 * x320 + x48 * (x321 + x322 * x48))
x324 = x300 * x99
x325 = x47 * (x283 * x300 + x48 * (x304 * x99 + x324))
x326 = x170 * x59 + x316 * x71
x327 = x326 * x53
x328 = x169 + x318 * x71
x329 = x47 * (x327 + x328 * x48)
x330 = x178 * x59 + x320 * x71
x331 = x330 * x53
x332 = x177 + x322 * x71
x333 = x47 * (x331 + x332 * x48)
x334 = x99 * (x306 + x307)
x335 = x334 * x53
x336 = x181 + x310 * x99
x337 = x47 * (x335 + x336 * x48)
x338 = x114 * x300
x339 = x47 * (x114 * x304 + x338)
x340 = x47 * (x187 + x328 * x71)
x341 = x47 * (x191 + x332 * x71)
x342 = x47 * (x197 + x336 * x71)
x343 = x47 * (x114 * x310 + x199)
x344 = x127 * x303
x345 = x128 * x214 - x211 * x8
x346 = x345 * x5
x347 = x128 * x210 - x216 * x301
x348 = x345 * x4 - x347 * x42
x349 = x47 * (x272 * x346 + x48 * (x144 * x346 + x48**2 * (x3 * x348 + 2.0 * x346)))
x350 = x221 + x345 * x8
x351 = x219 + x348 * x8
x352 = x47 * (x276 * x350 + x48 * (x158 * x350 + x48 * (x350 * x53 + x351 * x48)))
x353 = x11 * x345 + x140
x354 = x11 * x348 + x138
x355 = x47 * (x276 * x353 + x48 * (x158 * x353 + x48 * (x353 * x53 + x354 * x48)))
x356 = x228 + x350 * x71
x357 = x71 * (x219 + x351)
x358 = x47 * (x158 * x356 + x48 * (x356 * x53 + x357 * x48))
x359 = x237 + x353 * x71
x360 = x234 * x53 + x354 * x71
x361 = x47 * (x158 * x359 + x48 * (x359 * x53 + x360 * x48))
x362 = x162 + x353 * x80
x363 = x80 * (x138 + x354)
x364 = x47 * (x158 * x362 + x48 * (x362 * x53 + x363 * x48))
x365 = x241 + x356 * x71
x366 = x219 * x87 + x357 * x71
x367 = x47 * (x365 * x53 + x366 * x48)
x368 = x246 + x359 * x71
x369 = x234 * x245 + x360 * x71
x370 = x47 * (x368 * x53 + x369 * x48)
x371 = x253 + x362 * x71
x372 = x250 * x53 + x363 * x71
x373 = x47 * (x371 * x53 + x372 * x48)
x374 = x182 + x362 * x80
x375 = x138 * x99 + x363 * x80
x376 = x47 * (x374 * x53 + x375 * x48)
x377 = x47 * (x105 * x219 + x366 * x71)
x378 = x107 * x5
x379 = x47 * (x234 * x378 + x369 * x71)
x380 = x47 * (x245 * x250 + x372 * x71)
x381 = x47 * (x261 * x53 + x375 * x71)
x382 = x47 * (x114 * x138 + x375 * x80)
x383 = x221 * x272 + x225 * x48
x384 = x275 * x8
x385 = x221 * x384 + x231 * x48
x386 = x236 * x276 + x239 * x48
x387 = x221 * x257 + x242 * x48
x388 = x110 * x3
x389 = x388 * x5
x390 = x236 * x389 + x247 * x48
x391 = x158 * x252 + x254 * x48
x392 = x105 * x221
x393 = x105 * x222 + x392
x394 = x236 * x378
x395 = x234 * x257 + x394
x396 = x245 * x252
x397 = x230 * x250 + x396
x398 = x101 + x252 * x80
x399 = x398 * x53
x400 = x261 * x48 + x399
x401 = x119 * x215
x402 = x121 * x234
x403 = x107 * x250
x404 = x261 * x93
x405 = x261 * x80 + x296
x406 = -x11 * x211 + x209 * x214 + x31
x407 = x406 * x5
x408 = x11 * x15
x409 = x209 * x210 - x216 * x408 + x40
x410 = x4 * x406 - x409 * x42
x411 = x3 * x410
x412 = x47 * (x272 * x407 + x48 * (x144 * x407 + x48**2 * (2.0 * x407 + x411)))
x413 = x407 * x71
