well i was trying to use that example to see how i could work it in this
case
S = GF(5)
R.<z1, z2>=PolynomialRing(S, 2, "z");
f = z2^2+z1^2+3
T.<x>=PolynomialRing(S)
def factor_bivar(f):
q = S.cardinality()
fx0 = T(f(x,0))
fac = fx0.factor()
l = len(list(fac))
print l
degx= f.degree(z1)
degy= f.degree(z2)
degree=2*degx*degy
print degree
for n in xrange(0, l):
h = fac[n][0]
if (h.is_monic()):
if h == fx0:
break
return h
print h
E.<t> = S.extension(h)
G.<y> = E['y']
print G
df=diff(f,z1)
dif=E(df(t,0))
s=1/(dif)
print s
a0=E(t)
ak=a0
print ak
for k in xrange(0, degree):
ak=ak-s*G(f(ak,y))
ad=ak%y^(degree+1)
print ad
degad=ad.degree(y)
print degad
li=vector((ad^j)%y^(degree+1) for j in xrange(0,degx+1))
print li
lei=[]
for ja in range(0,degx):
for q in xrange(0,degree+1):
lee=li[ja].coeffs()
print lee
print parent(lee)
lei=lee[q].list
print lei
li is a vector of the powers of ad from ad^0 to ad^degx
lee should be a list of coefficients wrt y of all the li
so should have degx+1 of lee
1 for each power of ad
and length of lee should be degree+1
based on the powers of y from y^0 to y^degree
then lei should split wrt powers of t
so length of lei is (degree+1)*degx
and i want an output of lei for each power of ad^j
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