Hi, On 2016-12-06, David Joyner <[email protected]> wrote: > On Tue, Dec 6, 2016 at 12:21 PM, NITIN DARKUNDE <[email protected]> > wrote: >> Respected Sir, >> Yes sir, I am supposed to calculate Grobner basis for an >> ideal in a polynomial ring in 35 variables with coefficients from GF(2). >> > > Why don't you try it first using a code of length <10?
I can tell from my own experience that computing the Gröbner basis for a system of >30,000 nonhomogeneous polynomials of degree 3 with 42 variables may turn out to be feasible. But I can also tell from my own experience that computing the Gröbner basis for a system of a ~10 polynomials of degree 5 with 7 variables may turn out to be unfeasible. After all, computing a Gröbner basis has double exponential worst case complexity. Thus, it all depends on your example. It is very well possible that you are lucky and it just works. Or that your are almost lucky and it becomes solvable by, say, choosing a different monomial ordering resp. doing some manual preprocessing. Or that you are halfways lucky and some software can solve it while other can't: In my 42 variable example, Singular worked, Magma didn't; in other examples, Magma worked, Singular didn't. Or that you are just unlucky and the problem is too difficult. Working in GF(2) certainly helps. Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