x414 = x47 * (x384 * x407 + x48 * (x230 * x407 + x48 * (x411 * x71 + x413)))
x415 = x11 * x406 + 2.0 * x221
x416 = x415 * x53
x417 = x11 * x410 + x220
x418 = x47 * (x276 * x415 + x48 * (x158 * x415 + x48 * (x416 + x417 * x48)))
x419 = x407 * x87
x420 = x47 * (x257 * x407 + x48 * (x411 * x87 + x419))
x421 = x245 * x415
x422 = x47 * (x389 * x415 + x48 * (x230 * x417 + x421))
x423 = x236 * x59 + x415 * x80
x424 = x423 * x53
x425 = x235 + x417 * x80
x426 = x47 * (x158 * x423 + x48 * (x424 + x425 * x48))
x427 = x105 * x407
x428 = x47 * (x105 * x411 + x427)
x429 = x378 * x415
x430 = x47 * (x257 * x417 + x429)
x431 = x245 * x423
x432 = x47 * (x230 * x425 + x431)
x433 = x252 * x59 + x423 * x80
x434 = x433 * x53
x435 = x251 + x425 * x80
x436 = x47 * (x434 + x435 * x48)
x437 = x119 * x410
x438 = x121 * x417
x439 = x107 * x425
x440 = x435 * x93
x441 = x47 * (x262 + x435 * x80)
x442 = x117 * x3**4
x443 = x20 * x299
x444 = x117 * x271
x445 = x308 * x444
x446 = x11 * x444
x447 = x20 * x275
x448 = x12 * x6
x449 = x117 * x443
x450 = x157 * x20
x451 = x113 * x3
x452 = x285 * x59 + x326 * x71
x453 = x287 * x59 + x330 * x71
x454 = x289 * x59 + x334 * x71
x455 = x114 * (x306 + x307)
x456 = x128 * x299 + 2.0 * x132 - x301 * x302
x457 = x21 * x299
x458 = x456 * x8
x459 = 3.0 * x300
x460 = x458 + x459
x461 = 3.0 * x309 + x460 * x71
x462 = x21 * x275
x463 = x80 * (x458 + x459)
x464 = x117 * x456
x465 = x117 * x457
x466 = 3.0 * x317 + x461 * x71
x467 = x157 * x21
x468 = 3.0 * x321 + x463 * x71
x469 = x99 * (x458 + x459)
x470 = x128 * x345 + x213 - x301 * x347
x471 = x442 * x470
x472 = x22 * x299
x473 = 2.0 * x346
x474 = x470 * x8 + x473
x475 = x444 * x474
x476 = x11 * x470 + x300
x477 = x444 * x476
x478 = x350 * x59 + x474 * x71
x479 = x275 * x478
x480 = x22 * x275
x481 = x353 * x59
x482 = x476 * x71 + x481
x483 = x275 * x482
x484 = x313 + x476 * x80
x485 = x275 * x484
x486 = x117 * x472
x487 = x356 * x59 + x478 * x71
x488 = x157 * x487
x489 = x157 * x22
x490 = x359 * x59 + x482 * x71
x491 = x157 * x490
x492 = x362 * x59
x493 = x484 * x71 + x492
x494 = x157 * x493
x495 = x324 + x484 * x80
x496 = x157 * x495
x497 = x47 * (x365 * x59 + x487 * x71)
x498 = x47 * (x368 * x59 + x490 * x71)
x499 = x47 * (x371 * x59 + x493 * x71)
x500 = x374 * x59
x501 = x47 * (x495 * x71 + x500)
x502 = x47 * (x338 + x495 * x80)
x503 = x345 * x442
x504 = x20 * x444
x505 = x365 * x71 + x392
x506 = x368 * x71 + x394
x507 = x371 * x71 + x396
x508 = x374 * x71 + x399
x509 = x291 + x374 * x80
x510 = x21 * x444
x511 = x128 * x406 - x301 * x409
x512 = x442 * x511
x513 = x407 + x511 * x8
x514 = x444 * x513
x515 = x22 * x444
x516 = x11 * x511 + x473
x517 = x444 * x516
x518 = x413 + x513 * x71
x519 = x275 * x518
x520 = x416 + x516 * x71
x521 = x275 * x520
x522 = x481 + x516 * x80
x523 = x275 * x522
x524 = x419 + x518 * x71
x525 = x157 * x524
