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Computing differential numerators... | |
===================== | |
=== DIFFERENTIALS === | |
===================== | |
Singularities: | |
[((0, 0, 1), (2, 2, 1)), ((0, 1, 0), (2, 1, 2))] | |
--- LOOP --- | |
- singular point - | |
(0, 0, 1) | |
g transform: | |
x**4 - 2*x**2*y + y**2*(x**2 - x + 1) | |
P transform: | |
c_0_0 + c_0_1*y + c_1_0*x | |
- integral basis - | |
[1, y*(x**2 - x + 1)/x**2] | |
r = Poly(y*c_0_1 + x*c_1_0 + c_0_0, y, x, c_0_0, c_0_1, c_1_0, c_1_1, domain='QQ[I]') | |
denom = 1 | |
mult = 0 | |
[c_1_0, c_0_1, c_0_0] | |
[(1, 0), (0, 1), (0, 0)] | |
bi: 1 | |
conds: [] | |
r = Poly(y*x**3*c_1_0 + y*x**2*c_0_0 + 2*y*x**2*c_0_1 - y*x**2*c_1_0 - y*x*c_0_0 + y*x*c_1_0 + y*c_0_0 - x**4*c_0_1, y, x, c_0_0, c_0_1, c_1_0, c_1_1, domain='QQ[I]') | |
denom = x**2 | |
mult = 2 | |
[-c_0_1, c_1_0, c_0_0 + 2*c_0_1 - c_1_0, -c_0_0 + c_1_0, c_0_0] | |
[(4, 0), (3, 1), (2, 1), (1, 1), (0, 1)] | |
bi: y*(x**2 - x + 1)/x**2 | |
conds: [-c_0_0 + c_1_0, c_0_0] | |
- singular point - | |
(0, 1, 0) | |
g transform: | |
Poly(x**4 - 2*x**2*_z + x**2 - x*_z + _z**2, x, _z, domain='ZZ') | |
P transform: | |
Poly(c_1_0*x + c_0_0*_z + c_0_1, x, _z, domain='ZZ[c_0_0,c_0_1,c_1_0]') | |
- integral basis - | |
[1, _z/x] | |
r = Poly(_z*c_0_0 + x*c_1_0 + c_0_1, _z, x, c_0_0, c_0_1, c_1_0, c_1_1, domain='QQ[I]') | |
denom = 1 | |
mult = 0 | |
[c_1_0, c_0_0, c_0_1] | |
[(1, 0), (0, 1), (0, 0)] | |
bi: 1 | |
conds: [] | |
r = Poly(2*_z*x**2*c_0_0 + _z*x*c_0_0 + _z*x*c_1_0 + _z*c_0_1 - x**4*c_0_0 - x**2*c_0_0, _z, x, c_0_0, c_0_1, c_1_0, c_1_1, domain='QQ[I]') | |
denom = x | |
mult = 1 | |
[-c_0_0, 2*c_0_0, -c_0_0, c_0_0 + c_1_0, c_0_1] | |
[(4, 0), (2, 1), (2, 0), (1, 1), (0, 1)] | |
bi: _z/x | |
conds: [c_0_1] | |
--- END LOOP --- | |
all conds: | |
[-c_0_0 + c_1_0, c_0_0, c_0_1] | |
final P: 0 | |
NUMERATORS: | |
[] | |
...done. | |
Computing differential numerators... | |
===================== | |
=== DIFFERENTIALS === | |
===================== | |
Singularities: | |
[((0, 0, 1), (3, 4, 2)), ((0, 1, 0), (4, 9, 1))] | |
--- LOOP --- | |
- singular point - | |
(0, 0, 1) | |
g transform: | |
-x**7 + 2*x**3*y + y**3 | |
P transform: | |
