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The package provides two ways for computing minimal presentations. One is via Apéry sets and non-connected graphs (Betti elements), while the other uses elimination of variables in ideals of polynomials.
The first approach is faster when the number of generators is high and the multiplicity is small. However, in general, the elimination approach is faster, even more if one loads singular or 4ti2interface.
We should at some point decide what to do with this, or try to improve the Apéry set approach by using dynamic factorizations.
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