Hi -
I don't think giac can handle more than 15 variables in a Gröbner basis
calculation.
This limitation isn't really documented anywhere, but if you look in giac's
src/cocoa.cc around lines 490-500, function swap_indices and think about it
a few minutes, you'll see that it can't handle more than 15 variables, I
think. I'm looking at giac 1.9.0.
I tried a calculation on a ring with 67 variables and the algorithm went
into an infinite loop because it couldn't compare monomial exponents
properly. It produced a polynomial with two terms, both with the same
monomial (different coefficients), and that triggered the infinite loop in
the reduction code.
I hope somebody working with this code will check my work and verify that
giac is so limited. If so, we should add a check to the groebner_basis
routine in src/sage/libs/giac/__init__.py
agape
brent
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