Regina Calculation Engine
Public Member Functions | List of all members
regina::NGroupExpression Class Reference

Represents an expression involving generators from a group presentation or a free group. More...

#include <algebra/ngrouppresentation.h>

Inheritance diagram for regina::NGroupExpression:
regina::ShareableObject regina::boost::noncopyable

Public Member Functions

 NGroupExpression ()
 The terms that make up this expression. More...
 
 NGroupExpression (const NGroupExpression &cloneMe)
 Creates a new expression that is a clone of the given expression. More...
 
std::list< NGroupExpressionTerm > & getTerms ()
 Returns the list of terms in this expression. More...
 
const std::list
< NGroupExpressionTerm > & 
getTerms () const
 Returns a constant reference to the list of terms in this expression. More...
 
unsigned long getNumberOfTerms () const
 Returns the number of terms in this expression. More...
 
unsigned long wordLength () const
 Returns the length of the word, i.e. More...
 
void erase ()
 Erases all terms from this this word. More...
 
NGroupExpressionTermgetTerm (unsigned long index)
 Returns the term at the given index in this expression. More...
 
const NGroupExpressionTermgetTerm (unsigned long index) const
 Returns a constant reference to the term at the given index in this expression. More...
 
unsigned long getGenerator (unsigned long index) const
 Returns the generator corresonding to the term at the given index in this expression. More...
 
long getExponent (unsigned long index) const
 Returns the exponent corresonding to the term at the given index in this expression. More...
 
void addTermFirst (const NGroupExpressionTerm &term)
 Adds the given term to the beginning of this expression. More...
 
void addTermFirst (unsigned long generator, long exponent)
 Adds the given term to the beginning of this expression. More...
 
void addTermLast (const NGroupExpressionTerm &term)
 Adds the given term to the end of this expression. More...
 
void addTermLast (unsigned long generator, long exponent)
 Adds the given term to the end of this expression. More...
 
void addTermsLast (const NGroupExpression &word)
 Multiplies *this on the right by word. More...
 
void addTermsFirst (const NGroupExpression &word)
 Multiplies *this on the left by word. More...
 
void cycleRight ()
 Given a word of the form g_i1^j1 g_i2^j2 ... More...
 
void cycleLeft ()
 Given a word of the form g_i1^j1 g_i2^j2 ... More...
 
NGroupExpressioninverse () const
 Returns a newly created expression that is the inverse of this expression. More...
 
void invert ()
 Inverts this expression. More...
 
NGroupExpressionpower (long exponent) const
 Returns a newly created expression that is this expression raised to the given power. More...
 
bool simplify (bool cyclic=false)
 Simplifies this expression. More...
 
bool substitute (unsigned long generator, const NGroupExpression &expansion, bool cyclic=false)
 Replaces every occurrence of the given generator with the given substite expression. More...
 
void writeXMLData (std::ostream &out) const
 Writes a chunk of XML containing this expression. More...
 
std::string toTeX () const
 Returns a TeX representation of this expression. More...
 
void writeTeX (std::ostream &out) const
 Writes a TeX represesentation of this expression to the given output stream. More...
 
void writeText (std::ostream &out, bool shortword=false) const
 Writes a text representation of this expression to the given output stream, using either numbered generators or alphabetic generators. More...
 
virtual void writeTextShort (std::ostream &out) const
 The text representation will be of the form g2^4 g13^-5 g4. More...
 
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing. More...
 
virtual ~ShareableObject ()
 Default destructor that does nothing. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
std::string str () const
 Returns the output from writeTextShort() as a string. More...
 
std::string toString () const
 A deprecated alias for str(), which returns the output from writeTextShort() as a string. More...
 
std::string detail () const
 Returns the output from writeTextLong() as a string. More...
 
std::string toStringLong () const
 A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More...
 

Additional Inherited Members

- Protected Member Functions inherited from regina::boost::noncopyable
 noncopyable ()
 A constructor which does nothing. More...
 
 ~noncopyable ()
 A destructor which does nothing. More...
 

Detailed Description

Represents an expression involving generators from a group presentation or a free group.

An expression is represented as word, i.e, a sequence of powers of generators all of which are multiplied in order. Each power of a generator corresponds to an individual NGroupExpressionTerm.

