RestrictedWhiteheadAutoSet Class Reference

Implements a so-called restricted set of Whitehead automorphisms of a free group. More...

#include <WhiteheadAutoSet.h>

Inheritance diagram for RestrictedWhiteheadAutoSet:

AutoSet List of all members.

Public Member Functions

 RestrictedWhiteheadAutoSet (int n, bool use_conj=true)
 Constructor. Generates a set of restricted Whitehead automorphisms.
 ~RestrictedWhiteheadAutoSet ()
const Map & getRandomAuto () const
 Returns a random restricted Whitehead automorphism.
const SetOfMaps & getSet () const
 Returns the set of restricted Whitehead automorphisms.

Private Attributes

SetOfMaps theSet
int nGens

Detailed Description

Implements a so-called restricted set of Whitehead automorphisms of a free group.

In general the Restricted set of Whitehead automorphisms contains automorphisms of the type:

\[ x_i \rightarrow x_i x_j \]

\[ x_i \rightarrow x^{-1}_j x_i \]

\[ x_i \rightarrow x^{-1}_j x_i x_j, \]

where $ x_j, x_j \in X$ - generating set of the free group.

Definition at line 111 of file WhiteheadAutoSet.h.

Constructor & Destructor Documentation

RestrictedWhiteheadAutoSet::RestrictedWhiteheadAutoSet (  int  n,
bool  use_conj = true
) 
 

Constructor. Generates a set of restricted Whitehead automorphisms.

The set of restricted Whitehead automorphisms for a free group of rank n is generated.
Note, the whole set is generated by enumeration.

Parameters:
n - rank of a free group.
use_conj - if false the conjugation is excluded from the set. true is the default value.

RestrictedWhiteheadAutoSet::~RestrictedWhiteheadAutoSet (   )  [inline]
 

Definition at line 133 of file WhiteheadAutoSet.h.

Member Function Documentation

const Map& RestrictedWhiteheadAutoSet::getRandomAuto (   )  const
 

Returns a random restricted Whitehead automorphism.

Returns:
restricted Whitehead automorphisms selected uniformly randomly form the set.

const SetOfMaps& RestrictedWhiteheadAutoSet::getSet (   )  const [inline, virtual]
 

Returns the set of restricted Whitehead automorphisms.

Returns:
the set of restricted Whitehead automorphisms.

Implements AutoSet.

Definition at line 153 of file WhiteheadAutoSet.h.

References theSet.

Member Data Documentation

int RestrictedWhiteheadAutoSet::nGens [private]
 

Definition at line 156 of file WhiteheadAutoSet.h.

SetOfMaps RestrictedWhiteheadAutoSet::theSet [private]
 

Definition at line 155 of file WhiteheadAutoSet.h.

Referenced by getSet().

The documentation for this class was generated from the following file:
Generated on Sun Dec 3 10:59:04 2006 for CRyptography And Groups (CRAG) by  doxygen 1.4.6