RestrictedWhiteheadAutoSet Class Reference

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

Inheritance diagram for RestrictedWhiteheadAutoSet:

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.

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.

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.

Implements AutoSet.

Definition at line 153 of file WhiteheadAutoSet.h.

References theSet.

Definition at line 156 of file WhiteheadAutoSet.h.

Definition at line 155 of file WhiteheadAutoSet.h.

Referenced by getSet().

The documentation for this class was generated from the following file: