If you type x = polygen(GF(7))
before defining mpoly, then mpoly.factor() will factor it mod 7. Probably better though is to type x = polygen(ZZ) before defining mpoly, so that mpoly knows that it is an integer polynomial: sage: mpoly.parent() Univariate Polynomial Ring in x over Integer Ring and now you can do sage: mpoly.change_ring(GF(7)).factor() (x + 1) * (x + 6) * (x^15 + x^14 + 3*x^13 + 2*x^12 + 6*x^11 + 5*x^10 + 2*x^9 + 6*x^7 + 6*x^6 + 5*x^5 + 5*x^4 + x^2 + 2*x + 6) and easily change from 7 to other primes. On 15 January 2014 18:13, William Stein <wst...@gmail.com> wrote: > ---------- Forwarded message ---------- > From: "Stavros Garoufalidis" <stav...@math.gatech.edu> > Date: Jan 15, 2014 12:36 PM > Subject: factoring polynomials modulo primes in Mathematica/Sage? > To: <wst...@uw.edu> > Cc: "stavros" <stav...@math.gatech.edu> > > Dear William, > > I would like to ask you a Sage question: suppose we have a Mathematica > object in sage: > > sage: mpoly > 4096 - 8192*x + 63488*x^2 + 36864*x^3 + 216576*x^4 + 78080*x^5 + 215424*x^6 > - > 9472*x^7 + 106672*x^8 - 29200*x^9 + 34736*x^10 - 13528*x^11 + 3447*x^12 - > 893*x^13 + 561*x^14 - 124*x^15 + 8*x^16 + x^17 > > I would like to factor it (using Mathematica) inside Sage, modulo 7. > I know the command: > > sage: mpoly.Factor() > > which factors over Q. Mathematica has an option Factor[mpoly,Modulus->7]. > How can I access this option in Sage? > > Thank you very much, > > Stavros > > ----------------------------------------------------------------------- > | Stavros Garoufalidis | Phone: (404) 894-6614 | > | School of Mathematics | FAX: (404) 894-4409 | > | Georgia Institute of Technology | e-mail: stav...@math.gatech.edu | > | Atlanta, GA 30332-0160, USA | http://www.math.gatech.edu/~stavros | > ----------------------------------------------------------------------- > > -- > 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.
