On Nov 17, 9:28 pm, Robert Bradshaw <rober...@math.washington.edu> wrote: > How about doing > > sage: f = legendre_P(3, GF(11)['x'].gen()); f > 8*x^3 + 4*x > sage: parent(f) > Univariate Polynomial Ring in x over Finite Field of size 11 > sage: f(5) > 8 > > However, the implementation (manipulating strings) is pretty horrid.
That can be cleaned up quite a bit if this were rewritten to use maxima_lib. In that case the multiplications would probably be actual sage multiplications too, so would likely lead to the same errors as in Sage, though. The issue really is whether "rational number"*"finite field element" should be supported. The problem is of course that there is no common parent for *all* possible element pairs, so the coercion framework rightfully refuses. It would be awfully convenient if it were allowed when it makes sense (and just throw a ZeroDivision otherwise). Conversion does do the right thing,you just need to phrase your problem in a way that allows conversion rules come into play: sage: Qx.<x>=QQ[] sage: Fy.<y>=GF(101)[] sage: f=legendr legendre_P legendre_Q legendre_symbol sage: f=legendre_P(3,x) sage: f 5/2*x^3 - 3/2*x sage: Fy(f) 53*y^3 + 49*y After that you can of course evaluate the converted polynomial. The issue of course is that Legendre polynomials cannot be defined this way in all characteristics: sage: Fz.<z>=GF(2)[] sage: Fz(f) ZeroDivisionError: Inverse does not exist. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
