A random word of length at most n in the generators of M.
A random word (of length at most the order of M) in the generators of M.
Rep(M) : MonRWS -> MonRWSElt
An element chosen from M.
Search: MonStgElt Default: "DFS"
Create the set of words, w, in M with a ≤ length(w) ≤b.
If Search is set to "DFS" (depth-first search) then words
are enumerated in lexicographical order. If Search is
set to "BFS" (breadth-first-search) then words are enumerated in
lexicographical order for each individual length
(i.e. in short-lex order). Depth-first-search is marginally quicker.
Since the result is a set the words may not appear in the resultant
set in the search order specified (although internally they
will be enumerated in this order).
Search: MonStgElt Default: "DFS"
Create the set of words that is the carrier set of M.
If Search is set to "DFS" (depth-first search) then words
are enumerated in lexicographical order. If Search is
set to "BFS" (breadth-first-search) then words are enumerated in
lexicographical order for each individual length
(i.e. in short-lex order). Depth-first-search is marginally quicker.
Since the result is a set the words may not appear in the resultant
set in the search order specified (although internally they
will be enumerated in this order).
Search: MonStgElt Default: "DFS"
Create the sequence S of words, w, in M with a ≤ length(w) ≤b.
If Search is set to "DFS" (depth-first search) then words
will appear in S in lexicographical order. If Search is
set to "BFS" (breadth-first-search) then words will appear in S in
lexicographical order for each individual length
(i.e. in short-lex order). Depth-first-search is marginally quicker.
Search: MonStgElt Default: "DFS"
Create a sequence S of words from the carrier set of M.
If Search is set to "DFS" (depth-first search) then words
will appear in S in lexicographical order. If Search is
set to "BFS" (breadth-first-search) then words will appear in S in
lexicographical order for each individual length
(i.e. in short-lex order). Depth-first-search is marginally quicker.
We construct the group D 22, together with a representative
word from the group, a random word and a random word of length at most 5
from the group, and the set of elements of the group.
> FM<a,b,c,d,e,f> := FreeMonoid(6);
> Q := quo< FM | a^2=1, f^2=1,
> d*a=a*c, e*b=b*f, d*c=c*e, d*f=a*d, a*e=e*b, b*f*c=f >;
> M<a,b,c,d,e,f> := RWSMonoid(Q);
> print Order(M);
22
> print Representative(M);
Id(M)
> print Random(M);
c * e
> print Random(M, 5);
d
> Set(M);
{ a * c, e, a * d, f, a * e, a * f, Id(M), a * c * e, b * a,
b * d, a * d * b, b * e, c * e, a * b * a, d * b, a * b * d,
a, a * b * e, b, c, a * b, d }
> Seq(M : Search := "BFS");
[ Id(M), a, b, c, d, e, f, a * b, a * c, a * d, a * e, a * f,
b * a, b * d, b * e, c * e, d * b, a * b * a, a * b * d,
a * b * e, a * c * e, a * d * b ]
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