Differentials debugging output

out1

=====================
=== Differentials ===
=====================
- singular point -
(0, 0, 1)
g:
x^4 + x^2*y^2 + (-2)*x^2*y - x*y^2 + y^2
P:
c_1_0*x + c_0_1*y + c_0_0
-integral basis-
[1, (x^2*y - x*y + y)/x^2]


r = c_0_1*x + c_1_0*y + c_0_0
denom = 1
mult  = 0
[c_0_1, c_1_0, c_0_0]
[x, y, 1]



bi:  1
conds: []


r = c_1_0*x*y^3 + (-c_0_1)*y^4 + (c_0_0 + 2*c_0_1 - c_1_0)*x*y^2 + (-c_0_0 + c_1_0)*x*y + c_0_0*x
denom = x^2
mult  = 2
[c_1_0, -c_0_1, c_0_0 + 2*c_0_1 - c_1_0, -c_0_0 + c_1_0, c_0_0]
[x*y^3, y^4, x*y^2, x*y, x]



bi:  (x^2*y - x*y + y)/x^2
conds: [c_1_0, -c_0_1, c_0_0 + 2*c_0_1 - c_1_0, -c_0_0 + c_1_0, c_0_0]
- singular point -
(0, 1, 0)
g:
x^4 + (-2)*x^2*z + x^2 - x*z + z^2
P:
c_1_0*x + c_0_0*z + c_0_1
-integral basis-
[1, z/x]


r = c_0_0*x + c_1_0*z + c_0_1
denom = 1
mult  = 0
[c_0_0, c_1_0, c_0_1]
[x, z, 1]



bi:  1
conds: []


r = c_0_0*x^2 + c_1_0*x*z + c_0_1*x
denom = x
mult  = 1
[c_0_0, c_1_0, c_0_1]
[x^2, x*z, x]



bi:  z/x
conds: []


...done.


Computing differential numerators...
=====================
=== Differentials ===
=====================
- singular point -
(0, 0, 1)
g:
-x^7 + 2*x^3*y + y^3
P:
c_4_0*x^4 + c_3_1*x^3*y + c_2_2*x^2*y^2 + c_1_3*x*y^3 + c_0_4*y^4 + c_3_0*x^3 + c_2_1*x^2*y + c_1_2*x*y^2 + c_0_3*y^3 + c_2_0*x^2 + c_1_1*x*y + c_0_2*y^2 + c_1_0*x + c_0_1*y + c_0_0
-integral basis-
[1, y/x, y^2/x^3]


r = c_0_4*x^4 + c_1_3*x^3*y + c_2_2*x^2*y^2 + c_3_1*x*y^3 + c_4_0*y^4 + c_0_3*x^3 + c_1_2*x^2*y + c_2_1*x*y^2 + c_3_0*y^3 + c_0_2*x^2 + c_1_1*x*y + c_2_0*y^2 + c_0_1*x + c_1_0*y + c_0_0
denom = 1
mult  = 0
[c_0_4, c_1_3, c_2_2, c_3_1, c_4_0, c_0_3, c_1_2, c_2_1, c_3_0, c_0_2, c_1_1, c_2_0, c_0_1, c_1_0, c_0_0]
[x^4, x^3*y, x^2*y^2, x*y^3, y^4, x^3, x^2*y, x*y^2, y^3, x^2, x*y, y^2, x, y, 1]



bi:  1
conds: []


r = c_0_4*x^5 + c_1_3*x^4*y + c_2_2*x^3*y^2 + c_3_1*x^2*y^3 + c_4_0*x*y^4 + c_0_3*x^4 + c_1_2*x^3*y + c_2_1*x^2*y^2 + c_3_0*x*y^3 + c_0_2*x^3 + c_1_1*x^2*y + c_2_0*x*y^2 + c_0_1*x^2 + c_1_0*x*y + c_0_0*x
denom = x
mult  = 1
[c_0_4, c_1_3, c_2_2, c_3_1, c_4_0, c_0_3, c_1_2, c_2_1, c_3_0, c_0_2, c_1_1, c_2_0, c_0_1, c_1_0, c_0_0]
[x^5, x^4*y, x^3*y^2, x^2*y^3, x*y^4, x^4, x^3*y, x^2*y^2, x*y^3, x^3, x^2*y, x*y^2, x^2, x*y, x]



bi:  y/x
conds: []


r = c_0_4*x^6 + c_1_3*x^5*y + c_2_2*x^4*y^2 + c_3_1*x^3*y^3 + c_4_0*x^2*y^4 + c_0_3*x^5 + c_1_2*x^4*y + c_2_1*x^3*y^2 + c_3_0*x^2*y^3 + c_0_2*x^4 + c_1_1*x^3*y + c_2_0*x^2*y^2 + c_0_1*x^3 + c_1_0*x^2*y + c_0_0*x^2
denom = x^3
mult  = 3
[c_0_4, c_1_3, c_2_2, c_3_1, c_4_0, c_0_3, c_1_2, c_2_1, c_3_0, c_0_2, c_1_1, c_2_0, c_0_1, c_1_0, c_0_0]
[x^6, x^5*y, x^4*y^2, x^3*y^3, x^2*y^4, x^5, x^4*y, x^3*y^2, x^2*y^3, x^4, x^3*y, x^2*y^2, x^3, x^2*y, x^2]



