Basic Examples 
(3)
 

Get the orientation of a simplex:
In[1]:=
[◼]
SimplexOrientation
[Simplex[{a,b}]]
Out[1]=
1
In[2]:=
[◼]
SimplexOrientation
[Simplex[{b,a}]]
Out[2]=
-1
———
Find the permutations of the vertices of a simplex that are equivalent to the original simplex:
In[1]:=
s=Simplex[{a,b,c}]
Out[1]=
Simplex[{a,b,c}]
In[2]:=
p=Simplex/@Permutations@@s
Out[2]=
{Simplex[{a,b,c}],Simplex[{a,c,b}],Simplex[{b,a,c}],Simplex[{b,c,a}],Simplex[{c,a,b}],Simplex[{c,b,a}]}
In[3]:=
Selectp,
[◼]
SimplexOrientation
[#]===
[◼]
SimplexOrientation
[s]&
Out[3]=
{Simplex[{a,b,c}],Simplex[{b,c,a}],Simplex[{c,a,b}]}
———
Get orientations for a list of simplices:
In[1]:=
Simplex/@Permutations[{a,b,c}]
Out[1]=
{Simplex[{a,b,c}],Simplex[{a,c,b}],Simplex[{b,a,c}],Simplex[{b,c,a}],Simplex[{c,a,b}],Simplex[{c,b,a}]}
In[2]:=
[◼]
SimplexOrientation
[%]
Out[2]=
{1,-1,-1,1,1,-1}

Scope 
(6)
 


Properties and Relations 
(1)
 
