Ok! Thank you! Do you have some idea about the first question? *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* On Monday, April 21, 2014 3:52:53 PM UTC+2, John Cremona wrote: > > On 21 April 2014 13:58, Irene <irene....@gmail.com <javascript:>> wrote: > > I forgot to write what is repsq(): > > You could use the builtin function power_mod: > > sage: power_mod? > Type: function > String Form:<function power_mod at 0x1f78668> > File: > /usr/local/sage/sage-6.1.1/local/lib/python2.7/site-packages/sage/rings/arith.py > > > Definition: power_mod(a, n, m) > Docstring: > The n-th power of a modulo the integer m. > > > > #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 > >> > > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-support" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to sage-support...@googlegroups.com <javascript:>. > > To post to this group, send email to > > sage-s...@googlegroups.com<javascript:>. > > > Visit this group at http://groups.google.com/group/sage-support. > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
