Thank you very much, it woks perfectly. Samuele 2010/4/19 luisfe <[email protected]>: > > > On 19 abr, 12:07, "samuele.anni" <[email protected]> wrote: >> 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 > > If x is an element of K, x.polynomial() returns a representation of x > as a polynomial (the representative of x of minimal degree thinking > K=QQ[x]/f(x)) > > So, you can do > > sage: A1=[x.polynomial()(12) for x in A];A1 > [11, 1013/2, -1150, 117, 2278, -2298, -2289, 3093/2, -3543/2, 2415, > -1525/2, -892, -1236, 3561/2, -3287] > > -- > 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 >
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