c_0_0 + c_0_1*y + c_0_2*y**2 + c_0_3*y**3 + c_0_4*y**4 + c_1_0*x + c_1_1*x*y + c_1_2*x*y**2 + c_1_3*x*y**3 + c_2_0*x**2 + c_2_1*x**2*y + c_2_2*x**2*y**2 + c_3_0*x**3 + c_3_1*x**3*y + c_4_0*x**4 | |
- integral basis - | |
[1, y/x, y**2/x**3] | |
r = Poly(-2*y**2*x**3*c_0_4 + y**2*x**2*c_2_2 + y**2*x*c_1_2 + y**2*c_0_2 + y*x**7*c_0_4 - 2*y*x**4*c_1_3 - 2*y*x**3*c_0_3 + y*x**3*c_3_1 + y*x**2*c_2_1 + y*x*c_1_1 + y*c_0_1 + x**8*c_1_3 + x**7*c_0_3 + x**4*c_4_0 + x**3*c_3_0 + x**2*c_2_0 + x*c_1_0 + c_0_0, y, x, c_0_0, c_0_1, c_0_2, c_0_3, c_0_4, c_1_0, c_1_1, c_1_2, c_1_3, c_1_4, c_2_0, c_2_1, c_2_2, c_2_3, c_2_4, c_3_0, c_3_1, c_3_2, c_3_3, c_3_4, c_4_0, c_4_1, c_4_2, c_4_3, c_4_4, domain='QQ[I]') | |
denom = 1 | |
mult = 0 | |
[c_1_3, c_0_4, c_0_3, -2*c_1_3, c_4_0, -2*c_0_4, -2*c_0_3 + c_3_1, c_3_0, c_2_2, c_2_1, c_2_0, c_1_2, c_1_1, c_1_0, c_0_2, c_0_1, c_0_0] | |
[(8, 0), (7, 1), (7, 0), (4, 1), (4, 0), (3, 2), (3, 1), (3, 0), (2, 2), (2, 1), (2, 0), (1, 2), (1, 1), (1, 0), (0, 2), (0, 1), (0, 0)] | |
bi: 1 | |
conds: [] | |
r = Poly(y**2*x**7*c_0_4 - 2*y**2*x**4*c_1_3 - 2*y**2*x**3*c_0_3 + y**2*x**3*c_3_1 + y**2*x**2*c_2_1 + y**2*x*c_1_1 + y**2*c_0_1 + y*x**8*c_1_3 + y*x**7*c_0_3 + 4*y*x**6*c_0_4 - 2*y*x**5*c_2_2 - 2*y*x**4*c_1_2 + y*x**4*c_4_0 - 2*y*x**3*c_0_2 + y*x**3*c_3_0 + y*x**2*c_2_0 + y*x*c_1_0 + y*c_0_0 - 2*x**10*c_0_4 + x**9*c_2_2 + x**8*c_1_2 + x**7*c_0_2, y, x, c_0_0, c_0_1, c_0_2, c_0_3, c_0_4, c_1_0, c_1_1, c_1_2, c_1_3, c_1_4, c_2_0, c_2_1, c_2_2, c_2_3, c_2_4, c_3_0, c_3_1, c_3_2, c_3_3, c_3_4, c_4_0, c_4_1, c_4_2, c_4_3, c_4_4, domain='QQ[I]') | |
denom = x | |
mult = 1 | |
[-2*c_0_4, c_2_2, c_1_3, c_1_2, c_0_4, c_0_3, c_0_2, 4*c_0_4, -2*c_2_2, -2*c_1_3, -2*c_1_2 + c_4_0, -2*c_0_3 + c_3_1, -2*c_0_2 + c_3_0, c_2_1, c_2_0, c_1_1, c_1_0, c_0_1, c_0_0] | |
[(10, 0), (9, 0), (8, 1), (8, 0), (7, 2), (7, 1), (7, 0), (6, 1), (5, 1), (4, 2), (4, 1), (3, 2), (3, 1), (2, 2), (2, 1), (1, 2), (1, 1), (0, 2), (0, 1)] | |
bi: y/x | |
conds: [c_0_1, c_0_0] | |
r = Poly(y**2*x**8*c_1_3 + y**2*x**7*c_0_3 + 4*y**2*x**6*c_0_4 - 2*y**2*x**5*c_2_2 - 2*y**2*x**4*c_1_2 + y**2*x**4*c_4_0 - 2*y**2*x**3*c_0_2 + y**2*x**3*c_3_0 + y**2*x**2*c_2_0 + y**2*x*c_1_0 + y**2*c_0_0 - 4*y*x**10*c_0_4 + y*x**9*c_2_2 + y*x**8*c_1_2 + y*x**7*c_0_2 + 4*y*x**7*c_1_3 + 4*y*x**6*c_0_3 - 2*y*x**6*c_3_1 - 2*y*x**5*c_2_1 - 2*y*x**4*c_1_1 - 2*y*x**3*c_0_1 + x**14*c_0_4 - 2*x**11*c_1_3 - 2*x**10*c_0_3 + x**10*c_3_1 + x**9*c_2_1 + x**8*c_1_1 + x**7*c_0_1, y, x, c_0_0, c_0_1, c_0_2, c_0_3, c_0_4, c_1_0, c_1_1, c_1_2, c_1_3, c_1_4, c_2_0, c_2_1, c_2_2, c_2_3, c_2_4, c_3_0, c_3_1, c_3_2, c_3_3, c_3_4, c_4_0, c_4_1, c_4_2, c_4_3, c_4_4, domain='QQ[I]') | |
