WhiteheadMinimization Class Reference

Implements a greedy procedure of reducing a word to its minimal length. More...

#include <WhiteheadAutoSet.h>

List of all members.

Public Member Functions
	WhiteheadMinimization (int n)
	Constructor.
bool	isMinimal (const Word &w) const
	Test if the word is minimal.
Word	findMinimal (const Word &w, ostream *out=NULL) const
	Find a word of the minimal length.
const WhiteheadAutoSetType2 &	getSet () const
	Get the Whitehead set of type II.
Private Attributes
WhiteheadAutoSetType2	wSet

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Detailed Description

Implements a greedy procedure of reducing a word to its minimal length.

Greedy procedure applies automorphisms from a Whitehead set of type II to a word until its length is reduced. If a shorter image is found, procedure is applied to the shorten word. If none of the automorphisms can reduce the length, procedure stops and the shortest word is returned.

Definition at line 238 of file WhiteheadAutoSet.h.

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Constructor & Destructor Documentation

WhiteheadMinimization::WhiteheadMinimization

(

int

n

)

[inline]

Constructor.

A set of Whitehead automorphisms is created in the constructor. May not be applicable when the rank is large.

Parameters:

n

- the rank of a free group.

Definition at line 246 of file WhiteheadAutoSet.h.

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Member Function Documentation

Word WhiteheadMinimization::findMinimal	(	const Word &	w,
		ostream *	out = NULL
	)			const

Find a word of the minimal length.

Applies automorphisms from the Whitehead set to find a word of the minimal length in the automorphic orbit of a given word.

Parameters:

w

- initial word.

Returns:

a word of the minimal length in the orbit of w.

const WhiteheadAutoSetType2& WhiteheadMinimization::getSet

(

)

const [inline]

Get the Whitehead set of type II.

Returns:

the Whitehead set of type II.

Definition at line 271 of file WhiteheadAutoSet.h.

References wSet.

bool WhiteheadMinimization::isMinimal

(

const Word &

w

)

const

Test if the word is minimal.

Applies automorphisms from the Whitehead set to test if a given word has minimal length.

Parameters:

w

- word to be tested.

Returns:

true if w has the minimal length, false otherwise.

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Member Data Documentation

WhiteheadAutoSetType2 WhiteheadMinimization::wSet [private]

Definition at line 274 of file WhiteheadAutoSet.h.

Referenced by getSet().

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

• Maps/include/WhiteheadAutoSet.h