Opened 8 years ago

Closed 8 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:

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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 8 years ago.
trac_13725-sum-complex-review-ts.patch (5.2 KB) - added by tscrim 8 years ago.

Download all attachments as: .zip

Change History (7)

comment:1 Changed 8 years ago by jhpalmieri

  • Status changed from new to needs_review

comment:2 Changed 8 years ago by jhpalmieri

  • Cc tscrim stumpc5 added

Changed 8 years ago by jhpalmieri

comment:3 Changed 8 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.


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

Changed 8 years ago by tscrim

comment:4 Changed 8 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 8 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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