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May 28, 2013 at 17:22 comment added Charles Staats To express the new generators in terms of the old: when computing the Gröbner basis, use the ChangeMatrix => true option. Then, once you've computed a Gröbner basis b, call getChangeMatrix(b) to get the matrix of coefficients to express the new generators in terms of the old.
May 28, 2013 at 15:49 history answered Allen Knutson CC BY-SA 3.0