Opened 10 months ago

Last modified 3 months ago

#30095 new enhancement

sage.tensor.modules: Add SymPowerFreeModule

Reported by: mkoeppe Owned by:
Priority: major Milestone: sage-9.4
Component: linear algebra Keywords:
Cc: egourgoulhon, dimpase, yzh, tscrim, gh-mjungmath Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #30229 Stopgaps:

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Description (last modified by mkoeppe)

FiniteRankFreeModule defines a method exterior_power, creating an instance of ExtPowerFreeModule.

We propose to add a method symmetric_power and class SymPowerFreeModule. (More generally, we could have submodules of tensors with prescribed symmetries; this is currently only available on the level of elements, not parents.)

They will be submodules of TensorFreeModules. (#30169 makes ExtPowerFreeModules quotients.)

The existing method FiniteRankFreeModule.sym_bilinear_form might be changed to produce elements of it for p=2.

Change History (10)

comment:1 Changed 10 months ago by mkoeppe

  • Cc tscrim added

comment:2 Changed 10 months ago by mkoeppe

  • Description modified (diff)

comment:3 Changed 10 months ago by mkoeppe

  • Cc gh-mjungmath added

comment:4 Changed 10 months ago by mkoeppe

  • Description modified (diff)

comment:5 Changed 10 months ago by mkoeppe

  • Description modified (diff)

comment:6 Changed 10 months ago by mkoeppe

  • Dependencies set to #30229

comment:7 Changed 9 months ago by gh-mjungmath

I think one has to be very careful here, especially with the last proposal. If the base field has not characteristic zero, as described also on Wikipedia, a symmetric bilinear form cannot be identified with an element of the symmetric algebra.

Addendum: I just noticed, we are not even in the manifold setting.

Last edited 9 months ago by gh-mjungmath (previous) (diff)

comment:8 Changed 9 months ago by mkoeppe

Thanks. Yes, we'll have to be careful

comment:9 Changed 9 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3

comment:10 Changed 3 months ago by mkoeppe

  • Milestone changed from sage-9.3 to sage-9.4

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