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Recipe 1---existence of solutions

The polynomial system F has a solution if and only if the Gröbner basis with respect to any ordering is not the single polynomial .

Example. Suppose . Issuing the commands

gbasis(F, [x, y], tdeg);
yields . Hence the theory says there are no solutions to this system (well, you wouldn't expect any since there are three equations in 2 unknowns, and in fact this is easy to verify by hand in this example).

Robert Corless
Tue Mar 12 21:09:19 EST 1996