B = minimalBetti I
B = minimalBetti(I, DegreeLimit=>d, LengthLimit=>len, Weights=>h)
Given a singly-graded module, this function computes the minimal betti numbers of the module. If the input is an ideal $I \subset S$, it computes the minimal betti numbers of $S^1/I$.
The algorithm used is based on the FastNonminimal algorithm, except that the complex is not constructed, resulting in a smaller memory footprint and often reduced computation time.
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One can compute smaller parts of the Betti table, by using DegreeLimit and/or LengthLimit.
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This function computes only as much of the non-minimal resolution as needed to compute the desired Betti numbers. Further calls will generally not recompute previously computed parts of the resolution, except that if you ask for a longer resolution than previously, it currently will recompute the resolution. This behavior might change in later releases.
If one has already computed the non-minimal free resolution using FastNonminimal, then one can use betti(...,Minimize=>...), except that it doesn't currently have support for DegreeLimit and LengthLimit, and probably still computes more than is needed (it is still experimental).
Only works over finite prime field. If the ideal or module is a non-homogeneous or multi-homogeneous object, then this function will result in an error.
The object minimalBetti is a method function with options.