On 11/18/2012 01:31 AM, Nils Bruin wrote: > > 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. >
This works with the current legendre_P (as does Robert's solution) thanks to the string magic, but wouldn't work with my scaled implementation that tries to multiply/divide `x` by terms involving the endpoints of the interval. Ultimately it works if I stick to ZZ, and I was able to work around this one regression by checking for the special case where the endpoints are in ZZ. I just had to rearrange the terms a bit to avoid creating a rational. These both work: sage: ZZ(5) * GF(11)(5) 3 sage: GF(11)(5) / ZZ(8) 2 but this doesn't: sage: (ZZ(5)/ZZ(8)) * GF(11)(5) ... TypeError: unsupported operand parent(s) for '*': 'Rational Field' and 'Finite Field of size 11' I think it might as well be allowed, since this is: sage: GF(2)(1) / ZZ(2) ... ZeroDivisionError: Inverse does not exist. I left the case with rational endpoints unhandled; I don't think anyone is evaluating Legendre polynomials in GF(11), but I didn't want to cause an unnecessary regression. -- 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.
