Hi!

On 2012-12-13, Santanu Sarkar <sarkar.santanu....@gmail.com> wrote:
> When I want to calculate
> Groebner basis, I have following error.
>
>
> verbose 0 (3292: multi_polynomial_ideal.py, groebner_basis) Warning:
> falling back to very slow toy implementation.

This is not an error but a warning.

> P1=next_prime(2^100)
> R.<x,y,z>=GF(P1)[]

The warning tells you that your finite field is so big that it can not
be dealt with in (lib)Singular. Hence, if you want to compute a Gröbner
basis over such a big finite prime field, Sage can not use the fast
implementation in (lib)Singular; instead, Sage will try to use a generic
implementation of Buchberger's algorithm (that's what is called "toy
implementation" in the warning message). If you are lucky, the
computation will succeed soon, if you aren't lucky, then there is not
much one can do about it.

Are you sure that you need this particularly large finite field? Would a
smaller finite field do? Would QQ do?

Best regards,
Simon


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