Add graphical output to operation tables

[rbeezer]

Operation tables can be output as grids with color or grayscale squares representing the different elements of the algebraic structure. Adding these into sage.matrix.operation_table.OperationTable would be a nice self-contained project for someone looking for a project involving plotting and graphics. Despite the localized nature of the project, it would see wide applicability throughout Sage. Look for stubs in the source code,

I'm pretty sure Mathematica does this for groups (Cayley table), but I can't get Wolfram Alpha or MathWorld to cough it up again for me now that I want it.

Component: graphics

Keywords: plotting, cayley table

Author: Bruno Edwards

Branch/Commit: da8a8f5

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/8598

[DaveWitteMorris]

comment:1

The basic functionality can be obtained from matplotlib by using matrix_plot:

sage: def color_table(OT, cmap):
....:     return matrix_plot(matrix(OT._table), cmap=cmap)

sage: import matplotlib.cm
sage: from sage.matrix.operation_table import OperationTable
sage: OT = OperationTable(SymmetricGroup(3), operation=operator.mul)
sage: color_table(OT, matplotlib.cm.gist_rainbow)
Launched png viewer for Graphics object consisting of 1 graphics primitive

However, this picture has an unwanted border with tick marks, and the names of group elements should (optionally) be put in the boxes. See the multiplication tables created by Group Explorer for what the output should look like.

As in Group Explorer, there should be an option to organize the elements of the group by the cosets of a subgroup H (and use the same color for all elements of each coset), but that could be moved to a separate ticket if it turns out to be difficult.

This project will require an understanding of matplotlib and basic abstract algebra (groups, subgroups, and cosets). It will only be useful for fairly small groups, so there should not be any need for clever optimizations. The source code for OperationTable has stubs for color_table() and gray_table(), but only the color_table method is needed, because gray-scale output can be obtained by choosing a grayscale colormap.

[mkoeppe]

comment:4

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[Bruno-TT]

comment:9

I've just opened a PR here #109

Haven't contributed to sage before so please let me know if I've done anything wrong / need to do anything else!

[Bruno-TT]

comment:11

Replying to Dave Morris:

The basic functionality can be obtained from matplotlib by using matrix_plot:

sage: def color_table(OT, cmap):
....:     return matrix_plot(matrix(OT._table), cmap=cmap)

sage: import matplotlib.cm
sage: from sage.matrix.operation_table import OperationTable
sage: OT = OperationTable(SymmetricGroup(3), operation=operator.mul)
sage: color_table(OT, matplotlib.cm.gist_rainbow)
Launched png viewer for Graphics object consisting of 1 graphics primitive

However, this picture has an unwanted border with tick marks, and the names of group elements should (optionally) be put in the boxes. See the multiplication tables created by Group Explorer for what the output should look like.

As in Group Explorer, there should be an option to organize the elements of the group by the cosets of a subgroup H (and use the same color for all elements of each coset), but that could be moved to a separate ticket if it turns out to be difficult.

This project will require an understanding of matplotlib and basic abstract algebra (groups, subgroups, and cosets). It will only be useful for fairly small groups, so there should not be any need for clever optimizations. The source code for OperationTable has stubs for color_table() and gray_table(), but only the color_table method is needed, because gray-scale output can be obtained by choosing a grayscale colormap.

There's no immediately obvious way to implement coset functionality here, since the OperationTable type supports all magmas rather than just groups - I think we should have a separate ticket for this.

[dimpase]

comment:12

Replying to @Bruno-TT:

I've just opened a PR here #109

Haven't contributed to sage before so please let me know if I've done anything wrong / need to do anything else!

Could you please add a branch here? We don't take PRs on github yet.

To do so, upload a public ssh key from an ssh keypair to your github account, then
you can push your branch, whose name should have the correct prefix, u/gh-Bruno-TT/...

$ git remote add trac git@trac.sagemath.org:sage.git
$ git checkout -b u/gh-Bruno-TT/ticket_8598 # or something like this
$ git puch trac HEAD

and add the branch name, i.e. u/gh-Bruno-TT/ticket_8598 into Branch: field.

[Bruno-TT]

Author: gh-Bruno-TT