Wolfram Research, Inc.

Problem 6

Find a lexicographic Gröbner basis for the following polynomial system.

Result

Method: Use a built-in function.

The default term ordering for GroebnerBasis is the lexicographic ordering, so the input is straightforward.

The basis consists of a univariate polynomial in and three linear polynomials in , , and .

A numerical version of the Gröbner basis can be calculated more than 150 times faster.

This shows that the numerically calculated Gröbner basis and the exact one are the same.