On 23 October 2013 19:50, Juan Grados <[email protected]> wrote: > Is there in sage, any instruction to solve a linear system equations > module p(x) (polynomial over finite field), where the system coefficients > are polynomials over finite field?. I know that for integers exists, example > (thanks Purkayastha) > > sage: I6 = IntegerModRing(6) > sage: M = random_matrix(I6, 4, 4) > sage: v = random_vector(I6, 4) > sage: M \ v > (4, 0, 2, 1) >
You could try doing exactly the same thing, and it works: sage: R.<x> = PolynomialRing(GF(17)) sage: M = random_matrix(R, 4, 4) sage: v = random_vector(R,4) sage: M \ v ((12*x^8 + 10*x^7 + 11*x^6 + 7*x^5 + 10*x^4 + 16*x^3 + 11*x^2 + 6*x + 13)/(x^8 + 15*x^7 + 8*x^6 + 5*x^5 + 15*x^4 + 14*x^3 + x^2 + 4*x), (2*x^8 + 8*x^7 + 2*x^6 + 11*x^5 + 12*x^4 + 15*x^3 + 5*x^2 + 3*x + 5)/(x^8 + 15*x^7 + 8*x^6 + 5*x^5 + 15*x^4 + 14*x^3 + x^2 + 4*x), (12*x^8 + 3*x^7 + 12*x^6 + 10*x^5 + 14*x^4 + 7*x^3 + 7*x^2 + 7*x + 10)/(x^8 + 15*x^7 + 8*x^6 + 5*x^5 + 15*x^4 + 14*x^3 + x^2 + 4*x), (14*x^8 + 6*x^7 + 12*x^6 + 13*x^5 + 4*x^4 + 13*x^3 + 8*x^2 + 5*x + 3)/(x^8 + 15*x^7 + 8*x^6 + 5*x^5 + 15*x^4 + 14*x^3 + x^2 + 4*x)) John Cremona > thanks > > -- > --------------------------------------------------------------------- > MSc. Juan del Carmen Grados Vásquez > Laboratório Nacional de Computação Científica > Tel: +55 24 2233-6260 > (http://www.lncc.br/) > http://juaninf.blogspot.com > --------------------------------------------------------------------- > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
