On 17 April 2014 01:55, Irene irene.alv...@gmail.com wrote:
Hello!
I want to define a polynomial that I know lies in GF(p^2,'b')[x], p=371.
The problem is that I have to define it as a product
E=(X-a_1)*(X-a_2)*(X-a_3)*(X-a_4)*(X-a_5)*(X-a_6), where every a_j is in
GF(p^13,'a')[X].
I
Sorry, I didn't write it correctly. I meant GF(p^12,'a') instead of
GF(p^13,'a'). As 2 divides 12, GF(p^12,'a') is an extension of GF(p^2,'b').
My question is the same now with the correct data.
On Thursday, April 17, 2014 11:04:40 AM UTC+2, John Cremona wrote:
On 17 April 2014 01:55, Irene
OK, that makes sense now. It boils down to this: given an element of
F12=GF(p^12) which happens to lie in F2 = GF(p^2), how to express it
in terms of a generator of F2. This is not quite as easy as it should
be but this works (assuming that you have defined F12 with generator a
and F2 with
I think that this is exactly what I need. Nevertheless I cannot use neither
i.section() nor i.inverse_image(). The second one because of the same
reason as you, and the first one when I try it is says TypeError:
'NoneType' object is not callable.
On Thursday, April 17, 2014 12:07:18 PM UTC+2,
On 17 April 2014 08:43, Irene irene.alv...@gmail.com wrote:
I think that this is exactly what I need. Nevertheless I cannot use neither
i.section() nor i.inverse_image(). The second one because of the same reason
as you, and the first one when I try it is says TypeError: 'NoneType'
object is
p=371
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
This works for me in Sage 5.13 (I don't have an older version installed),
after replacing the definition of FFps by
FFps.X=PolynomialRing(Fps) # the .X was missing
However, without the .X the error I got was different from yours
(TypeError: You must specify the names of the variables.)
Op
Your code works ok with Sage 6.1.1 (apart from a small slip in the
code you posted: the line
FFps=PolynomialRing(Fps)
should say
FFpsX=PolynomialRing(Fps)
and the result is
x^6 + (973912*b + 2535329)*x^5 + (416282*b + 3608920)*x^4 + (686636*b
+ 908282)*x^3 + (2100014*b + 2063451)*x^2 +
I got it in another version! Thank you very much!
On Thursday, April 17, 2014 6:18:56 PM UTC+2, John Cremona wrote:
Your code works ok with Sage 6.1.1 (apart from a small slip in the
code you posted: the line
FFps=PolynomialRing(Fps)
should say
FFpsX=PolynomialRing(Fps)
and the
