Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
KlausSutner`Automata`Sgroup`
SemigroupElements  |
| SemigroupElements[S] returns a list of the elements of a transformation semigroup S. | |
Examples
(1)
Basic Examples
(1)
A small transformation semigroup (actually, a monoid) from generators.
In[1]:=
S=Semigroup
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In[2]:=
 | SemigroupElements |
Out[2]=
{SGT[{1,2,3,4,5,6,7,8}],SGT[{2,3,5,7,5,7,3,2}],SGT[{1,4,6,8,6,8,4,1}],SGT[{3,5,5,3,5,3,5,3}],SGT[{4,6,6,4,6,4,6,4}],SGT[{2,7,7,2,7,2,7,2}],SGT[{1,8,8,1,8,1,8,1}],SGT[{5,5,5,5,5,5,5,5}],SGT[{6,6,6,6,6,6,6,6}],SGT[{7,7,7,7,7,7,7,7}],SGT[{8,8,8,8,8,8,8,8}],SGT[{3,3,3,3,3,3,3,3}],SGT[{4,4,4,4,4,4,4,4}],SGT[{2,2,2,2,2,2,2,2}],SGT[{1,1,1,1,1,1,1,1}]}
We can extract elements with various special properties.
In[3]:=
Tabletp
[S,tp],{tp,{"Idempotent","RightNull","LeftNull","Null","RightUnit","LeftUnit","Unit","Regular"}}//Column
 | SemigroupElements |
Out[3]=
Idempotent{SGT[{1,2,3,4,5,6,7,8}],SGT[{5,5,5,5,5,5,5,5}],SGT[{6,6,6,6,6,6,6,6}],SGT[{7,7,7,7,7,7,7,7}],SGT[{8,8,8,8,8,8,8,8}],SGT[{3,3,3,3,3,3,3,3}],SGT[{4,4,4,4,4,4,4,4}],SGT[{2,2,2,2,2,2,2,2}],SGT[{1,1,1,1,1,1,1,1}]} |
RightNull{SGT[{5,5,5,5,5,5,5,5}],SGT[{6,6,6,6,6,6,6,6}],SGT[{7,7,7,7,7,7,7,7}],SGT[{8,8,8,8,8,8,8,8}],SGT[{3,3,3,3,3,3,3,3}],SGT[{4,4,4,4,4,4,4,4}],SGT[{2,2,2,2,2,2,2,2}],SGT[{1,1,1,1,1,1,1,1}]} |
LeftNull{} |
Null{} |
RightUnit{SGT[{1,2,3,4,5,6,7,8}]} |
LeftUnit{SGT[{1,2,3,4,5,6,7,8}]} |
Unit{SGT[{1,2,3,4,5,6,7,8}]} |
Regular{SGT[{1,2,3,4,5,6,7,8}],SGT[{5,5,5,5,5,5,5,5}],SGT[{6,6,6,6,6,6,6,6}],SGT[{7,7,7,7,7,7,7,7}],SGT[{8,8,8,8,8,8,8,8}],SGT[{3,3,3,3,3,3,3,3}],SGT[{4,4,4,4,4,4,4,4}],SGT[{2,2,2,2,2,2,2,2}],SGT[{1,1,1,1,1,1,1,1}]} |
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