For instance, the expression g1^2 g3^-1 g6 contains the three terms g1^2, g3^-1 and g6^1 in that order.

Constructor & Destructor Documentation

regina::NGroupExpression::NGroupExpression ( )
inline

The terms that make up this expression.

Creates a new expression with no terms.

regina::NGroupExpression::NGroupExpression ( const NGroupExpression cloneMe)
inline

Creates a new expression that is a clone of the given expression.

Parameters
cloneMethe expression to clone.

Member Function Documentation

void regina::NGroupExpression::addTermFirst ( const NGroupExpressionTerm term)
inline

Adds the given term to the beginning of this expression.

Parameters
termthe term to add.
void regina::NGroupExpression::addTermFirst ( unsigned long  generator,
long  exponent 
)
inline

Adds the given term to the beginning of this expression.

Parameters
generatorthe number of the generator corresponding to the new term.
exponentthe exponent to which the given generator is raised.
void regina::NGroupExpression::addTermLast ( const NGroupExpressionTerm term)
inline

Adds the given term to the end of this expression.

Parameters
termthe term to add.
void regina::NGroupExpression::addTermLast ( unsigned long  generator,
long  exponent 
)
inline

Adds the given term to the end of this expression.

Parameters
generatorthe number of the generator corresponding to the new term.
exponentthe exponent to which the given generator is raised.
void regina::NGroupExpression::addTermsFirst ( const NGroupExpression word)

Multiplies *this on the left by word.

void regina::NGroupExpression::addTermsLast ( const NGroupExpression word)

Multiplies *this on the right by word.

void regina::NGroupExpression::cycleLeft ( )

Given a word of the form g_i1^j1 g_i2^j2 ...

g_in^jn converts the word into g_in^jn g_i1^j1 g_i1^j1 ... g_in-1^jn-1

void regina::NGroupExpression::cycleRight ( )

Given a word of the form g_i1^j1 g_i2^j2 ...

g_in^jn converts the word into g_i2^j2 ... g_in^jn g_i1^j1

void regina::NGroupExpression::erase ( )
inline

Erases all terms from this this word.

This effectively turns this word into the identity element.

long regina::NGroupExpression::getExponent ( unsigned long  index) const
inline

Returns the exponent corresonding to the term at the given index in this expression.

Index 0 represents the first term, index 1 represents the second term and so on.

Warning
This routine is O(n) where n is the number of terms in this expression.
Parameters
indexthe index of the term to return; this must be between 0 and getNumberOfTerms()-1 inclusive.
Returns
the requested exponent.
unsigned long regina::NGroupExpression::getGenerator ( unsigned long  index) const
inline

Returns the generator corresonding to the term at the given index in this expression.

Index 0 represents the first term, index 1 represents the second term and so on.

Warning
This routine is O(n) where n is the number of terms in this expression.
Parameters
indexthe index of the term to return; this must be between 0 and getNumberOfTerms()-1 inclusive.
Returns
the number of the requested generator.
unsigned long regina::NGroupExpression::getNumberOfTerms ( ) const
inline

Returns the number of terms in this expression.

For instance, the expression g1^2 g3^-1 g6 contains three terms. See also getWordLength().

Returns
the number of terms.
NGroupExpressionTerm& regina::NGroupExpression::getTerm ( unsigned long  index)

Returns the term at the given index in this expression.

Index 0 represents the first term, index 1 represents the second term and so on.

Warning
This routine is O(n) where n is the number of terms in this expression.
Parameters
indexthe index of the term to return; this must be between 0 and getNumberOfTerms()-1 inclusive.
Returns
the requested term.
const NGroupExpressionTerm& regina::NGroupExpression::getTerm ( unsigned long  index) const

Returns a constant reference to the term at the given index in this expression.

Index 0 represents the first term, index 1 represents the second term and so on.

Warning
This routine is O(n) where n is the number of terms in this expression.
Python:
Not present; only the non-const version of this routine is available.
Parameters
indexthe index of the term to return; this must be between 0 and getNumberOfTerms()-1 inclusive.
Returns
the requested term.
std::list< NGroupExpressionTerm > & regina::NGroupExpression::getTerms ( )
inline

Returns the list of terms in this expression.