x526 = x421 + x520 * x71
x527 = x157 * x526
x528 = x424 + x522 * x71
x529 = x157 * x528
x530 = x492 + x522 * x80
x531 = x157 * x530
x532 = x47 * (x427 + x524 * x71)
x533 = x47 * (x429 + x526 * x71)
x534 = x47 * (x431 + x528 * x71)
x535 = x47 * (x434 + x530 * x71)
x536 = x47 * (x500 + x530 * x80)
x537 = x20 * x406
x538 = x406 * x8
x539 = x117 * x6
x540 = x539 * x9
x541 = x539 * x8
x542 = x20 * x415
x543 = x121 * x3
x544 = x117 * x3 * x9
x545 = x388 * x423
x546 = x121 * x415
x547 = x107 * x423
x548 = x433 * x93
x549 = x398 * x59 + x433 * x80
x550 = x21 * x406
x551 = x21 * x415
x552 = x209 * x406 + 2.0 * x213 - x408 * x409
x553 = x22 * x406
x554 = x11 * x552 + 3.0 * x407
x555 = x22 * x415
x556 = 3.0 * x416 + x554 * x80
x557 = 3.0 * x424 + x556 * x80
# 270 item(s)
result[0, 0, 0] = numpy.sum(
x70
* (
x47 * (x48 * (x48 * (x48 * (x44 + x46) + x52 * x54) + x54 * x60) + x54 * x64)
+ x66 * x67
)
)
result[0, 0, 1] = numpy.sum(
x79
* (x47 * (x48 * (x48 * x71 * (x44 + x46) + x54 * x72) + x54 * x75) + x67 * x77)
)
result[0, 0, 2] = numpy.sum(
x79
* (x47 * (x48 * (x48 * x80 * (x44 + x46) + x54 * x81) + x54 * x84) + x67 * x85)
)
result[0, 0, 3] = numpy.sum(
x92 * (x47 * (x48 * x87 * (x44 + x46) + x54 * x88) + x67 * x90)
)
result[0, 0, 4] = numpy.sum(
x98 * (x47 * (x48 * x94 * (x44 + x46) + x54 * x95) + x67 * x97)
)
result[0, 0, 5] = numpy.sum(
x92 * (x102 * x67 + x47 * (x100 * x54 + x48 * x99 * (x44 + x46)))
)
result[0, 0, 6] = numpy.sum(x79 * (x105 * x47 * (x44 + x46) + x106 * x67))
result[0, 0, 7] = numpy.sum(x98 * (x108 * x47 * (x44 + x46) + x109 * x67))
result[0, 0, 8] = numpy.sum(x98 * (x111 * x47 * (x44 + x46) + x112 * x67))
result[0, 0, 9] = numpy.sum(x79 * (x114 * x47 * (x44 + x46) + x115 * x67))
result[0, 0, 10] = numpy.sum(x70 * (x116 * x118 + x119 * x120))
result[0, 0, 11] = numpy.sum(x79 * (x103 * x11 * x118 + x120 * x122))
result[0, 0, 12] = numpy.sum(x123 * x92 * (x118 + x124))
result[0, 0, 13] = numpy.sum(x125 * x79 * (x118 + x124))
result[0, 0, 14] = numpy.sum(x70 * (x118 * x126 + x120 * x127))
result[0, 1, 0] = numpy.sum(x70 * (x146 + x147 * x66))
result[0, 1, 1] = numpy.sum(x79 * (x147 * x77 + x160))
result[0, 1, 2] = numpy.sum(x79 * (x147 * x85 + x166))
result[0, 1, 3] = numpy.sum(x92 * (x147 * x90 + x172))
result[0, 1, 4] = numpy.sum(x98 * (x147 * x97 + x180))
result[0, 1, 5] = numpy.sum(x92 * (x102 * x147 + x184))
result[0, 1, 6] = numpy.sum(x79 * (x106 * x147 + x188))
result[0, 1, 7] = numpy.sum(x98 * (x109 * x147 + x192))
result[0, 1, 8] = numpy.sum(x98 * (x112 * x147 + x198))
result[0, 1, 9] = numpy.sum(x79 * (x115 * x147 + x200))
result[0, 1, 10] = numpy.sum(x70 * (x119 * x202 + x201))
result[0, 1, 11] = numpy.sum(x79 * (x122 * x202 + x203))
result[0, 1, 12] = numpy.sum(x92 * (x123 * x205 + x204))
result[0, 1, 13] = numpy.sum(x79 * (x125 * x205 + x207))
