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Add part for graded objects and other improvements #3522

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@mahrud mahrud commented Oct 16, 2024

This PR is on top of #3519.

Summary of changes:

  • added part for modules, matrices, ideals, and rings
    • this is the same as part(ZZ, Complex), but for other graded objects
  • added cover, super, and ambient for Complex
  • added cover, super, and ambient for ComplexMap
    • these two are mostly for compatibility (e.g. I used them)
  • added basis(ZZ, Complex)
  • added basis(ZZ, ComplexMap)
    • this is a similar to part(ZZ, Complex), but the base ring is the original ring, not its coefficient ring
  • simplified part(ZZ, Complex)
  • simplified part(ZZ, ComplexMap)
  • simplified part using cover
    • the main reason I added cover here was so I could make this simplification
  • added better algorithm for basis(ZZ, Complex)
  • added better algorithm for truncate(ZZ, Complex)
  • added better algorithm for truncate(ZZ, ComplexMap)
    • this is way faster for large enough complexes
  • added tests for basis of Complex and ComplexMap
  • added method for truncating source of map more than target
    • we use this frequently in Varieties

The rest are optimizations in line with #3352 to eliminate unnecessary gb computations, though there's more work left.

  • cached subquotient gens in M.cache.Monomial
  • optimized basis(ZZ, Matrix)
  • used ??= to cache image, coker, coimage
  • added ways to avoid gb calls in inducedMap

@mahrud mahrud linked an issue Oct 16, 2024 that may be closed by this pull request
@mahrud mahrud requested a review from ggsmith October 16, 2024 03:52
@mahrud mahrud force-pushed the quickfix/part branch 2 times, most recently from be82d3e to b1eb629 Compare October 18, 2024 11:44
@mahrud mahrud marked this pull request as ready for review October 18, 2024 18:55
f := truncate(degs, dd^C_lo, opts);
complex hashTable for i from lo+1 to hi list i => (
f = inducedTruncationMap(source f, truncate(degs, C_i, opts), dd^C_i))
))

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Can we avoid calling Truncation within part?

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We do not call truncate within part. We do however call basis.

complex hashTable for i from lo+1 to hi list i => (
f = inducedBasisMap(source f, image basis(deg, C_i, opts), dd^C_i))
))

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The phrase basis of complex seems particularly unfortunate.

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From my perspective, the proposed changes need (at a minimum) documentation and tests before being accepted. In particular, I suspect that several of the methods do not typically return well-defined complexes or complex maps.

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mahrud commented Oct 28, 2024

From my perspective, the proposed changes need (at a minimum) documentation and tests before being accepted.

Tests have been included, I'm happy to add some documentation this week if otherwise the changes are acceptable.

In particular, I suspect that several of the methods do not typically return well-defined complexes or complex maps.

I'm happy to remove super and ambient for now if you suspect those are not well-defined (though I'm still curious to know why you suspect that or whether there are obvious examples I'm missing), but I use cover in the simplified version of part. Are there specifically issues for cover of a complex?

Alternatively, would it make sense to have an internal method for cover Complex that is used in part?

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mahrud commented Oct 29, 2024

I removed cover, super, ambient, and changed part to use an unexported cover' method.

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mahrud commented Oct 29, 2024

I also changed this PR to only depend on 4 specific commits from the basis PR, which in particular don't include any breaking change.

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bug in part(Complex)
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