Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
KlausSutner`Automata`Sgroup`
Semigroup  |
| Semigroup[el,prop] represents a transformation semigroup. el prop | |
Examples
(1)
Basic Examples
(1)
In[1]:=
S=Semigroup
;
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In[2]:=
S//InputForm
Out[2]//InputForm=
Semigroup[{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}]},
<|Generators -> {SGT[{2, 3, 5, 7, 5, 7, 3, 2}],
SGT[{1, 4, 6, 8, 6, 8, 4, 1}]}, Witnesses ->
{a, b, aa, ab, ba, bb, aaa, aab, aba,
abb, baa, bab, bba, bbb},
Equations -> {aaaa -> aaa, aaab -> aab,
aaba -> aba, aabb -> abb, abaa -> baa,
abab -> bab, abba -> bba, abbb -> bbb,
baaa -> aaa, baab -> aab, baba -> aba,
babb -> abb, bbaa -> baa, bbab -> bab,
bbba -> bba, bbbb -> bbb}|>]
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}]},
<|Generators -> {SGT[{2, 3, 5, 7, 5, 7, 3, 2}],
SGT[{1, 4, 6, 8, 6, 8, 4, 1}]}, Witnesses ->
{a, b, aa, ab, ba, bb, aaa, aab, aba,
abb, baa, bab, bba, bbb},
Equations -> {aaaa -> aaa, aaab -> aab,
aaba -> aba, aabb -> abb, abaa -> baa,
abab -> bab, abba -> bba, abbb -> bbb,
baaa -> aaa, baab -> aab, baba -> aba,
babb -> abb, bbaa -> baa, bbab -> bab,
bbba -> bba, bbbb -> bbb}|>]
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""