Implement tables indexed by arbitrary sage objects

[AndrewMathas]

Implement a wrapper for tables/matrices which are indexed by arbitrary sage objects. For example, this would allow for things like

EXAMPLES::

    sage: ct=CharacterTable( SymmetricGroup(5) ).display()
    Character table of Symmetric group of order 5! as a permutation group
    -------------------------
       | 1a 2a 2b 3a 6a 4a 5a
    ---|---------------------
    X0 |  1 -1  1  1 -1 -1  1
    X1 |  4 -2  0  1  1  0 -1
    X2 |  5 -1  1 -1 -1  1  0
    X3 |  6  0 -2  0  0  0  1
    X4 |  5  1  1 -1  1 -1  0
    X5 |  4  2  0  1 -1  0 -1
    X6 |  1  1  1  1  1  1  1
    sage: ct['X3']
    [6, 0, -2, 0, 0, 0, 1]
    sage: ct[3]
    [6, 0, -2, 0, 0, 0, 1]
    sage: ct[:,'3a']
    [1, 1, -1, 0, -1, 1, 1]
    sage: ct['X3','3a']
    0
    sage: ct.html_display()   # display in web browser using #14104

There should also be an HTML interface as per #14104.

This is related to #13131, which provides better formatting for tables in sage, however the main thrust here is different as we want to index matrices/tables by other sage objects.

Preliminary patch is attached. It has quite a lot of documentation, however, I would like to add sections on how the labelled, reordering, options, ... all work. Some of the examples depend upon #13605 which gives extended options for printing partitions. The are a few minor issues to be fixed including refactoring the repr/latex/html methods.

Comments welcome.

Depends on #14104
Depends on #13605

CC: @jhpalmieri @sagetrac-nborie @nthiery @slel @tscrim @zerline

Component: user interface

Keywords: days45

Author: Andrew Mathas

Branch/Commit: u/andrew.mathas/ticket/14103 @ e99e281

Issue created by migration from https://trac.sagemath.org/ticket/14103

[AndrewMathas]

Dependencies: 14104

[AndrewMathas]

Changed dependencies from 14104 to 14104, 13605

[AndrewMathas]

Fixing function call to html_display which changed in #14104

[AndrewMathas]

comment:13

Attachment: trac_14103--labelled_matrices-am.patch.gz

[AndrewMathas]

Changed keywords from none to sage45

[AndrewMathas]

Changed keywords from sage45 to days45

[AndrewMathas]

Branch: u/andrew.mathas/ticket/14103

[tscrim]

Commit: 9b3a91f

[tscrim]

New commits:

9b3a91f

Implment matrices/arrays in sage which can be indexed by arbitrary sage objects

[sagetrac-git]

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

0745281

Merge branch 'master' into labelled_matrices-14103

[sagetrac-git]

Changed commit from 9b3a91f to 0745281

[sagetrac-elixyre]

Changed commit from 0745281 to b0f5503

[sagetrac-elixyre]

Changed branch from u/andrew.mathas/ticket/14103 to u/elixyre/ticket/14103

[sagetrac-elixyre]

Changed dependencies from 14104, 13605 to #14104, #13605

[sagetrac-elixyre]

comment:21

Please load #14104 in repository too.

---

New commits:

96201fd	Merge branch '63b4' into labelled_matricess/14103
b0f5503	Ticket 14103: please load 14104 in the git repository

[AndrewMathas]

comment:22

I thought that I'd already created a git branch for this commit? Perhaps I didn't push it? As far as I can see your commit didn't change the ticket is that right. I'll update both of these tickets when I get a chance but it may not be until next week as I am travelling.

[AndrewMathas]

Changed branch from u/elixyre/ticket/14103 to u/andrew.mathas/ticket/14103

[sagetrac-git]

Changed commit from b0f5503 to e99e281

[sagetrac-git]

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

c917c14	20618: imported sage.modules.tutorial_free_modules and thematic_tutorials/tutorial-implementing-algebraic-structures from the Sage-Combinat queue
7b7706c	20618: fixed missing file
a9af7a4	Merge branch 'develop' of git://trac.sagemath.org/sage into develop
5fae48b	Fixing src/sage/modules/all.py
6d89fe5	Merge branch 'develop' of git://trac.sagemath.org/sage into develop
f433f7b	Merge branch 'develop' of git://trac.sagemath.org/sage into develop
8cc9856	Merge branch 'develop' into labelled_matrices-14103
e99e281	Updating doc-tests