>
> 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 q in xrange(0,degree+1):
> for ja in range(0,degx):
> lee=li[ja].coeffs()
> print 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
>
>> and at moment i get this as output
>
1
8
Univariate Polynomial Ring in y over Univariate Quotient Polynomial Ring in
t over Finite Field of size 5 with modulus t^2 + 3
4*t
t
3*t*y^6 + 2*t*y^4 + t*y^2 + t
6
(1, 3*t*y^6 + 2*t*y^4 + t*y^2 + t, 4*y^2 + 2)
[1]
[1, 0]
[t, 0, t, 0, 2*t, 0, 3*t]
[0, 1]
[1]
Traceback (most recent call last):
File "quickfact.py", line 72, in <module>
print factor_bivar(f)
File "quickfact.py", line 63, in factor_bivar
lei=lee[q].list()
IndexError: list index out of range
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