Fixed bug in the matroid realization space code - #6207
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…on can kill the saturated ideal.
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topic: combinatorics
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antonydellavecchia
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Sep 1, 2026
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looks good for the most part I would just make sure to use the accesor functions
Co-authored-by: antonydellavecchia <antonydellavecchia@gmail.com>
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Thanks for the comment. I now edited the code to use the access functions consistently. |
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…e-after-reduce # Conflicts: # experimental/MatroidRealizationSpaces/test/runtests.jl
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The last commit just fixes the small merge conflict in the runtests. |
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The reduction pass that runs after saturation can destroy saturatedness:
eliminating a variable via a solution with a nontrivial denominator (a
unit on the localized space, certified through the inequations) clears
that denominator into the substituted generators, and the resulting
ideal can pick up components supported inside its vanishing locus. The
chart stays correct as a localized scheme, but the returned defining
ideal is then not saturated, contrary to what saturate=true promises —
on the matroid in the added test, a non-basis minor of the returned
matrix does not even lie in the returned ideal.
Fix: alternate reduction and stepwise saturation until the reduction
stabilizes; saturation runs only after a reduction that eliminated
variables, and each productive reduction strictly decreases the
variable count, so the loop terminates.
I added a test case which failed before and now works fine.