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I would like to put a time limit on computation of Groebner basis in libSingular, but I have trouble finding out how to do that. I know Singular command groebner takes a second argument, which would do exactly that, but I don't know how to pass it there from SAGE. Is there a way to do that?

Hello,

I am working in multivariate polynomial rings over small finite fields (with less then 15, or currently less than 10 elements). I have an algorithm, that outputs a system of equations. I need to find out if the system has a solution and if so, to find one. I am using calculation of groebner basis for this. But since my system typically has 20 or more variables and quite complicated polynomials, it seems that SINGULAR has problem to find the basis in reasonable time. Is there a way to speed up the calculation? For example, since I work in finite field, I can try all possible values for some variable. This simplifies the system and in some cases it seems to really help SINGULAR. But I can do that for only a very few variables.

Currently I work in PolynomialRing and before the grobner basis algorithm, I reduce my polynomials by FieldIdeal (x_0^n - x_0, ..., x_m^n - x_m) of the polynomial ring and add this equations to the system, to force the solution in the finite field. I tried to work in the quotient ring from the start, but it looks like it slowed down my whole algorithm and also slowed down the computation of the groebner basis (which is a little suprising for me). I found that for GF(2) PolyBoRi is optimized for the kind of work I need, but I am not restricted to GF(2). Is there something similar for other finite fields?

I would appreciate any tips how to speed up the whole process. Thank you.

I did, but I don't see it. Could you point me to the sentence that answers my question?

I edited the question. There is a case that fits your last situation, and it does not raise an error. I would like to know the difference.

I would like to ask, why following code ends with error:

R = PolynomialRing(GF(3),'x3,x5,x4,x7,x6')

U = PolynomialRing(GF(3), 'x2, x5, x4, x1, x0, x6')

f = U.gens()[1] + U.gens()[2]

g = R(f)

because when I remove x0 from the generators, it works fine.

R = PolynomialRing(GF(3),'x3,x5,x4,x7,x6')

U = PolynomialRing(GF(3), 'x2, x5, x4, x1, x6')

f = U.gens()[1] + U.gens()[2]

g = R(f)

Thanks for the answer, but there is still an open question. I have been working with this for a few days, and up untill this case, I had no trouble getting the same polynomial in a ring with fewer genarators, if the original polynomial contained only those. I tried and the followng code works fine, and it also fits your last case which according to you should raise an error, because U has more generators than R.

R = PolynomialRing(GF(3),'x5,x4,x7,x6')

U = PolynomialRing(GF(3), 'x2, x5, x4, x1, x6')

f = U.gens()[1] + U.gens()[2]

g = R(f)