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=371
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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