I just opened,
http://trac.sagemath.org/sage_trac/ticket/13720
intending to submit a patch a few minutes later, but I've hit a problem.
The current examples feature,
sage: legendre_P(3, GF(11)(5))
8
which works due to a quirk in Maxima's string representation of the
polynomial:
sage: maxima.eval('legendre_p(%s,x)'%ZZ(3))
'-6*(1-x)-5*(1-x)^3/2+15*(1-x)^2/2+1'
In Sage, this becomes,
sage: -6*(1-x)-5*(1-x)^3/2+15*(1-x)^2/2+1
5/2*(x - 1)^3 + 15/2*(x - 1)^2 + 6*x - 5
with division (in Maxima) replaced by rational multiplication in Sage.
This kills the last example:
sage: GF(11)(5) / 2
8
sage: (1/2) * GF(11)(5)
----------------------------------------------------------------------
TypeError
...
TypeError: unsupported operand parent(s) for '*': 'Rational Field'
and 'Finite Field of size 11'
So, substituting GF(11)(5) into the equation before converting it to
Sage works. But doing the entire computation in Sage fails.
How easy would this be to fix? I could convert my polynomials to Maxima
and back I guess, but that seems a little goofy.
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