Further Examples: GroebnerBasis
Groebner bases are a generalization of row reduction.
The time and memory required to calculate a Groebner basis depend very much on the variable ordering, monomial ordering, and on which (if any) variables are regarded as constants.
For example, it is typical for degree reverse lexicographic monomial ordering to be faster and to give simpler output than pure lexicographic ordering, other things being the same.
We define a function to show the timing for six variations, as well as the number of polynomials, the number of terms in each polynomial, the total degree of each polynomial, and the largest coefficient in each polynomial.
Here is a set of polynomials. We do six Groebner bases on this set.