denom = x**3 | |
mult = 3 | |
[c_0_4, -2*c_1_3, -4*c_0_4, -2*c_0_3 + c_3_1, c_2_2, c_2_1, c_1_3, c_1_2, c_1_1, c_0_3, c_0_2 + 4*c_1_3, c_0_1, 4*c_0_4, 4*c_0_3 - 2*c_3_1, -2*c_2_2, -2*c_2_1, -2*c_1_2 + c_4_0, -2*c_1_1, -2*c_0_2 + c_3_0, -2*c_0_1, c_2_0, c_1_0, c_0_0] | |
[(14, 0), (11, 0), (10, 1), (10, 0), (9, 1), (9, 0), (8, 2), (8, 1), (8, 0), (7, 2), (7, 1), (7, 0), (6, 2), (6, 1), (5, 2), (5, 1), (4, 2), (4, 1), (3, 2), (3, 1), (2, 2), (1, 2), (0, 2)] | |
bi: y**2/x**3 | |
conds: [c_2_0, c_1_0, c_0_0] | |
- singular point - | |
(0, 1, 0) | |
g transform: | |
Poly(-x**7 + 2*x**3*_z**3 + _z**4, x, _z, domain='ZZ') | |
P transform: | |
Poly(c_4_0*x**4 + c_3_0*x**3*_z + c_3_1*x**3 + c_2_0*x**2*_z**2 + c_2_1*x**2*_z + c_2_2*x**2 + c_1_0*x*_z**3 + c_1_1*x*_z**2 + c_1_2*x*_z + c_1_3*x + c_0_0*_z**4 + c_0_1*_z**3 + c_0_2*_z**2 + c_0_3*_z + c_0_4, x, _z, domain='ZZ[c_0_0,c_0_1,c_0_2,c_0_3,c_0_4,c_1_0,c_1_1,c_1_2,c_1_3,c_2_0,c_2_1,c_2_2,c_3_0,c_3_1,c_4_0]') | |
- integral basis - | |
[1, _z/x, _z**2/x**3, _z**3/x**5] | |
r = Poly(-2*_z**3*x**3*c_0_0 + _z**3*x*c_1_0 + _z**3*c_0_1 + _z**2*x**2*c_2_0 + _z**2*x*c_1_1 + _z**2*c_0_2 + _z*x**3*c_3_0 + _z*x**2*c_2_1 + _z*x*c_1_2 + _z*c_0_3 + x**7*c_0_0 + x**4*c_4_0 + x**3*c_3_1 + x**2*c_2_2 + x*c_1_3 + c_0_4, _z, x, c_0_0, c_0_1, c_0_2, c_0_3, c_0_4, c_1_0, c_1_1, c_1_2, c_1_3, c_1_4, c_2_0, c_2_1, c_2_2, c_2_3, c_2_4, c_3_0, c_3_1, c_3_2, c_3_3, c_3_4, c_4_0, c_4_1, c_4_2, c_4_3, c_4_4, domain='QQ[I]') | |
denom = 1 | |
mult = 0 | |
[c_0_0, c_4_0, -2*c_0_0, c_3_0, c_3_1, c_2_0, c_2_1, c_2_2, c_1_0, c_1_1, c_1_2, c_1_3, c_0_1, c_0_2, c_0_3, c_0_4] | |
[(7, 0), (4, 0), (3, 3), (3, 1), (3, 0), (2, 2), (2, 1), (2, 0), (1, 3), (1, 2), (1, 1), (1, 0), (0, 3), (0, 2), (0, 1), (0, 0)] | |
bi: 1 | |
conds: [] | |
