Finite dimensional invariant algebra

[trevorkarn]

As part of the GSoC project #31929, we will implement a class for invariant algebras, given a group action on the basis of an algebra.

Depends on #31987

CC: @tscrim @trevorkarn

Component: algebra

Keywords: gsoc2021 invariant

Author: Trevor K. Karn

Branch/Commit: 2a64c19

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/31939

[trevorkarn]

New commits:

35f43f3	Initial commit
5526500	Add `__init__` and tests

[trevorkarn]

Commit: 5526500

[trevorkarn]

Branch: u/tkarn/invariant_modules_31939

[sagetrac-git]

Changed commit from 5526500 to c8b769b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

466a9bc	Add .invariant_algebra() method to ParentMethods of FiniteDimensionalModuleWithBasis
c8b769b	Rewrite FiniteDimensionalInvariantAlgebra to subclass UniqueRepresentation and SubmoduleWithBasis

[sagetrac-git]

Changed commit from c8b769b to 3c2a2f9

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

c1bafa5	Fix bad merge
775fae7	Remove @cached_method decorator from .invariant_algebra()
842b314	Move from algebras.invariants to modules.with_basis.invariant
37dafe9	WIP
3c2a2f9	Add FiniteDiimensionalInvariantModule with no tests/documentation

[trevorkarn]

Dependencies: #31987

[trevorkarn]

Changed keywords from gsoc invariant to gsoc2021 invariant

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

f0cadcc	Fix typos and whitespace issues
263b385	Initial commit of FiniteDimensionalTwistedInvariantModule
e767248	Fix multiplication and add tests
374207f	Fix cyclic action on generators of ExteriorAlgebra, add tests for the multiplication of group elements on the group algebra as a representation
7e423f8	Merge branch 'catrep' into invariants
5351ebb	Fix PEP8 spacing issue, simplify tuple
469286c	Merge branch 'catrep' into invariants
dc9a3d0	Fix whitespace issues
81f3bc4	Add tests and `_repr_` to finite_dimensional_invariant_algebras
beeda87	WIP

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Changed commit from 3c2a2f9 to beeda87

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Changed commit from beeda87 to 7cf2cf0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

7cf2cf0

WIP

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

a70d92c	WIP
3748265	Remove invariant algebra class
e981555	Remove OS changes
e0712a4	Modify invariant.py to work only in the Representation (not in the ambient module of the Representation)

[sagetrac-git]

Changed commit from 7cf2cf0 to e0712a4

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Changed commit from e0712a4 to 2c6ada7

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2c6ada7

Add tests for arithmetic in FiniteDimensionalInvariantModule, fix bug with multiplication of the underlying representation's underlying module's base ring

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f08d6f9	Add tests to invariant.py for full coverage
a5fab0c	Fix error introduced in representation.py
ff2047d	Add reference for invariants/twisted invariants
a15d52e	WIP
d2d1dde	Add check for valid characters for finite semigroups
d89c264	Add basis computation and initial commit of Element class

[sagetrac-git]

Changed commit from 2c6ada7 to d89c264

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

730baae	Add tests and `_repr_` to finite_dimensional_invariant_algebras
f4d5ed6	WIP
6ae01b4	Remove invariant algebra class
63ddf15	Remove OS changes
f93c224	Modify invariant.py to work only in the Representation (not in the ambient module of the Representation)
1c87493	Add tests for arithmetic in FiniteDimensionalInvariantModule, fix bug with multiplication of the underlying representation's underlying module's base ring
1792be1	Add tests to invariant.py for full coverage
d5bb24c	Remove draft of twisted invariant. Moved to trac #32145
f121263	Fix whitespace
f519fbc	Add _test_invariant for TestSuite

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Changed commit from d89c264 to f519fbc

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

3519cf1	Add _test_invariant for TestSuite
0b000e1	Add exposition to examples of invariant.py
f6f76c5	Fix invariant_module method inside the FiniteDimensionalModuleWithBasis.ParentMethods class
ac750a4	Add example of symmetric functions with monomial basis
42d5e34	Fix `_mul_` to assume that both are in same parent
c038ef5	Edit exposition in symmetric function example

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Changed commit from f519fbc to c038ef5

[trevorkarn]

comment:18

It was suggested to change the FiniteDimensionalInvariantModule._semigroup_representation attribute to be an alias of FiniteDimensionalInvariantModule._ambient. I chose not to use this suggestion because the semigroup representation is required to build the basis which we use to call the SubmoduleWithBasis.__init__ via super(), but the ._ambient attribute is defined in SubmoduleWithBasiis.__init__, so it seemed circular.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a75293a

Add exposition in examples

[sagetrac-git]

Changed commit from c038ef5 to a75293a

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

Changed branch from u/tkarn/invariant_modules_31939 to public/algebras/invariant_modules-31939

[tscrim]

Changed commit from a75293a to 553dc56

[tscrim]

comment:20

Thank you. I have made my reviewer pass through the code. Overall it looks great. However, I thought some more about what type of constructions we want it to handle. As a result, I made what the invariant module can handle much more general. This allows us to use a natural action, should it exist, or pass a general action (not necessarily one defined on the basis).

In order to make things work smoothly, I had to extend some stuff for Representation so it more naturally works with subgroups and coercion. I also removed the _l/rmul_ as those are generically implemented in the IndexedModuleElement class (I forgot about this; sorry!). I did some other documentation tweaks.

If my changes are good with you, then you can set a positive review.

---

New commits:

553dc56

Reviewer changes for invariant modules.

[sagetrac-git]

Changed commit from 553dc56 to 2a64c19

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2a64c19

Update input documentation

[trevorkarn]

comment:22

The changes made before commit 2a64c19 look good to me. If the changes to the documentation I made are good, then you can set a positive review.

[tscrim]

comment:23

Thanks.

[vbraun]

Changed branch from public/algebras/invariant_modules-31939 to 2a64c19