William,
I can factor polynomials with coefficients in QQ fine. Here are the
examples I mentioned in greater detail:
# define the coefficient field K and R=K[x,y]
K.<a>=PolynomialRing(QQ,1)
K=FractionField(K)
R.<x,y>=PolynomialRing(K,2)
# the following works:
(x^2-y^2).factor()
# answer: (x - y) * (x + y)
# this one also works:
(x^2-a^2*y^2).factor()
# answer: (x + (-a)*y) * (x + a*y)
# the following two are the simplest ones that fail:
x.factor()
# raises NotImplementedError
R(1).factor()
# raises IndexError: list index out of range
If x^2-y^2 can be factored correctly, wouldn't I expect that factoring
just x is also implemented? Maybe it's also just a bug.
If I replace the definition of the ring R by
R.<x,y,a>=PolynomialRing(QQ,3)
then all four examples work correctly.
Stefan
Am 28.11.2009 um 17:17 schrieb William Stein:
> On Sat, Nov 28, 2009 at 3:06 PM, Stefan Boettner
> <sboet...@tulane.edu> wrote:
>> Hello,
>>
>> I would like to factor multivariate polynomials that have parameters
>> in the coefficient field, for example:
>>
>> K.<a>=PolynomialRing(QQ,1)
>> K=FractionField(K)
>> R.<x,y>=PolynomialRing(K,2)
>>
>> Now I would like to factor elements in R, such as x^2-m^2*y^2, which
>> actually works. However, when I ask to have "more trivial" elements
>> such as x or 1 factored, it fails with a NotImplementedError (for x)
>> or IndexError ("list index out of range" for 1). What's wrong?
>
> Please give the simplest explicit example that raise IndexError, as
> that might be a bug. Regarding NotImplementedError, it means what it
> sounds like -- the capability you want isn't
> implemented. That said, can't you just factor over a polynomial
> ring in x,y,a?
>
> -- William
>
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