sum complexes: another example of simplicial complexes

[jhpalmieri]

The attached patch adds a new collection of examples of simplicial complexes called "sum complexes". I'm interested in them because their homology can have large torsion groups relative to the number of vertices. For example:

sage: simplicial_complexes.SumComplex(13, [0,1,2,3,5]).homology(3)
C3 x C237 x C706565607945

That's a very large torsion group for a complex with only 13 vertices!

Depends on #12587

CC: @tscrim @stumpc5

Component: algebraic topology

Author: John Palmieri

Reviewer: Travis Scrimshaw

Merged: sage-5.6.beta2

Issue created by migration from https://trac.sagemath.org/ticket/13725

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

Dependencies: #12587

[tscrim]

comment:3

Attachment: trac_13725-sum-complex.patch.gz

Hey John,

I'm uploaded a small review patch which tweaks the generation code (basically I removed the temp variable k since len() is called only once for the for loop and made the output immutable from #12587), and separates out the doctests into generating the simplicial complex and the homology calculations. If you agree with the changes, feel free to set this to positive review.

Best,

Travis

PS - This applied cleanly for me over #12587, and I love the somewhat pathological examples that these simplicial complexes are.

[jhpalmieri]

comment:4

Attachment: trac_13725-sum-complex-review-ts.patch.gz

Your patch looks good to me. By the way, since writing my patch, I found an example, simplicial_complexes.SumComplex(13, [0,1,2,3,4,7]), whose fourth homology group is

C3 x C3 x C37209 x C14755222692546209667

It takes Sage several minutes to calculate this, so we shouldn't add it to the examples, but it's interesting to see how large the torsion can be for a complex with 13 vertices.

[jdemeyer]

Merged: sage-5.6.beta2