ThompsonGroupFNormalForm Class Reference

Class ThompsonGroupFNormalForm (defines a representation of a normal form of an element of the Thompson's group F (infinitely generated))//. More...

#include <ThompsonGroupFNormalForm.h>

Inheritance diagram for ThompsonGroupFNormalForm:

List of all members.

Public Member Functions
	ThompsonGroupFNormalForm ()
	ThompsonGroupFNormalForm (const Word &w)
bool	operator== (const ThompsonGroupFNormalForm &nf) const
	Comparison operator.
ThompsonGroupFNormalForm &	operator*= (const ThompsonGroupFNormalForm &nf)
	Multiply the word on the right by another word (the result is reduced).
ThompsonGroupFNormalForm	operator* (const ThompsonGroupFNormalForm &nf) const
	Multiply two normal forms (the result is a normal form).
ThompsonGroupFNormalForm	operator- () const
	Multiply two normal forms (the result is a normal form).
Static Private Member Functions
static Word	semiNormalFormFor (const Word &w)
	Function returns a "sorted peak-like word" which can contain bad pairs of generators.
static list< int >	mergeUnits (list< int > &unit1, list< int > &unit2)
	Function merges 2 seminormal forms.
static int	nextOperation (int n1, int n2, int n3, int n4)
	Auxiliary function used in "mergeUnits".
static Word	removeBadPairs (const Word &w)
	Remove pairs of inverse generators in a seminormal form.
Friends
ostream &	operator<< (ostream &os, const ThompsonGroupFNormalForm &nf)

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Detailed Description

Class ThompsonGroupFNormalForm (defines a representation of a normal form of an element of the Thompson's group F (infinitely generated))//.

A normal form of an element of the Thompson's group F is a word To be finished.

Definition at line 29 of file ThompsonGroupFNormalForm.h.

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Constructor & Destructor Documentation

ThompsonGroupFNormalForm::ThompsonGroupFNormalForm

(

)

Referenced by operator-().

ThompsonGroupFNormalForm::ThompsonGroupFNormalForm

(

const Word &

w

)

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Member Function Documentation

static list< int > ThompsonGroupFNormalForm::mergeUnits	(	list< int > &	unit1,
		list< int > &	unit2
	)			[static, private]

Function merges 2 seminormal forms.

Referenced by operator*(), and operator*=().

static int ThompsonGroupFNormalForm::nextOperation	(	int	n1,
		int	n2,
		int	n3,
		int	n4
	)			[static, private]

Auxiliary function used in "mergeUnits".

ThompsonGroupFNormalForm ThompsonGroupFNormalForm::operator*

(

const ThompsonGroupFNormalForm &

nf

)

const [inline]

Multiply two normal forms (the result is a normal form).

Reimplemented from Word.

Definition at line 68 of file ThompsonGroupFNormalForm.h.

References Word::getList(), mergeUnits(), and removeBadPairs().

ThompsonGroupFNormalForm& ThompsonGroupFNormalForm::operator*=

(

const ThompsonGroupFNormalForm &

nf

)

[inline]

Multiply the word on the right by another word (the result is reduced).

Reimplemented from Word.

Definition at line 58 of file ThompsonGroupFNormalForm.h.

References Word::getList(), mergeUnits(), and removeBadPairs().

ThompsonGroupFNormalForm ThompsonGroupFNormalForm::operator-

(

)

const [inline]

Multiply two normal forms (the result is a normal form).

Reimplemented from Word.

Definition at line 76 of file ThompsonGroupFNormalForm.h.

References ThompsonGroupFNormalForm().

bool ThompsonGroupFNormalForm::operator==

(

const ThompsonGroupFNormalForm &

wr

)

const [inline]

Comparison operator.

Reimplemented from Word.

Definition at line 52 of file ThompsonGroupFNormalForm.h.

static Word ThompsonGroupFNormalForm::removeBadPairs

(

const Word &

w

)

[static, private]

Remove pairs of inverse generators in a seminormal form.

Referenced by operator*(), and operator*=().

static Word ThompsonGroupFNormalForm::semiNormalFormFor

(

const Word &

w

)

[static, private]

Function returns a "sorted peak-like word" which can contain bad pairs of generators.

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Friends And Related Function Documentation

ostream& operator<<	(	ostream &	os,
		const ThompsonGroupFNormalForm &	nf
	)			[friend]

Reimplemented from Word.

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

• ThompsonGroup/include/ThompsonGroupFNormalForm.h