On 10/23/07, Steffen <[EMAIL PROTECTED]> wrote:
> > Given this definition (which I agree is correct), I would expect that
> > if I ask for a total degree of 4, I would sometimes see monomials like
> > x^4 or x*y^3. I think the lack of these monomials is what surprises
> > (and, coincidentally, pleases) Steffen.
> >
> > Carl
>
> Exactly, thats one of two points. The maximum degree in every variable
> is (maximum total degree of resulting polynomial) / (number of
> varialbes of the polynomial). Thus for example GF(10007)
> ['x,y,z'].random_element(5,9) will be limited in every variable to
> degree 5/3 = 1 !!!. This is not what the upper definition says.
> The second point is about the number of coefficients that are set to
> 0. This might a point to argue about, but if I create a random
> polynomial with a (maximum number of terms to generate) then I expect
> that the 0 occurs with the same probability and thus as often as every
> other element. Thats why I am not happy if 20% or more of the
> parameters are 0.
>
It sounds to me like you should implement a variant of random_element
for polynomial rings that you like, and post a patch. You could:
(1) fix the docstring to be correct,
(2) make your variant available via an option, e.g.,
random_element(something='blah')
-- William
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