Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Taggar`SimplicialHomology`
SimplicialIsomorphicQ  |
|
| | ||||
▪
constructs the incidence graphs of both complexes and tests them for isomorphism.
Examples
(6)
Basic Examples
(6)
Check whether two simplicial complexes are isomorphic:
In[1]:=
 | SimplicialIsomorphicQ |
 | SimplicialComplex |
| SimplicialComplex |
Out[1]=
True
Equal complexes are trivially isomorphic:
In[2]:=
 | SimplicialComplex |
| SimplicialComplex |
Out[2]=
True
Check that two unequal complexes are isomorphic:
In[1]:=
| SimplicialIsomorphicQ |
| SimplicialComplex |
| SimplicialComplex |
Out[1]=
True
Example of complexes that are not isomorphic:
In[1]:=
| SimplicialIsomorphicQ |
| SimplicialComplex |
| SimplicialComplex |
Out[1]=
False
A non-trivial example of isomorphism:
In[1]:=
| SimplicialIsomorphicQ |
| SimplicialComplex |
| SimplicialComplex |
Out[1]=
True
The Ziegler ball is not isomorphic to the Rudin ball:
In[1]:=
| SimplicialIsomorphicQ |
| SimplicialComplex |
| SimplicialComplex |
Out[1]=
False
Prove that the Poincare homology 3-sphere is not isomorphic to even though they have the same homology:
3
S
In[1]:=
| SimplicialIsomorphicQ |
| SimplicialComplex |
| SimplicialComplex |
Out[1]=
False
In[2]:=
| HomologyGroup |
| SimplicialComplex |
Out[2]=
0,10,20,3
In[3]:=
| HomologyGroup |
| SimplicialComplex |
Out[3]=
0,10,20,3
 |
|
 |
|
""