Opened 7 years ago

Closed 7 years ago

#13725 closed enhancement (fixed)

sum complexes: another example of simplicial complexes

Reported by: jhpalmieri Owned by: jhpalmieri
Priority: minor Milestone: sage-5.6
Component: algebraic topology Keywords:
Cc: tscrim, stumpc5 Merged in: sage-5.6.beta2
Authors: John Palmieri Reviewers: Travis Scrimshaw
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #12587 Stopgaps:

Description

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!

Attachments (2)

trac_13725-sum-complex.patch (4.8 KB) - added by jhpalmieri 7 years ago.
trac_13725-sum-complex-review-ts.patch (5.2 KB) - added by tscrim 7 years ago.

Download all attachments as: .zip

Change History (7)

comment:1 Changed 7 years ago by jhpalmieri

  • Status changed from new to needs_review

comment:2 Changed 7 years ago by jhpalmieri

  • Cc tscrim stumpc5 added

Changed 7 years ago by jhpalmieri

comment:3 Changed 7 years ago by tscrim

  • Dependencies set to #12587
  • Reviewers set to Travis Scrimshaw

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.

Changed 7 years ago by tscrim

comment:4 Changed 7 years ago by jhpalmieri

  • Status changed from needs_review to positive_review

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.

comment:5 Changed 7 years ago by jdemeyer

  • Merged in set to sage-5.6.beta2
  • Resolution set to fixed
  • Status changed from positive_review to closed
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