Yes, but p(x) is fixed polynomial here my code m = 4;delta = 3;N = 2^m K_.<a> = GF(2); F.<a> = GF(2^m) PR = PolynomialRing(F,'X') X = PR.gen() a11 = (a^2)*(X^3)+(a^11)*(X^2)+1 a12 = (a)*(X^4)+(a^13)*(X^3)+X+1 a13 = X^2+(a^13)*(X^3)+a*(X^2)+1 a21 = X^3 a22 = X+a a23 = X^2+X^3+a*X a31 = (a^12)*X+a*(X^2) a32 = (a^8)*(X^2)+X^2+X^3 a33 = a*X + (a^2)*(X^3) A = matrix([[a11,a12,a13],[a21,a22,a23],[a31,a32,a33]]) b = vector([(a^6)*(X^14)+X^13+X,a*(X^2)+(X^3)*(a^11)+X^2+X+a^12,(a^8)*(X^7)+a*(X^2)+(a^12)*(X^13)+X^3+X^2+X+1]) p = (a^2 + a)*X^3 + (a + 1)*X^2 + (a^2 + 1)*X + 1
I need matrix(PolynomialModRing(p),A)\vector(PolynomialModRing(p),b) but PolynomialModRing not exist ... 2013/10/23 John Cremona <[email protected]> > 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. > -- --------------------------------------------------------------------- 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.
