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Monomial Orders vs. Run time

The command SetUnknowns[x, ..., x] imposes a pure lex order

x « x « ... « x

on monomials in the unknowns x, ..., x . In the examples of this paper, we did each of our experiments with a multigraded lex order. We found that this did not effect the answer. In the commutative case, a typical GBA runs faster with a graded lex order than a pure lex order. Thus, in practice, one might be advised to set a graded lex order on the unknowns using the command SetUnknowns[{x, ..., x}].

Wed Jul 3 10:27:42 PDT 1996