On 17 Okt., 06:20, cwitty <[EMAIL PROTECTED]> wrote:
> On Oct 16, 8:32 pm, "didier deshommes" <[EMAIL PROTECTED]> wrote:
>
> > 2007/10/16, Steffen <[EMAIL PROTECTED]>:
>
> > > Hi didier,
>
> > > the implementation does not return a polynomial of a total degree of
> > > at most 4, but a polynomial of total degree of at most 4/2 = 2 in x
> > > and in y. If I change the total degree to 5, nothing happens, since
> > > 5/2 = 2. This might be a bug in the implementation. However I am happy
> > > with this behaviour and maybe there should be the option for choosing
> > > the total degree or the degree in every variable.
>
> > For total degree, I'm using the definition
> > here:http://planetmath.org/encyclopedia/OrderAndDegreeOfPolynomial.html
>
> > So I am not concerned about individual degrees at all.
>
> 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.
Steffen
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