A random word of length at most n in the generators of G.
A random word (of length at most the order of G) in the generators of G.
An element chosen from G.
Search: MonStgElt Default: "DFS"
Create the set of reduced words, w, in G 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 reduced words that is the carrier set of G. 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 reduced words, w, in G 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 reduced words in the carrier set of G. 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 D22, 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.
> FG<a,b,c,d,e,f> := FreeGroup(6);
> Q := quo< FG | a*c^-1*a^-1*d=1, b*f*b^-1*e^-1=1, c*e*c^-1*d^-1=1,
> d*f^-1*d^-1*a=1, e*b*e^-1*a^-1=1, f*c^-1*f^-1*b^-1=1>;
> G<a,b,c,d,e,f> := RWSGroup(Q);
> Representative(G);
Id(G)
> Random(G);
b
> Random(G, 5);
a * d * b
> Set(G);
{ a * d * b, a * b, a * b * e, a * c, a * d, d * b, b * e, a * b * a,
a * b * d, b * a, a * c * e, Id(G), b * d, c * e, e, f, a, a * e, b,
c, a * f, d }
> Seq(G : Search := "DFS");
[ Id(G), a, a * b, a * b * a, a * b * d, a * b * e, a * c, a * c * e,
a * d, a * d * b, a * e, a * f, b, b * a, b * d, b * e, c, c * e, d,
d * b, e, f ]