r = Poly(4*_z**3*x**6*c_0_0 - 2*_z**3*x**4*c_1_0 - 2*_z**3*x**3*c_0_1 + _z**3*x**2*c_2_0 + _z**3*x*c_1_1 + _z**3*c_0_2 + _z**2*x**3*c_3_0 + _z**2*x**2*c_2_1 + _z**2*x*c_1_2 + _z**2*c_0_3 + _z*x**7*c_0_0 + _z*x**4*c_4_0 + _z*x**3*c_3_1 + _z*x**2*c_2_2 + _z*x*c_1_3 + _z*c_0_4 - 2*x**10*c_0_0 + x**8*c_1_0 + x**7*c_0_1, _z, x, c_0_0, c_0_1, c_0_2, c_0_3, c_0_4, c_1_0, c_1_1, c_1_2, c_1_3, c_1_4, c_2_0, c_2_1, c_2_2, c_2_3, c_2_4, c_3_0, c_3_1, c_3_2, c_3_3, c_3_4, c_4_0, c_4_1, c_4_2, c_4_3, c_4_4, domain='QQ[I]') | |
denom = x | |
mult = 1 | |
[-2*c_0_0, c_1_0, c_0_0, c_0_1, 4*c_0_0, -2*c_1_0, c_4_0, -2*c_0_1, c_3_0, c_3_1, c_2_0, c_2_1, c_2_2, c_1_1, c_1_2, c_1_3, c_0_2, c_0_3, c_0_4] | |
[(10, 0), (8, 0), (7, 1), (7, 0), (6, 3), (4, 3), (4, 1), (3, 3), (3, 2), (3, 1), (2, 3), (2, 2), (2, 1), (1, 3), (1, 2), (1, 1), (0, 3), (0, 2), (0, 1)] | |
bi: _z/x | |
conds: [c_0_2, c_0_3, c_0_4] | |
r = Poly(-8*_z**3*x**9*c_0_0 + 4*_z**3*x**7*c_1_0 + 4*_z**3*x**6*c_0_1 - 2*_z**3*x**5*c_2_0 - 2*_z**3*x**4*c_1_1 - 2*_z**3*x**3*c_0_2 + _z**3*x**3*c_3_0 + _z**3*x**2*c_2_1 + _z**3*x*c_1_2 + _z**3*c_0_3 + _z**2*x**7*c_0_0 + _z**2*x**4*c_4_0 + _z**2*x**3*c_3_1 + _z**2*x**2*c_2_2 + _z**2*x*c_1_3 + _z**2*c_0_4 - 2*_z*x**10*c_0_0 + _z*x**8*c_1_0 + _z*x**7*c_0_1 + 4*x**13*c_0_0 - 2*x**11*c_1_0 - 2*x**10*c_0_1 + x**9*c_2_0 + x**8*c_1_1 + x**7*c_0_2, _z, x, c_0_0, c_0_1, c_0_2, c_0_3, c_0_4, c_1_0, c_1_1, c_1_2, c_1_3, c_1_4, c_2_0, c_2_1, c_2_2, c_2_3, c_2_4, c_3_0, c_3_1, c_3_2, c_3_3, c_3_4, c_4_0, c_4_1, c_4_2, c_4_3, c_4_4, domain='QQ[I]') | |
denom = x**3 | |
mult = 3 | |
[4*c_0_0, -2*c_1_0, -2*c_0_0, -2*c_0_1, -8*c_0_0, c_2_0, c_1_0, c_1_1, 4*c_1_0, c_0_0, c_0_1, c_0_2, 4*c_0_1, -2*c_2_0, -2*c_1_1, c_4_0, -2*c_0_2 + c_3_0, c_3_1, c_2_1, c_2_2, c_1_2, c_1_3, c_0_3, c_0_4] | |
[(13, 0), (11, 0), (10, 1), (10, 0), (9, 3), (9, 0), (8, 1), (8, 0), (7, 3), (7, 2), (7, 1), (7, 0), (6, 3), (5, 3), (4, 3), (4, 2), (3, 3), (3, 2), (2, 3), (2, 2), (1, 3), (1, 2), (0, 3), (0, 2)] | |
bi: _z**2/x**3 | |
conds: [c_2_1, c_2_2, c_1_2, c_1_3, c_0_3, c_0_4] | |
r = Poly(16*_z**3*x**12*c_0_0 - 8*_z**3*x**10*c_1_0 - 8*_z**3*x**9*c_0_1 + 4*_z**3*x**8*c_2_0 + _z**3*x**7*c_0_0 + 4*_z**3*x**7*c_1_1 + 4*_z**3*x**6*c_0_2 - 2*_z**3*x**6*c_3_0 - 2*_z**3*x**5*c_2_1 - 2*_z**3*x**4*c_1_2 + _z**3*x**4*c_4_0 - 2*_z**3*x**3*c_0_3 + _z**3*x**3*c_3_1 + _z**3*x**2*c_2_2 + _z**3*x*c_1_3 + _z**3*c_0_4 - 2*_z**2*x**10*c_0_0 + _z**2*x**8*c_1_0 + _z**2*x**7*c_0_1 + 4*_z*x**13*c_0_0 - 2*_z*x**11*c_1_0 - 2*_z*x**10*c_0_1 + _z*x**9*c_2_0 + _z*x**8*c_1_1 + _z*x**7*c_0_2 - 8*x**16*c_0_0 + 4*x**14*c_1_0 + 4*x**13*c_0_1 - 2*x**12*c_2_0 - 2*x**11*c_1_1 - 2*x**10*c_0_2 + x**10*c_3_0 + x**9*c_2_1 + x**8*c_1_2 + x**7*c_0_3, _z, x, c_0_0, c_0_1, c_0_2, c_0_3, c_0_4, c_1_0, c_1_1, c_1_2, c_1_3, c_1_4, c_2_0, c_2_1, c_2_2, c_2_3, c_2_4, c_3_0, c_3_1, c_3_2, c_3_3, c_3_4, c_4_0, c_4_1, c_4_2, c_4_3, c_4_4, domain='QQ[I]') | |
denom = x**5 | |
mult = 5 | |
[-8*c_0_0, 4*c_1_0, 4*c_0_0, 4*c_0_1, 16*c_0_0, -2*c_2_0, -2*c_1_0, -2*c_1_1, -8*c_1_0, -2*c_0_0, -2*c_0_1, -2*c_0_2 + c_3_0, -8*c_0_1, c_2_0, c_2_1, 4*c_2_0, c_1_0, c_1_1, c_1_2, c_0_0 + 4*c_1_1, c_0_1, c_0_2, c_0_3, 4*c_0_2 - 2*c_3_0, -2*c_2_1, -2*c_1_2 + c_4_0, -2*c_0_3 + c_3_1, c_2_2, c_1_3, c_0_4] | |
[(16, 0), (14, 0), (13, 1), (13, 0), (12, 3), (12, 0), (11, 1), (11, 0), (10, 3), (10, 2), (10, 1), (10, 0), (9, 3), (9, 1), (9, 0), (8, 3), (8, 2), (8, 1), (8, 0), (7, 3), (7, 2), (7, 1), (7, 0), (6, 3), (5, 3), (4, 3), (3, 3), (2, 3), (1, 3), (0, 3)] | |
bi: _z**3/x**5 | |
conds: [-2*c_1_2 + c_4_0, -2*c_0_3 + c_3_1, c_2_2, c_1_3, c_0_4] | |
--- END LOOP --- | |
all conds: | |
[c_0_1, c_0_0, c_2_0, c_1_0, c_0_0, c_0_2, c_0_3, c_0_4, c_2_1, c_2_2, c_1_2, c_1_3, c_0_3, c_0_4, -2*c_1_2 + c_4_0, -2*c_0_3 + c_3_1, c_2_2, c_1_3, c_0_4] | |
final P: c_1_1*x*y + c_3_0*x**3 | |
NUMERATORS: | |
[x*y, x**3] | |
...done. | |
Computing differential numerators... | |
===================== | |
=== DIFFERENTIALS === | |
===================== | |
Singularities: | |
[((0, 0, 1), (2, 1, 2))] | |
--- LOOP --- | |
- singular point - | |
(0, 0, 1) | |
g transform: | |
x**3 - x**2 + y**2 | |
P transform: | |
c_0_0 | |
- integral basis - | |
[1, y/x] | |
r = Poly(c_0_0, y, x, c_0_0, domain='QQ[I]') | |
denom = 1 | |
mult = 0 | |
[c_0_0] | |
[(0, 0)] | |
bi: 1 | |
conds: [] | |
r = Poly(y*c_0_0, y, x, c_0_0, domain='QQ[I]') | |
denom = x | |
mult = 1 | |
[c_0_0] | |
[(0, 1)] | |
bi: y/x | |
conds: [c_0_0] | |
--- END LOOP --- | |
all conds: | |
[c_0_0] | |
final P: 0 | |
NUMERATORS: | |
[] | |
...done. | |
Computing differential numerators... | |
===================== | |
=== DIFFERENTIALS === | |
===================== |
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