result[0, 1, 14] = numpy.sum(x70 * (x127 * x202 + x208))
result[0, 2, 0] = numpy.sum(x70 * (x226 + x227 * x66))
result[0, 2, 1] = numpy.sum(x79 * (x227 * x77 + x232))
result[0, 2, 2] = numpy.sum(x79 * (x227 * x85 + x240))
result[0, 2, 3] = numpy.sum(x92 * (x227 * x90 + x243))
result[0, 2, 4] = numpy.sum(x98 * (x227 * x97 + x248))
result[0, 2, 5] = numpy.sum(x92 * (x102 * x227 + x255))
result[0, 2, 6] = numpy.sum(x79 * (x106 * x227 + x256))
result[0, 2, 7] = numpy.sum(x98 * (x109 * x227 + x258))
result[0, 2, 8] = numpy.sum(x98 * (x112 * x227 + x259))
result[0, 2, 9] = numpy.sum(x79 * (x115 * x227 + x263))
result[0, 2, 10] = numpy.sum(x70 * (x119 * x265 + x264))
result[0, 2, 11] = numpy.sum(x79 * (x122 * x265 + x266))
result[0, 2, 12] = numpy.sum(x92 * (x123 * x268 + x267))
result[0, 2, 13] = numpy.sum(x79 * (x125 * x268 + x269))
result[0, 2, 14] = numpy.sum(x70 * (x127 * x265 + x270))
result[1, 0, 0] = numpy.sum(x274 * (x146 + x273 * x67))
result[1, 0, 1] = numpy.sum(x278 * (x160 + x277 * x67))
result[1, 0, 2] = numpy.sum(x278 * (x166 + x279 * x67))
result[1, 0, 3] = numpy.sum(x98 * (x172 + x280 * x67))
result[1, 0, 4] = numpy.sum(x282 * (x180 + x281 * x67))
result[1, 0, 5] = numpy.sum(x98 * (x184 + x284 * x67))
result[1, 0, 6] = numpy.sum(x278 * (x188 + x286 * x67))
result[1, 0, 7] = numpy.sum(x282 * (x192 + x288 * x67))
result[1, 0, 8] = numpy.sum(x282 * (x198 + x290 * x67))
result[1, 0, 9] = numpy.sum(x278 * (x200 + x292 * x67))
result[1, 0, 10] = numpy.sum(x274 * (x201 + x293 * x67))
result[1, 0, 11] = numpy.sum(x278 * (x203 + x294 * x67))
result[1, 0, 12] = numpy.sum(x98 * (x204 + x295 * x67))
result[1, 0, 13] = numpy.sum(x278 * (x207 + x297 * x67))
result[1, 0, 14] = numpy.sum(x274 * (x20 * x298 + x208))
result[1, 1, 0] = numpy.sum(x274 * (x147 * x273 + x305))
result[1, 1, 1] = numpy.sum(x278 * (x147 * x277 + x312))
result[1, 1, 2] = numpy.sum(x278 * (x147 * x279 + x315))
result[1, 1, 3] = numpy.sum(x98 * (x147 * x280 + x319))
result[1, 1, 4] = numpy.sum(x282 * (x147 * x281 + x323))
result[1, 1, 5] = numpy.sum(x98 * (x147 * x284 + x325))
result[1, 1, 6] = numpy.sum(x278 * (x147 * x286 + x329))
result[1, 1, 7] = numpy.sum(x282 * (x147 * x288 + x333))
result[1, 1, 8] = numpy.sum(x282 * (x147 * x290 + x337))
result[1, 1, 9] = numpy.sum(x278 * (x147 * x292 + x339))
result[1, 1, 10] = numpy.sum(x274 * (x147 * x293 + x340))
result[1, 1, 11] = numpy.sum(x278 * (x147 * x294 + x341))
result[1, 1, 12] = numpy.sum(x98 * (x147 * x295 + x342))
result[1, 1, 13] = numpy.sum(x278 * (x147 * x297 + x343))
result[1, 1, 14] = numpy.sum(x274 * (x21 * x298 + x344))
result[1, 2, 0] = numpy.sum(x274 * (x227 * x273 + x349))
result[1, 2, 1] = numpy.sum(x278 * (x227 * x277 + x352))
result[1, 2, 2] = numpy.sum(x278 * (x227 * x279 + x355))
result[1, 2, 3] = numpy.sum(x98 * (x227 * x280 + x358))
