|
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
In this section we describe functions which allow the user to enumerate
various sets of elements of an automatic group G.
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.
Rep(G) : GrpAtc -> GrpAtcElt
An element chosen from G.
Search: MonStgElt Default: "DFS"
Create the set of 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 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 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 words from 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);
> F := 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 >;
> f, G<a,b,c,d,e,f> := IsAutomaticGroup(F);
Running Knuth-Bendix with the following parameter values
MaxRelations = 200
MaxStates = 0
TidyInt = 20
MaxWdiffs = 512
HaltingFactor = 100
MinTime = 5
#System is confluent.
#Halting with 41 equations.
#First word-difference machine with 16 states computed.
#Second word-difference machine with 17 states computed.
#System is confluent, or halting factor condition holds.
#Word-acceptor with 6 states computed.
#General multiplier with 58 states computed.
#Validity test on general multiplier succeeded.
#Checking inverse and short relations.
#Axiom checking succeeded.
> Representative(G);
Id(G)
> Random(G);
a*c;
> Random(G, 5);
a * 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 := "BFS");
[ Id(G), 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 ]
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
|
