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mahrud
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Feb 25, 2026
mahrud
commented
- fixed documentation of WeylAlgebras
- added minor improvements in WeylAlgebras
- cached holonomic basis in holonomicRank
antonleykin
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antonleykin
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Most of the cnages are straightforward and good.
There is an issue in holonomicRank that should be addressed but I'm not sure the current solution is the right one.
| else holRank = numgens source basis redI; | ||
| holRank | ||
| ) | ||
| -- Note: we don't compute dim redI, because coefficientRing W might nonzero dimension |
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What is your definition of the holonomic rank when the coefficient ring is not a field?
Can you give a use example?
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Good question! I haven't thought about the case when the coefficient ring is not a field, but as for use case, this is the backbone of the ConnectionMatrices packages, where a modified version of this method is currently being used:
https://github.com/Macaulay2/M2/blob/stable/M2/Macaulay2/packages/ConnectionMatrices/holonomic.m2
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I guess really the question is what does "basis" do when the coefficient ring is not a field, and I think it just gives a generating set? I'm not an expert, is holonomic rank over integers well defined?
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I'm not sure how to resolve this.
@mahrud, can you figure out what ConnectionMatrices authors think?
@michaelPerlman @lorinczandras @christineBerkesch , any opinion on generalization of holonomic rank?
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Sorry, I think I'm confused. I thought you were asking out of curiosity. Is anything else in Dmodules packages designed with non-field coefficient rings in mind? The package tutorial explicitly says:
This package is mostly concerned with computations in the Weyl algebra, the ring of differential operators over affine space (over a field of characteristic zero).
I also can't find any algorithms in the SST book that don't assume working over a field either.
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