Opened 3 years ago

Closed 3 years ago

Last modified 4 months ago

#20751 closed enhancement (fixed)

Check easy invariants first for simplicial complex isomorphism

Reported by: tscrim Owned by: tscrim
Priority: major Milestone: sage-7.3
Component: algebraic topology Keywords: days74
Cc: jhpalmieri, jeremy.l.martin Merged in:
Authors: Travis Scrimshaw Reviewers: John Palmieri
Report Upstream: N/A Work issues:
Branch: fbe4c3d (Commits) Commit:
Dependencies: #20720 Stopgaps:

Description (last modified by tscrim)

In order to more quickly check if two simplicial complexes are not isomorphic, we should check that their (ordered) facet dimension sequences agree.

We also check that edge labels are respected for the isomorphism, so isomorphisms of the fake degree vertex is not part of the isomorphism.

Change History (13)

comment:1 Changed 3 years ago by tscrim

  • Branch set to public/simplicial_complex/check_easy_invariants-20751
  • Commit set to 00c48e8de85d04e6001b739c6341cf5eb10341fe
  • Dependencies set to #20720
  • Status changed from new to needs_review

New commits:

7b1a299Having vertices() return a tuple instead of a Simplex.
3ace10eFixing a doctest in combinat/cluster_complex.py.
00c48e8trac 20720: referee changes

comment:2 Changed 3 years ago by git

  • Commit changed from 00c48e8de85d04e6001b739c6341cf5eb10341fe to 0af2d7ff13b3b8aea808f64810f73d1abd1cd2b7

Branch pushed to git repo; I updated commit sha1. New commits:

0af2d7fAdded check against the facet dimension sequence.

comment:3 Changed 3 years ago by git

  • Commit changed from 0af2d7ff13b3b8aea808f64810f73d1abd1cd2b7 to 69709a2e19a2cc6cd9633e31850dc0a38d7a5c24

Branch pushed to git repo; I updated commit sha1. New commits:

69709a2Make sure edge labels are respected

comment:4 Changed 3 years ago by git

  • Commit changed from 69709a2e19a2cc6cd9633e31850dc0a38d7a5c24 to fbe4c3df5d54c56812bb09b01f76826b6d7a7226

Branch pushed to git repo; I updated commit sha1. New commits:

fbe4c3dSome doc tweaks reflecting then new behavior.

comment:5 Changed 3 years ago by tscrim

  • Description modified (diff)

comment:6 Changed 3 years ago by jhpalmieri

I think the initial checks can slow things down. Actually, if two complexes are not isomorphic for "obvious" reasons, it is now much faster (by a factor of 40 on my machine) to check that they are not, but if they are actually isomorphic, it is slower (by a factor of 2) to check that. For these timings, I used the complexes Z1, Z2, Z3 from the doctests, and ran

%timeit Z1.is_isomorphic(Z2)  # True
%timeit Z1.is_isomorphic(Z3)  # False

comment:7 Changed 3 years ago by tscrim

It is not the initial checks that are slowing it down, it is the additional check(s) of edge labels for the graph isomorphism. The additional checks are very small (< 1%) in comparison to the isomorphism check (both with and without edge label checks), which you can see via

%lprun -f X.is_isomorphic X.is_isomorphic(X)

However, Jeremy found it necessary to check the edge labels, at least when we want the certificate. Yet we don't have an example where there is not an isomorphism but the graphs are isomorphic without preserving edge labels. So it might be feasible that we don't need to check the edge labels in that case...

comment:8 Changed 3 years ago by jhpalmieri

  • Reviewers set to John Palmieri
  • Status changed from needs_review to positive_review

comment:9 Changed 3 years ago by vbraun

  • Branch changed from public/simplicial_complex/check_easy_invariants-20751 to fbe4c3df5d54c56812bb09b01f76826b6d7a7226
  • Resolution set to fixed
  • Status changed from positive_review to closed

comment:10 Changed 4 months ago by jdemeyer

  • Commit fbe4c3df5d54c56812bb09b01f76826b6d7a7226 deleted

Exactly what is this doctest supposed to test?

        We check that :trac:`20751` is fixed::

            sage: C1 = SimplicialComplex([[1,2,3], [1,2,4], [1,3,4]])
            sage: C2 = SimplicialComplex([['j','k','l'], ['j','l','m'], ['j','k','m']])
            sage: C1.is_isomorphic(C2, certificate=True)
            (True, {1: 'j', 2: 'k', 3: 'l', 4: 'm'})

I am asking because the output is not unique (one can exchange vertices 2, 3 and 4).

Last edited 4 months ago by jdemeyer (previous) (diff)

comment:11 Changed 4 months ago by jdemeyer

I'll update that test to one with a unique output at #27027.

comment:12 Changed 4 months ago by tscrim

I believe the fake_vertex was getting added to the certificate in that test before this ticket.

comment:13 Changed 4 months ago by jdemeyer

Thanks for the info. So it shouldn't be a problem to replace that test with a different one.

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