Yes it is! Many thanks. I get the detail on the polynomial ring construction.
On Monday, July 25, 2016 at 12:38:29 PM UTC+2, Dima Pasechnik wrote: > > > > On Monday, July 25, 2016 at 11:24:56 AM UTC+1, [email protected] wrote: >> >> Hello, >> >> I'm stalled try to calculate a division in a polynomial ring defined over >> a field that is a finite field. >> >> sage: _.<z> = GF(2)[] >> sage: K.<z> = GF(2^8, modulus=z^8+z^4+z^3+z+1) >> > > this looks fishy, to re-use z this way. See below. > > >> sage: R = PolynomialRing(K,'x') >> sage: l = x^4 + 1 >> sage: c = (z+1)*x^3+x^2+x+(z) >> sage: l/c >> (x^4 + 1)/((z + 1)*x^3 + x^2 + x + z) >> >> But I like to find the quotient and the reminder of this division. How >> should I write it? >> > > sage: _.<z0>=GF(2)[] > sage: K.<z> = GF(2^8, modulus=z0^8+z0^4+z0^3+z0+1) > sage: R.<x>=K[] > sage: l = x^4 + 1 > sage: c = (z+1)*x^3+x^2+x+(z) > sage: l.quo_rem(c) > ((z^7 + z^6 + z^5 + z^4 + z^2 + z)*x + z^6 + z^4 + z, > (z^7 + z^5 + z^2)*x^2 + (z^7 + z^5 + z^2 + 1)*x + z^7 + z^5 + z^2 + 1) > sage: qo,re=l.quo_rem(c) > sage: qo*c+re > x^4 + 1 > > > So qo and re are what you are looking for. > > >> I've tried in all the ways I've thought and searched for similar >> questions, but looks like using a finite field to define the ring may need >> something specific. >> >> Thanks >> >> /Sergi. >> >> -- 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 https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
