On Sat, Apr 4, 2015 at 8:29 PM, absinthe <kpat...@gmail.com> wrote: > Dear all, > > I'm trying to work with polynomials modulo x^N-1 whose coefficients belong > to Z_p (If it helps p is a power of a prime). I know that I'm doing > something wrong, but I cannot figure out what so any help is welcome. > p=32 > N=100 > ZZp.<x> = PolynomialRing(Integers(p)) > #find an element that can be inverted > pp=ZZp.random_element() > while True: > try: > ppInv=pp.inverse_mod(x^N-1) > break > except: > pp=ZZp.random_element() > #multiply the inverses > print (pp*ppInv).mod(x^N-1) > > The result is not always 1 (sometimes it is though). So the question is why? > From their definition, the two polynomials are inverse but their product is > not 1? Am I interprenting wrong? >
Maybe you want a polynomial f(x) in GF(p)[x] with the property that f(x) has an inverse in GF(p)[x]/(x^N - 1)? An f(x) in GF(p)[x] has this property if an only if gcd(f(x), x^N - 1) = 1. Moreover, you can find the inverse of f(x) in this ring using xgcd. All this is implemented in Sage. > Thanks in advance. > > -- > 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/d/optout. -- 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/d/optout.
