morphisms of simplicial complexes and the associated chain complex morphisms

[antieau]

Add functionality to sage to create morphisms between simplicial complexes, and to associate to these morphisms the chain complex maps on the homological and cohomological chain complexes.

CC: @jhpalmieri

Component: algebraic topology

Author: D. Benjamin Antieau

Reviewer: John Palmieri

Merged: sage-4.3.alpha1

Issue created by migration from https://trac.sagemath.org/ticket/6099

[antieau]

Attachment: 12335.patch.gz

This patch implements the chain complex morphisms part of this trac ticket.

[antieau]

Attachment: 6099-1.patch.gz

This patch implements the chain complex morphisms part of this trac ticket.

[antieau]

comment:1

Ignore 12335.patch. I would take it off, but I do not know how.

[antieau]

comment:2

Attachment: 6099-2.patch.gz

[antieau]

Attachment: 6099-3.patch.gz

tweak to be compatibe with #6141, which changes facets to facets().

[jhpalmieri]

comment:3

It's great that you're working on this. It looks very good, but there are a few issues:

• in the docstring for effective_vertices, you might mention that it returns a Simplex. The docstring could start "The set of vertices belonging to some face, as a simplex", and you could also put in a doctest like

sage: type(S.effective_vertices())
<class 'sage.homology.simplicial_complex.Simplex'>

• I had a few doctest failures which I think are fixed in miscellaneous additions to simplicial complex class; clique complex method for graphs #6309 (two extra periods), but they should be fixed here.

• Is it a good idea to have domain and codomain methods for morphisms? I can imagine someone wanting to use the domain of the fiber product, for example, but they won't see the _domain attribute on tab completion.

• You don't have 100% documentation and doctest coverage. Type 'sage -coverage ...insert_path_here.../sage/homology' to get a summary. When you do this, note that messages like

Possibly wrong (function name doesn't occur in doctests):
    * _repr_(self):

can be avoided if you add "# indirect doctest", like this:

           sage: x = i.associated_chain_complex_morphism()
           sage: x # indirect doctest

• Should "product" be renamed "fiber_product" so it's less ambiguous?

• I wonder if ChainComplexMorphism should inherit from ModuleElement rather than SageObject. Then you would define a method _mul_ (rather than __mul__), and similarly for _add_, and you could also define _lmul_ and _rmul_ to deal with scalar multiplication. Check the Sage reference manual, the "Coercion" section. (This section is newly added to the reference manual, as of Sage 4.0.1 or 4.0.2, I think.)

• I'm attaching a small patch which adds the new files to the reference manual. (This involves editing one file, doc/en/reference/homology.rst, and also because of the way reST works, I had to change

- D. Benjamin Antieau <d.ben.antieau@gmail.com> (2009.06)

to

- \D. Benjamin Antieau <d.ben.antieau@gmail.com> (2009.06)

(The "D." at essentially the beginning of the line seemed to tell Sphinx that this was part of a numbered list, starting with number 4.) Feel free to incorporate my changes and produce one single patch which does everything here.