gen_Monte_Carlo_check(check, l, kind, qvar, sigma, gen) returns Monte Carlo check for solutions to guessing problem. If Monte Carlo check is unavailable returns check.
HP_solve(l, degs, kind, sigma, gen check) finds a sigma basis with degree bounds given by degs. It returns false if there is no interpolating vector that is correct up to (and including) z^(sigma-1) with sigma >= |degs+[1, 1, ..., 1]| or if check rejects all solutions. It returns true if it can not handle given problem.