Opened 10 months ago
Last modified 3 months ago
#30095 new enhancement
sage.tensor.modules: Add SymPowerFreeModule
Reported by: | mkoeppe | Owned by: | |
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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: |
Description (last modified by )
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 TensorFreeModule
s. (#30169 makes ExtPowerFreeModule
s 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
- Cc tscrim added
comment:2 Changed 10 months ago by
- Description modified (diff)
comment:3 Changed 10 months ago by
- Cc gh-mjungmath added
comment:4 Changed 10 months ago by
- Description modified (diff)
comment:5 Changed 10 months ago by
- Description modified (diff)
comment:6 Changed 10 months ago by
- Dependencies set to #30229
comment:7 Changed 9 months ago by
comment:8 Changed 9 months ago by
Thanks. Yes, we'll have to be careful
comment:9 Changed 9 months ago by
- Milestone changed from sage-9.2 to sage-9.3
comment:10 Changed 3 months ago by
- Milestone changed from sage-9.3 to sage-9.4
Setting new milestone based on a cursory review of ticket status, priority, and last modification date.
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.