Which command should be used for getting the best performance for computing Groebner bases of Hidden Field Equations (HFE) ? I tried "groebner" and "std", both seem to be giving the same performance.
Thanks,
Yashodhan Karandikar
Singular's std command is just one among others (see, e.g., slimgb, stdhilb, fglm, modStd, ...) to compute Gröbner bases. It is in principle based on Buchberger's algorithm. In contrast to this, the groebner command heuristically chooses one method that is known to be fast in most such cases.
So maybe you get similar timings for std and groebner in your case because groebner in fact calls std.
Note that the relatively new command modStd (from modstd.lib), which makes use of parallelization, is not yet included in groebner, so it might be worth trying this.
Best regards,
Andreas