result[1, 2, 4] = numpy.sum(x282 * (x227 * x281 + x361))
result[1, 2, 5] = numpy.sum(x98 * (x227 * x284 + x364))
result[1, 2, 6] = numpy.sum(x278 * (x227 * x286 + x367))
result[1, 2, 7] = numpy.sum(x282 * (x227 * x288 + x370))
result[1, 2, 8] = numpy.sum(x282 * (x227 * x290 + x373))
result[1, 2, 9] = numpy.sum(x278 * (x227 * x292 + x376))
result[1, 2, 10] = numpy.sum(x274 * (x227 * x293 + x377))
result[1, 2, 11] = numpy.sum(x278 * (x227 * x294 + x379))
result[1, 2, 12] = numpy.sum(x98 * (x227 * x295 + x380))
result[1, 2, 13] = numpy.sum(x278 * (x227 * x297 + x381))
result[1, 2, 14] = numpy.sum(x274 * (x22 * x298 + x382))
result[2, 0, 0] = numpy.sum(x274 * (x226 + x383 * x67))
result[2, 0, 1] = numpy.sum(x278 * (x232 + x385 * x67))
result[2, 0, 2] = numpy.sum(x278 * (x240 + x386 * x67))
result[2, 0, 3] = numpy.sum(x98 * (x243 + x387 * x67))
result[2, 0, 4] = numpy.sum(x282 * (x248 + x390 * x67))
result[2, 0, 5] = numpy.sum(x98 * (x255 + x391 * x67))
result[2, 0, 6] = numpy.sum(x278 * (x256 + x393 * x67))
result[2, 0, 7] = numpy.sum(x282 * (x258 + x395 * x67))
result[2, 0, 8] = numpy.sum(x282 * (x259 + x397 * x67))
result[2, 0, 9] = numpy.sum(x278 * (x263 + x400 * x67))
result[2, 0, 10] = numpy.sum(x274 * (x20 * x401 + x264))
result[2, 0, 11] = numpy.sum(x278 * (x20 * x402 + x266))
result[2, 0, 12] = numpy.sum(x98 * (x20 * x403 + x267))
result[2, 0, 13] = numpy.sum(x278 * (x20 * x404 + x269))
result[2, 0, 14] = numpy.sum(x274 * (x270 + x405 * x67))
result[2, 1, 0] = numpy.sum(x274 * (x147 * x383 + x349))
result[2, 1, 1] = numpy.sum(x278 * (x147 * x385 + x352))
result[2, 1, 2] = numpy.sum(x278 * (x147 * x386 + x355))
result[2, 1, 3] = numpy.sum(x98 * (x147 * x387 + x358))
result[2, 1, 4] = numpy.sum(x282 * (x147 * x390 + x361))
result[2, 1, 5] = numpy.sum(x98 * (x147 * x391 + x364))
result[2, 1, 6] = numpy.sum(x278 * (x147 * x393 + x367))
result[2, 1, 7] = numpy.sum(x282 * (x147 * x395 + x370))
result[2, 1, 8] = numpy.sum(x282 * (x147 * x397 + x373))
result[2, 1, 9] = numpy.sum(x278 * (x147 * x400 + x376))
result[2, 1, 10] = numpy.sum(x274 * (x21 * x401 + x377))
result[2, 1, 11] = numpy.sum(x278 * (x21 * x402 + x379))
result[2, 1, 12] = numpy.sum(x98 * (x21 * x403 + x380))
result[2, 1, 13] = numpy.sum(x278 * (x21 * x404 + x381))
result[2, 1, 14] = numpy.sum(x274 * (x147 * x405 + x382))
result[2, 2, 0] = numpy.sum(x274 * (x227 * x383 + x412))
result[2, 2, 1] = numpy.sum(x278 * (x227 * x385 + x414))
result[2, 2, 2] = numpy.sum(x278 * (x227 * x386 + x418))
result[2, 2, 3] = numpy.sum(x98 * (x227 * x387 + x420))
result[2, 2, 4] = numpy.sum(x282 * (x227 * x390 + x422))
result[2, 2, 5] = numpy.sum(x98 * (x227 * x391 + x426))
result[2, 2, 6] = numpy.sum(x278 * (x227 * x393 + x428))
result[2, 2, 7] = numpy.sum(x282 * (x227 * x395 + x430))
result[2, 2, 8] = numpy.sum(x282 * (x227 * x397 + x432))
