Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Taggar`SimplicialHomology`
SimplicialAutomorphismGroup  |
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Examples
(3)
Basic Examples
(3)
Find the automorphism group of a simplicial complex:
In[1]:=
 | SimplicialAutomorphismGroup |
 | SimplicialComplex |
Out[1]=
PermutationGroup[{Cycles[{{3,4}}],Cycles[{{2,3}}],Cycles[{{1,2}}]}]
In[2]:=
ResourceFunction["FindGroupIsomorphism"][%,SymmetricGroup[4]]
Out[2]=
{{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}}
In[1]:=
ResourceFunction["FindGroupIsomorphism"]
["RealProjectivePlane"],AlternatingGroup[5]
 | SimplicialAutomorphismGroup |
 | SimplicialComplex |
Out[1]=
{{1,4,14,19,57,60,27,34,42,47,12,9,50,55,35,30,37,40,17,20,23,18,54,59,46,39,8,5,28,25,52,49,31,26,44,41,24,21,11,6,32,29,45,48,3,10,16,13,58,51,43,38,15,22,33,36,7,2,53,56}}
Symmetries of a regular pentagon:
In[1]:=
| SimplicialAutomorphismGroup |
| SimplicialComplex |
Out[1]=
PermutationGroup[{Cycles[{{2,3},{4,5}}],Cycles[{{1,2},{3,4}}]}]
In[2]:=
GroupOrder[%]
Out[2]=
10
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""