I'm not at my computer to check, but maybe ratsimpmodprime is what you want.

Aaron Meurer

On Nov 26, 2012, at 5:24 AM, Simon Burton <[email protected]> wrote:

> Hi,
>
> I am using the groebner basis, reduce, etc. for working
> with polynomials in roots of unity. Eg. If w is a third
> root of unity then:
>
>>>> import sympy as sy
>>>> w = sy.symbols("w")
>>>> p = w**2 + w + 1
>>>> basis = sy.groebner([p])
>
> now we can work out polynomials in w:
>
>>>> q = w**5 + w + 2
>>>> _, q = basis.reduce(q)
>>>> q
> 1
>
> (And this generalizes to polynomials with multiple different
> roots of unity.)
>
> Ok, so this is all very cool, I finally found a use for
> groebner bases, but it occurs to me that there might be a simpler
> way of achieving this?
>
> Simon.
>
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