result[2, 2, 9] = numpy.sum(x278 * (x227 * x400 + x436))
result[2, 2, 10] = numpy.sum(x274 * (x22 * x401 + x437))
result[2, 2, 11] = numpy.sum(x278 * (x22 * x402 + x438))
result[2, 2, 12] = numpy.sum(x98 * (x22 * x403 + x439))
result[2, 2, 13] = numpy.sum(x278 * (x22 * x404 + x440))
result[2, 2, 14] = numpy.sum(x274 * (x227 * x405 + x441))
result[3, 0, 0] = numpy.sum(x70 * (x305 + x442 * x443))
result[3, 0, 1] = numpy.sum(x79 * (x20 * x445 + x312))
result[3, 0, 2] = numpy.sum(x79 * (x315 + x443 * x446))
result[3, 0, 3] = numpy.sum(x92 * (x316 * x447 + x319))
result[3, 0, 4] = numpy.sum(x98 * (x320 * x447 + x323))
result[3, 0, 5] = numpy.sum(x92 * (x325 + x448 * x449))
result[3, 0, 6] = numpy.sum(x79 * (x326 * x450 + x329))
result[3, 0, 7] = numpy.sum(x98 * (x330 * x450 + x333))
result[3, 0, 8] = numpy.sum(x98 * (x334 * x450 + x337))
result[3, 0, 9] = numpy.sum(x79 * (x339 + x449 * x451))
result[3, 0, 10] = numpy.sum(x70 * (x340 + x452 * x67))
result[3, 0, 11] = numpy.sum(x79 * (x341 + x453 * x67))
result[3, 0, 12] = numpy.sum(x92 * (x342 + x454 * x67))
result[3, 0, 13] = numpy.sum(x79 * (x343 + x455 * x67))
result[3, 0, 14] = numpy.sum(x70 * (x127 * x443 + x344))
result[3, 1, 0] = numpy.sum(x442 * x70 * (x456 + x457))
result[3, 1, 1] = numpy.sum(x79 * (x21 * x445 + x444 * x460))
result[3, 1, 2] = numpy.sum(x446 * x79 * (x456 + x457))
result[3, 1, 3] = numpy.sum(x92 * (x275 * x461 + x316 * x462))
result[3, 1, 4] = numpy.sum(x98 * (x275 * x463 + x320 * x462))
result[3, 1, 5] = numpy.sum(x448 * x92 * (x464 + x465))
result[3, 1, 6] = numpy.sum(x79 * (x157 * x466 + x326 * x467))
result[3, 1, 7] = numpy.sum(x98 * (x157 * x468 + x330 * x467))
result[3, 1, 8] = numpy.sum(x98 * (x157 * x469 + x334 * x467))
result[3, 1, 9] = numpy.sum(x451 * x79 * (x464 + x465))
result[3, 1, 10] = numpy.sum(x70 * (x147 * x452 + x47 * (3.0 * x327 + x466 * x71)))
result[3, 1, 11] = numpy.sum(x79 * (x147 * x453 + x47 * (3.0 * x331 + x468 * x71)))
result[3, 1, 12] = numpy.sum(x92 * (x147 * x454 + x47 * (3.0 * x335 + x469 * x71)))
result[3, 1, 13] = numpy.sum(x79 * (x114 * x47 * (x458 + x459) + x147 * x455))
result[3, 1, 14] = numpy.sum(x127 * x70 * (x456 + x457))
result[3, 2, 0] = numpy.sum(x70 * (x442 * x472 + x471))
result[3, 2, 1] = numpy.sum(x79 * (x22 * x445 + x475))
result[3, 2, 2] = numpy.sum(x79 * (x446 * x472 + x477))
result[3, 2, 3] = numpy.sum(x92 * (x316 * x480 + x479))
result[3, 2, 4] = numpy.sum(x98 * (x320 * x480 + x483))
result[3, 2, 5] = numpy.sum(x92 * (x448 * x486 + x485))
result[3, 2, 6] = numpy.sum(x79 * (x326 * x489 + x488))
result[3, 2, 7] = numpy.sum(x98 * (x330 * x489 + x491))
result[3, 2, 8] = numpy.sum(x98 * (x334 * x489 + x494))
result[3, 2, 9] = numpy.sum(x79 * (x451 * x486 + x496))
result[3, 2, 10] = numpy.sum(x70 * (x227 * x452 + x497))
result[3, 2, 11] = numpy.sum(x79 * (x227 * x453 + x498))
result[3,