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:
Word ObjectOf< WordRep >

List of all members.

Public Member Functions

 ThompsonGroupFNormalForm ()
 ThompsonGroupFNormalForm (const Word &w)
bool operator== (const ThompsonGroupFNormalForm &nf) const
 Comparison operator.
ThompsonGroupFNormalFormoperator*= (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)

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 $w = n\cdot p$ To be finished.

Definition at line 29 of file ThompsonGroupFNormalForm.h.


Constructor & Destructor Documentation

ThompsonGroupFNormalForm::ThompsonGroupFNormalForm (  ) 

Referenced by operator-().

ThompsonGroupFNormalForm::ThompsonGroupFNormalForm ( const Word w  ) 

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.


Friends And Related Function Documentation

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

Reimplemented from Word.


The documentation for this class was generated from the following file:
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Generated on Mon Sep 26 18:43:51 2011 for CRyptography And Groups (CRAG) by  doxygen 1.6.1