You should use on of the following two commands: A1.<theta>=FFpr.quotient(ep)
A1.<theta>=PolynomialQuotientRing(FFpr,ep) Le lundi 7 avril 2014 16:33:00 UTC+2, Irene a écrit : > > I am programming an example about elliptic curves but I need to define a > couple of field extensions to make there some operations and Sage consider > them as rings, then it doesn't allow me to compute divisions. > What can I do? > Here is the code: > > p=3700001 > Fp=GF(p) > E=EllipticCurve([Fp(3),Fp(5)]) > j=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 > > #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 > > d=E.division_polynomial(13) > Fps=GF(repsq(p,s),'a') > Fpr=GF(repsq(p,r),'b') > FFpr.<x>=PolynomialRing(Fpr) > Fl=GF(l) > c=GF(2) > rts=d.roots(Fps,multiplicities=False) > Px=rts[0] > Py2=Px^3+3*Px+5 > c=Fl.multiplicative_generator() > > def produx(n,Qx): > if is_odd(n): > > pro=Qx-(E.division_polynomial(n-1,(Qx,1),two_torsion_multiplicity=1)*E.division_polynomial(n+1,(Qx,1),two_torsion_multiplicity=1))/((E.division_polynomial(n,(Qx,1),two_torsion_multiplicity=1)^2) > > * (Qx+3*Qx+5)) > else: > > pro=Qx-(E.division_polynomial(n-1,(Qx,1),two_torsion_multiplicity=1)*E.division_polynomial(n+1,(Qx,1),two_torsion_multiplicity=1))*(Qx^3+3*Qx+5)/(E.division_polynomial(n,(Qx,1),two_torsion_multiplicity=1)^2) > return pro > > #Ray-polynomial > def EP(x,Qx,n): > i=2 > m=(x-Qx) > while i<=n: > m=m*(x-produx(n,Qx)) > i=i+1 > return m > > ep=EP(x,Px,n) > #A1.<theta>=FFpr.extension(ep) > #A1.<theta>=PolynomialQuotientRing(Fpr,ep) > > -- 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.
