The solution you proposed worked. What is the explanation for why it worked?
I am now trying to implement Y in SageMath.
B2 = (2*G).basis_function_space()
R.<y> = Fq[]
Q = R.irreducible_element(16)
L.<z> = Fq.extension(Q)
div = Q(x).divisor()
P = None;
for place in div.support():
if(place.degree() == 16):
P = place
Y_matrix = matrix([morph(a).list() for a in [f.evaluate(P) for f in
B2]]).transpose()
def Y(f):
return morph(f.evaluate(P))
def Y_inv(alpha):
coeffs = Y_matrix.solve_right(vector(alpha.list()))
print(len(coeffs))
#return sum(coeff * b for coeff, b in zip(coeffs, B2))
However, Y_matrix.solve_right() has no solutions. I created the morphism in
order to get a result of length 16.
My Magma code for Y:
m := 16;
P := RandomPlace(F, m);
Fqm := ResidueClassField(P);
Y_matrix := Matrix([Eltseq(a): a in [Evaluate(f, P): f in B2]]);
Y := function(f)
return Evaluate(f, P);
end function;
Y_inv := function(alpha)
coeffs := Solution(Y_matrix, Vector(Eltseq(alpha)));
return &+[coeffs[i] * B2[i]: i in [1..#B2]];
end function;
On Thursday, January 2, 2025 at 4:17:34 PM UTC-8 Kwankyu wrote:
> X_matrix = matrix([[f.evaluate(p) for p in places] for f in
> B1]).transpose()
>
> will work for you.
>
>
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