I know there are a number of different packages in Sage capable of computing Groebner basis but I don't have much experience with these tools. I am wondering which option and specifically which routine might be most suitable for very large (50,000 generators) but relatively sparse (polynomials of degree less than 4 and with 4 or fewer terms over 64 variables). I am interested in basis and prime decomposition in relation to classifying low dimensional Frobenius algebras. I am currently using groeber and the primdec library from Singular in Sage but I am up against significant performance limits.
Also, does any have an recommended methods of pre-processing sparse sets of generators prior to calling groebner? And are there any packages capable of exploiting multi-processor architecture?
