I forgot to write what is repsq():
#repsq(a,n) computes a^n
def repsq(a,n):
B = Integer(n).binary()
C=list(B)
k=len(B)-1
bk=a
i=1
while i <= k:
if C[i]=="1":
bk=(bk^2)*a
else:
bk=bk^2
i=i+1
return bk
On Monday, April 21, 2014 11:48:10 AM UTC+2, Irene wrote:
>
> *Hello,*
> *I have the following defined:*
>
> p=3700001
> Fp=GF(p)
> E=EllipticCurve([Fp(3),Fp(5)])
> j_inv=E.j_invariant()
> l=13#Atkin prime
> n=((l-1)/2).round()
> r=2# Phi_13 factorize in factors of degree 2
> s=12#Psi_13 factorize in factors of degree 12
> Fps=GF(repsq(p,s),'a')
> a=Fps.gen()
> Fpr=GF(repsq(p,r),'b')
> b=Fpr.gen()
> FFps.<X>=PolynomialRing(Fps)
> FFpr.<x>=PolynomialRing(Fpr)
> EP=x^6 + (973912*b + 2535329)*x^5 + (416282*b + 3608920)*x^4 + (686636*b
> + 908282)*x^3 + (2100014*b + 2063451)*x^2 + (2563113*b + 751714)*x +
> 2687623*b + 1658379
> A1.<theta>=Fpr.extension(EP)
>
> *and now I want to "add" to A1 the square root of theta^3+3*theta+5.*
> *The problem is that when I consider the following:*
>
> gamma2=theta^3+3*theta+5
> AA1.<xbar>=PolynomialRing(A1)
> AA.<gamma>=A1.extension(xbar^2-gamma2)
> (xbar^2-gamma2).roots(AA,multiplicities=False)
>
> it gives me a NotImplementedError. Any idea? Thank you in advance.
> *Irene*
>
>
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