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meataxe: extend invariant form detection #5803

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fingolfin
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TODO: complete it, add tests

@hulpke
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hulpke commented Sep 30, 2024

A main change seems a change from IsomorphismIrred to IsomorphismModules. What I want to make sure is that there will not be a chance of running in infinite recursion.

I have not looked again into the code of these two functions, but the former is a straightforward spinning algorithm, while the second is a rather elaborate calculation that uses a lot of other MeatAxe routines.
This means that with this change, InvariantXXXForm cannot be used within routines that might get called from IsomorphismModules. This means that the tests need to cover a variety of module structures (direct sums of multiple isomorphic and non-isomorphic indecomposable components).

@fingolfin
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Calls to MTX.Invariant*Form in GAP:

$ git grep -P -l '\.Invariant.*Form' grp lib
lib/meataxe.gi

So nothing outside of lib/meataxe.gi calls this.
Looking closer at those calls in lib/meataxe.gi:

  • SMTX.InvariantQuadraticForm calls InvariantBilinearForm as a first step
  • SMTX.OrthogonalSign calls MTX.InvariantBilinearForm and MTX.InvariantQuadraticForm
  • however nothing in the library calls OrthogonalSign (only tests)

So all in all I don't see how this could cause a problem?

@fingolfin fingolfin added this to the GAP 4.14.0 milestone Oct 13, 2024
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