Hello, I'm trying to implement an algorithm for complete my thesis work about congruence between modular forms and Galois representation. A step of the algorithm I am working on consists in replacing a generator of the number field with a fixed value obtained, clearly the command substitute cannot work because the elements of the matrix are algebraic integers of the number field so nothing is seen as a “variable”. The only thing that comes in my mind is to find a way to convert my vector into a polynomial vector substituing to alpha a variable x, but I cannot find a way to do this.
>>sage: K.<alpha> = NumberField(x^4 - 30*x^2 - 40*x + 5);K Number Field in alpha with defining polynomial x^4 - 30*x^2 - 40*x + 5 >>sage: A=[alpha - 1, 1/2*alpha^3 - 5/2*alpha^2 - 1/2*alpha + 17/2, -alpha^3 >>+4*alpha^2 + alpha - 10, alpha^2 - 2*alpha - 3, 2*alpha^3 - 8*alpha^2 >>-4*alpha + 22, -2*alpha^3 + 8*alpha^2 + 2*alpha - 18, -2*alpha^3 +8*alpha^2 + >>3*alpha - 21, 3/2*alpha^3 - 15/2*alpha^2 + 3/2*alpha + 33/2,-3/2*alpha^3 + >>11/2*alpha^2 + 7/2*alpha - 27/2, 2*alpha^3 - 7*alpha^2 -4*alpha + 15, >>-1/2*alpha^3 + 1/2*alpha^2 + 5/2*alpha - 1/2, -alpha^3 +6*alpha^2 - alpha - >>16, -alpha^3 + 3*alpha^2 + 6*alpha - 12, 3/2*alpha^3- 11/2*alpha^2 - >>5/2*alpha + 21/2, -3*alpha^3 + 13*alpha^2 + 5*alpha -35]; >>sage: A1=[A[i].substitute(alpha=12) for i in range(0, len(A))];A1 [alpha - 1, 1/2*alpha^3 - 5/2*alpha^2 - 1/2*alpha + 17/2, -alpha^3 + 4*alpha^2 + alpha - 10, alpha^2 - 2*alpha - 3, 2*alpha^3 - 8*alpha^2 - 4*alpha + 22, -2*alpha^3 + 8*alpha^2 + 2*alpha - 18, -2*alpha^3 + 8*alpha^2 + 3*alpha - 21, 3/2*alpha^3 - 15/2*alpha^2 + 3/2*alpha + 33/2, -3/2*alpha^3 + 11/2*alpha^2 + 7/2*alpha - 27/2, 2*alpha^3 - 7*alpha^2 - 4*alpha + 15, -1/2*alpha^3 + 1/2*alpha^2 + 5/2*alpha - 1/2, -alpha^3 + 6*alpha^2 - alpha - 16, -alpha^3 + 3*alpha^2 + 6*alpha - 12, 3/2*alpha^3 - 11/2*alpha^2 - 5/2*alpha + 21/2, -3*alpha^3 + 13*alpha^2 + 5*alpha - 35] Does anybody know a way to solve my problem? Thanks for the help Samuele -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
