You can try to compute over ZZ with p added as a generator, because J in Z^n/<p> ~= J + <p> in Z^n
sage: p = next_prime(2^100) sage: R.<x,y,z> = ZZ[] sage: I = Ideal(R.random_element() for _ in range(R.ngens())) sage: I += [p] sage: I.groebner_basis() [x^2 + 380295180068468820449010961696*x*z + 253530120045645880299340641111*z^2 + 1014120480182583521197362564522*z, y^2 + x*z + 6*y*z + 2*y, 1267650600228229401496703205653] It won't be efficient but better than the toy implementation I guess. On Thursday 13 Dec 2012, Santanu Sarkar wrote: > Thanks for your information. No, I need large > prime field. > > On 13 December 2012 12:19, Simon King <[email protected]> wrote: > > Hi! > > > > On 2012-12-13, Santanu Sarkar <[email protected]> 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 > > > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sage-support" group. > > To post to this group, send email to [email protected]. > > To unsubscribe from this group, send email to > > [email protected]. > > Visit this group at http://groups.google.com/group/sage-support?hl=en. Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF _www: http://martinralbrecht.wordpress.com/ _jab: [email protected] -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
