Thanks, Now I'm trying to apply the Chinese Theorem Remainder after the code, then .... I defined
q = X^18 + a*X^15 + a*X^12 + X^11 + (a + 1)*X^2 + a r = a^3*X^3 + (a^3 + a^2 + a)*X^2 + (a^2 + 1)*X + a^3 + a^2 + a #p,q and r are relatively prime and I'm trying ... crt([(A\b)[0],(A\b)[1],(A\b)[2]],[p,q,r]) but I get File "element.pyx", line 344, in sage.structure.element.Element.__getattr__ (sage/structure/element.c:3871) File "misc.pyx", line 251, in sage.structure.misc.getattr_from_other_class (sage/structure/misc.c:1606) AttributeError: 'PolynomialQuotientRing_field_with_category.element_class' object has no attribute 'quo_rem' When I maked the similar to integers that crt works fine, but in this case not. I'm thinking that problem is the change Xbar to X Here my complete example to integers from numpy import arange, eye, linalg #2x-3y+2z=21 #x+4y-z=1 #-x+2y+z=17 A = matrix([[2,-3,2],[1,4,-1],[-1,2,1]]) b=vector([21,1,17]) p=[17,11,13] d=det(A) dlist=[0,0,0] ylist=matrix(IntegerModRing(p[i]),[[2,-3,2],[1,4,-1],[-1,2,1]])\vector(IntegerModRing(p[i]),[21,1,17]) p1=[int(ylist[0]),int(ylist[1]),int(ylist[2])] CRT(p1,p) 2013/10/23 Ivan Andrus <darthand...@gmail.com> > Do you mean something like: > > R.<Xbar> = PR.quotient(PR.ideal(p)) > # change your formulas to Xbar instead of X > A \ b > # ==> (a^3 + a, a^2, (a^3 + a^2)*Xbar^2 + (a + 1)*Xbar + a^3 + a) > > -Ivan > > On Oct 23, 2013, at 1:14 PM, Juan Grados <juan...@gmail.com> wrote: > > 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 <john.crem...@gmail.com> > >> On 23 October 2013 19:50, Juan Grados <juan...@gmail.com> 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 sage-support+unsubscr...@googlegroups.com. >> > To post to this group, send email to sage-support@googlegroups.com. >> > 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 sage-support+unsubscr...@googlegroups.com. >> To post to this group, send email to sage-support@googlegroups.com. >> 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 sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > 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 sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > 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 sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