bi:  y^2/x^3
conds: [c_4_0, c_3_0, c_2_0, c_1_0, c_0_0]
- singular point -
(0, 1, 0)
g:
-x^7 + 2*x^3*z^3 + z^4
P:
c_4_0*x^4 + c_3_0*x^3*z + c_2_0*x^2*z^2 + c_1_0*x*z^3 + c_0_0*z^4 + c_3_1*x^3 + c_2_1*x^2*z + c_1_1*x*z^2 + c_0_1*z^3 + c_2_2*x^2 + c_1_2*x*z + c_0_2*z^2 + c_1_3*x + c_0_3*z + c_0_4
-integral basis-
[1, z/x, z^2/x^3, z^3/x^5]


r = c_0_0*x^4 + c_1_0*x^3*z + c_2_0*x^2*z^2 + c_3_0*x*z^3 + c_4_0*z^4 + c_0_1*x^3 + c_1_1*x^2*z + c_2_1*x*z^2 + c_3_1*z^3 + c_0_2*x^2 + c_1_2*x*z + c_2_2*z^2 + c_0_3*x + c_1_3*z + c_0_4
denom = 1
mult  = 0
[c_0_0, c_1_0, c_2_0, c_3_0, c_4_0, c_0_1, c_1_1, c_2_1, c_3_1, c_0_2, c_1_2, c_2_2, c_0_3, c_1_3, c_0_4]
[x^4, x^3*z, x^2*z^2, x*z^3, z^4, x^3, x^2*z, x*z^2, z^3, x^2, x*z, z^2, x, z, 1]



bi:  1
conds: []


r = c_0_0*x^5 + c_1_0*x^4*z + c_2_0*x^3*z^2 + c_3_0*x^2*z^3 + c_4_0*x*z^4 + c_0_1*x^4 + c_1_1*x^3*z + c_2_1*x^2*z^2 + c_3_1*x*z^3 + c_0_2*x^3 + c_1_2*x^2*z + c_2_2*x*z^2 + c_0_3*x^2 + c_1_3*x*z + c_0_4*x
denom = x
mult  = 1
[c_0_0, c_1_0, c_2_0, c_3_0, c_4_0, c_0_1, c_1_1, c_2_1, c_3_1, c_0_2, c_1_2, c_2_2, c_0_3, c_1_3, c_0_4]
[x^5, x^4*z, x^3*z^2, x^2*z^3, x*z^4, x^4, x^3*z, x^2*z^2, x*z^3, x^3, x^2*z, x*z^2, x^2, x*z, x]



bi:  z/x
conds: []


r = c_0_0*x^6 + c_1_0*x^5*z + c_2_0*x^4*z^2 + c_3_0*x^3*z^3 + c_4_0*x^2*z^4 + c_0_1*x^5 + c_1_1*x^4*z + c_2_1*x^3*z^2 + c_3_1*x^2*z^3 + c_0_2*x^4 + c_1_2*x^3*z + c_2_2*x^2*z^2 + c_0_3*x^3 + c_1_3*x^2*z + c_0_4*x^2
denom = x^3
mult  = 3
[c_0_0, c_1_0, c_2_0, c_3_0, c_4_0, c_0_1, c_1_1, c_2_1, c_3_1, c_0_2, c_1_2, c_2_2, c_0_3, c_1_3, c_0_4]
[x^6, x^5*z, x^4*z^2, x^3*z^3, x^2*z^4, x^5, x^4*z, x^3*z^2, x^2*z^3, x^4, x^3*z, x^2*z^2, x^3, x^2*z, x^2]



bi:  z^2/x^3
conds: [c_4_0, c_3_1, c_2_2, c_1_3, c_0_4]


r = c_0_0*x^7 + c_1_0*x^6*z + c_2_0*x^5*z^2 + c_3_0*x^4*z^3 + c_4_0*x^3*z^4 + c_0_1*x^6 + c_1_1*x^5*z + c_2_1*x^4*z^2 + c_3_1*x^3*z^3 + c_0_2*x^5 + c_1_2*x^4*z + c_2_2*x^3*z^2 + c_0_3*x^4 + c_1_3*x^3*z + c_0_4*x^3
denom = x^5
mult  = 5
[c_0_0, c_1_0, c_2_0, c_3_0, c_4_0, c_0_1, c_1_1, c_2_1, c_3_1, c_0_2, c_1_2, c_2_2, c_0_3, c_1_3, c_0_4]
[x^7, x^6*z, x^5*z^2, x^4*z^3, x^3*z^4, x^6, x^5*z, x^4*z^2, x^3*z^3, x^5, x^4*z, x^3*z^2, x^4, x^3*z, x^3]



bi:  z^3/x^5
conds: [c_3_0, c_4_0, c_2_1, c_3_1, c_1_2, c_2_2, c_0_3, c_1_3, c_0_4]


...done.


Computing differential numerators...
=====================
=== Differentials ===
=====================
- singular point -
(0, 0, 1)
g:
x^3 - x^2 + y^2
P:
c_0_0
-integral basis-
[1, y/x]


r = c_0_0
denom = 1
mult  = 0
[c_0_0]
[1]



bi:  1
conds: []


r = c_0_0*x
denom = x
mult  = 1
[c_0_0]
[x]



bi:  y/x
conds: []
Traceback (most recent call last):
  File "foo.py", line 30, in <module>
    nums = differentials_numerators(f)
  File "/Users/cswiercz/abelfunctions/abelfunctions/differentials.py", line 227, in differentials_numerators
    P_reduced = P(T(x),T(y)).reduce(ideal)
  File "/Users/cswiercz/sage-6.8/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_element.py", line 1846, in reduce
    if P.monomial_divides(gilm, plm):
  File "/Users/cswiercz/sage-6.8/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ring.py", line 810, in monomial_divides
    raise ZeroDivisionError
ZeroDivisionError