Orlik-Solomon invariant algebra

[tkarn]

Implement a subclass of FiniteDimensionalInvariantModule specifically for the Orlik-Solomon algebra of a matroid, given an action on the groundset.

C.f. the related implementation for the Orlik-Terao algebra #32293 (which is not a dependency for this ticket).

[tkarn]

Last 10 new commits:

​372d407	Add example of symmetric functions with monomial basis
​4230c46	Fix _mul_ to assume that both are in same parent
​9914403	Edit exposition in symmetric function example
​c5f68e6	Add exposition in examples
​7863dc8	Reviewer changes for invariant modules.
​1be9d6f	Update input documentation
​051a45b	Add _test_invariant for TestSuite
​9b1bb9a	Initial commit
​abe0b40	Add tests
​9bd35c3	Add some tests, fix some tests, break some tests

[git]

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

​5eb896d

Fix mathematical error in tests and type error by adding Representation (mirroring the .invariant_module method of categories.FiniteDimensionalModuleWithBasis)

[git]

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

​3487e96

Clean up unneccessary actions, fix multiplication

[git]

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

​3436ce8

Add invariant option to Orlik-Solomon and to matroids

[tscrim]

New commits:

​e2491e2	Merge branch 'u/tkarn/os-invariants-32027' of git://trac.sagemath.org/sage into u/tkarn/os-invariants-32027
​d6ff85b	Reworking implementation to use OS algebra as ambient.

[git]

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

​5df9133

Initial review. Bug hunt is needed.

[git]

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

​f1f1d96

Adding an additional test for the vertex action. Agrees with known results.

[tkarn]

Reviewer changes look good to me.

[tkarn]

It occurred to me that we can speed this up for large examples by computing the annihilator_basis of each individual homogeneous component and forming a submodule from those since we know that the group action preserves degree when the group acts by ring automorphisms.

Preliminary testing indicates that the code as currently written performs better on small examples (groundset size < 5) and the computation degree-by-degree performs better when the groundset is bigger.

Should this optimization be implemented? If so in this ticket, or in another?

[tscrim]

I would do the optimization here since it would give more reason for having this subclass. Also I would always just do it in each degree since the small examples will be relatively fast (I would be surprised if they showed up in a tight loop).

[tscrim]

-        - optional parameter ``invariant`` -- (optional, default: None) either
-        a semigroup ``G`` whose ``__call__`` acts on the groundset, or pair
-        ``(G, action)`` where ``G`` is a semigroup and ``action``
-        is a function ``action(g,e)`` which takes a pair of a group
-        element and a grounset element and returns the groundset
-        element which is the result of ``e`` acted upon by ``g``
+        - ``invariant`` -- (optional) either a semigroup ``G`` such
+          that ``g(e)`` defines the action of a group element ``g``
+          on the groundset element ``e`` or pair ``(G, action)``,
+          where ``action(g, e)`` returns the action of ``g`` on ``e``

[tkarn]

New commits:

​5fec89e	Add invariant option to Orlik-Solomon and to matroids
​12689fb	Add reviewer changes to local branch
​1d1a9e0	Add note and fix minor typo
​c6d3b87	Fix PEP8 issues
​dc7ee44	Optimize computation of OS invariant via degree-by-degree computation. Fix PEP8 issues

[tscrim]

Just take care of the pyflakes warnings:

-import operator

-self._side = side = kwargs.pop('side', 'left')
+self._side = kwargs.pop('side', 'left')

and then this is a positive review.

[git]

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

​c12c512

Fix pyflakes issues

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​4006b40

Add kwargs to hyperplane OS