These are the actual terms stored internally; any modifications made to this list will show up in the expression itself.

For instance, the expression g1^2 g3^-1 g6 has list consisting of three terms g1^2, g3^-1 and g6^1 in that order.

Python:
Not present; only the const version of this routine is available.
Returns
the list of terms.
const std::list< NGroupExpressionTerm > & regina::NGroupExpression::getTerms ( ) const
inline

Returns a constant reference to the list of terms in this expression.

For instance, the expression g1^2 g3^-1 g6 has list consisting of three terms g1^2, g3^-1 and g6^1 in that order.

Python:
This routine returns a python list of copied NGroupExpressionTerm objects. In particular, modifying this list or the terms within it will not modify the group expression from which they came.
Returns
the list of terms.
NGroupExpression* regina::NGroupExpression::inverse ( ) const

Returns a newly created expression that is the inverse of this expression.

The terms will be reversed and the exponents negated.

Returns
the inverse of this expression.
void regina::NGroupExpression::invert ( )

Inverts this expression.

Does not allocate or deallocate anything.

NGroupExpression* regina::NGroupExpression::power ( long  exponent) const

Returns a newly created expression that is this expression raised to the given power.

Note that the given exponent may be positive, zero or negative.

Parameters
exponentthe power to which this expression should be raised.
Returns
this expression raised to the given power.
bool regina::NGroupExpression::simplify ( bool  cyclic = false)

Simplifies this expression.

Adjacent powers of the same generator will be combined, and terms with an exponent of zero will be removed. Note that it is not assumed that the underlying group is abelian.

You may declare that the expression is cyclic, in which case it is assumed that terms may be moved from the back to the front and vice versa. Thus expression g1 g2 g1 g2 g1 simplifies to g1^2 g2 g1 g2 if it is cyclic, but does not simplify at all if it is not cyclic.

Parameters
cyclictrue if and only if the expression may be assumed to be cyclic.
Returns
true if and only if this expression was changed.
bool regina::NGroupExpression::substitute ( unsigned long  generator,
const NGroupExpression expansion,
bool  cyclic = false 
)

Replaces every occurrence of the given generator with the given substite expression.

If the given generator was found, the expression will be simplified once the substitution is complete.

Parameters
generatorthe generator to be replaced.
expansionthe substitute expression that will replace every occurrence of the given generator.
cyclictrue if and only if the expression may be assumed to be cyclic; see simplify() for further details.
Returns
true if and only if any substitutions were made.
std::string regina::NGroupExpression::toTeX ( ) const

Returns a TeX representation of this expression.

See writeTeX() for details on how this is formed.

Returns
a TeX representation of this expression.
unsigned long regina::NGroupExpression::wordLength ( ) const
inline

Returns the length of the word, i.e.

the number of letters with exponent +1 or -1 for which this word is expressable as a product.

For instance, the expression g1^2 g3^-1 g6 is a word of length four. See also getNumberOfTerms().

No attempt is made to remove redundant terms (so the word g g^-1 will count as length two).

Returns
the length of the word.
void regina::NGroupExpression::writeTeX ( std::ostream &  out) const

Writes a TeX represesentation of this expression to the given output stream.

The text representation will be of the form g_2^4 g_{13}^{-5} g_4.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
void regina::NGroupExpression::writeText ( std::ostream &  out,
bool  shortword = false 
) const

Writes a text representation of this expression to the given output stream, using either numbered generators or alphabetic generators.

The text representation will be of the form g2^4 g13^-5 g4. If the shortword flag is true, it will assume your word is in an alphabet of no more than 26 letters, and will write the word using lower-case ASCII, i.e. c^4 n^-5 e.

Precondition
If shortword is true, the number of generators in the corresponding group must be 26 or fewer.
Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
shortwordindicates whether to use numbered or alphabetic generators, as described above.
virtual void regina::NGroupExpression::writeTextShort ( std::ostream &  out) const
virtual

The text representation will be of the form g2^4 g13^-5 g4.

Implements regina::ShareableObject.

void regina::NGroupExpression::writeXMLData ( std::ostream &  out) const

Writes a chunk of XML containing this expression.

Python:
Not present.
Parameters
outthe output stream to which the XML should be written.

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

Copyright © 1999-2013, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).