MatrixMorphism: add support for morphisms acting on the left

[rud]

Morphisms between free modules over PIDs are always represented by matrices acting on the right.

The goal of this ticket is to modify matrix morphisms (sage/modules/matrix_morphism.py) by adding an optional keyword for left actions. This will have applications Ticket 25902 in which we build equivariant left-morphisms between G-lattices.

[git]

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

​e3eb2f7

fixed typos

[git]

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

​ffd5b16

fixed typos

[git]

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

​b779f07

free module morphisms are in a working state, vector space morphisms need to be modified to handle base ring extensions

[git]

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

​d7e1666

added sides to vector space morphisms

[git]

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

​f6071d1

fixed hom when codomains are not provided, changed basis and _matrix_space to cached methods

[git]

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

​4de01e3

added a method to switch sides, finished adapting methods, fixed a bug in hom where it could guess the wrong base ring if no codomain is specified, added tests

[roed]

Setting to needs review for patchbot.

[git]

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

​443cf6a	first commit, added a pushout, now the example in the description works as intended
​a209a54	commented the change
​9a66ea5	changed the pushout to an error
​67fb789	switched the fix to free modules homspaces
​25c62c1	fixed bugs
​4d9fd9a	changed the error type
​8f17598	added a test for the fix
​a6898b0	merged with t/31818

[git]

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

​fa796d1	fixed a typo
​15807ec	Merge branch 'u/rud/creating_a_module_homomorphism_with_a_matrix_may_build_the_wrong_codomain' of git://trac.sagemath.org/sage into t/31737/matrixmorphism__add_support_for_morphisms_acting_on_the_left
​dd528ed	completed a test
​da7a09b	Merge branch 'u/rud/creating_a_module_homomorphism_with_a_matrix_may_build_the_wrong_codomain' of git://trac.sagemath.org/sage into t/31737/matrixmorphism__add_support_for_morphisms_acting_on_the_left
​0548148	changed the pushout to hom

[git]

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

​a19088c

fixed a test

[git]

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

​4b66508

fixed typos

[tkarn]

Thanks for this! I'm a bit confused by the default side argument on line 72. I see that it defaults to side='left', but based on the description, it seems like side='right' might be "mathematical default." Does this make sense or am I missing something?

[rud]

Hi, it is indeed a little confusing. The "mathematical default" is indeed side='right', which corresponds to left-multiplication. The reason being that sage's side is the side of the vector relative to the matrix, whereas in mathematics we almost always refer to the side of the matrix relative to the vector.

The side argument already existed in the MatrixMorphism.matrix method, with this choice of left/right. The methods left_kernel/right_kernel, left_eigenspaces/right_eigenspaces also work with that convention.

Now the small problem that remains is that the default is side="left", but the way some methods are coded are done the other way and taking the transpose. For instance, matrix.kernel takes the transpose and calls the right_kernel method, which feels a little off. After this ticket, methods of MatrixMorphism? will call the appropriate one.

I realise this text might sound confusing, that's because it is somewhat confusing.

[git]

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

​2f73c05

fixed a typo

[git]

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

​58315ff

fixed some documentation

[git]

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

​b49d57c

fixed more documentation

[git]

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

​550a375

fixed a test in hom

[git]

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

​2999315

fixed some bugs by adding side arguments to hecke morphisms, and morphisms of abelian varieties

[mkoeppe]

Needs rebase

[git]

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

​cb41278

merged with develop

[git]

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

​536aaff

removed the pushout in hom

[git]

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

​c9fab37

fixed the restrict method

[git]

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

​178bac9

fixed typo

[roed]

New commits:

​37f25b3	Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism
​0acd41a	Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism
​b1aad89	Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism
​9d62ddf	Fix some doctest failures, remove trailing whitespace, add pushout back in
​3fb6c65	fixed blocks
​c4ebbea	Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism

[roed]

The build error doesn't seem to be from the changes in this ticket.