Regina Calculation Engine
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regina::NPerm3 Class Reference

Represents a permutation of {0,1,2}. More...

#include <maths/nperm3.h>

Public Types

enum  { nPerms = 6, nPerms_1 = 2 }
 
enum  {
  code012 = 0, code021 = 1, code120 = 2, code102 = 3,
  code201 = 4, code210 = 5
}
 

Public Member Functions

 NPerm3 ()
 Creates the identity permutation. More...
 
 NPerm3 (int a, int b)
 Creates the transposition of a and b. More...
 
 NPerm3 (int a, int b, int c)
 Creates a permutation mapping (0,1,2) to (a,b,c) respectively. More...
 
 NPerm3 (const int *image)
 Creates a permutation mapping i to image[i] for each i = 0,1,2. More...
 
 NPerm3 (const NPerm3 &cloneMe)
 Creates a permutation that is a clone of the given permutation. More...
 
unsigned char getPermCode () const
 Returns the internal code representing this permutation. More...
 
void setPermCode (unsigned char code)
 Sets this permutation to that represented by the given internal code. More...
 
NPerm3operator= (const NPerm3 &cloneMe)
 Sets this permutation to be equal to the given permutation. More...
 
NPerm3 operator* (const NPerm3 &q) const
 Returns the composition of this permutation with the given permutation. More...
 
NPerm3 inverse () const
 Finds the inverse of this permutation. More...
 
int sign () const
 Determines the sign of this permutation. More...
 
int operator[] (int source) const
 Determines the image of the given integer under this permutation. More...
 
int preImageOf (int image) const
 Determines the preimage of the given integer under this permutation. More...
 
bool operator== (const NPerm3 &other) const
 Determines if this is equal to the given permutation. More...
 
bool operator!= (const NPerm3 &other) const
 Determines if this differs from the given permutation. More...
 
int compareWith (const NPerm3 &other) const
 Lexicographically compares the images of (0,1,2) under this and the given permutation. More...
 
bool isIdentity () const
 Determines if this is the identity permutation. More...
 
std::string toString () const
 A deprecated alias for str(), which returns a string representation of this permutation. More...
 
std::string str () const
 Returns a string representation of this permutation. More...
 
std::string trunc2 () const
 Returns a string representation of this permutation with only the images of 0 and 1. More...
 
int S3Index () const
 Returns the index of this permutation in the NPerm3::S3 array. More...
 
int SnIndex () const
 Returns the index of this permutation in the NPerm3::S3 array. More...
 
int orderedS3Index () const
 Returns the index of this permutation in the NPerm3::orderedS3 array. More...
 
int orderedSnIndex () const
 Returns the index of this permutation in the NPerm3::orderedS3 array. More...
 

Static Public Member Functions

static NPerm3 fromPermCode (unsigned char code)
 Creates a permutation from the given internal code. More...
 
static bool isPermCode (unsigned char code)
 Determines whether the given integer is a valid internal permutation code. More...
 

Static Public Attributes

static const NPerm3 S3 [6]
 Contains all possible permutations of three elements. More...
 
static const NPerm3Sn
 A dimension-agnostic alias for NPerm3::S3. More...
 
static const unsigned invS3 [6]
 Contains the inverses of the permutations in the array S3. More...
 
static const unsigned * invSn
 A dimension-agnostic alias for NPerm3::invS3. More...
 
static const NPerm3 orderedS3 [6]
 Contains all possible permutations of three elements in lexicographical order. More...
 
static const NPerm3orderedSn
 A dimension-agnostic alias for NPerm3::orderedS3. More...
 
static const NPerm3 S2 [2]
 Contains all possible permutations of two elements. More...
 
static const NPerm3Sn_1
 A dimension-agnostic alias for NPerm3::S2. More...
 

Friends

std::ostream & operator<< (std::ostream &out, const NPerm3 &p)
 Writes a string representation of the given permutation to the given output stream. More...
 

Detailed Description

Represents a permutation of {0,1,2}.

These objects are small enough to pass about by value instead of by reference. Moreover, they are extremely fast to work with.

Each permutation has an internal code, and this code is sufficient to reconstruct the permutation. Thus the internal code may be a useful means for passing permutation objects to and from the engine.

The internal code is an integer between 0 and 5 inclusive, representing the index of the permutation in the array NPerm3::S3.

This class is faster and sleeker than related classes such as NPerm4 and NPerm5. On the other hand, this class does not offer quite as rich an interface as the others.

Constructor & Destructor Documentation

regina::NPerm3::NPerm3 ( )
inline

Creates the identity permutation.

regina::NPerm3::NPerm3 ( int  a,
int  b 
)
inline

Creates the transposition of a and b.

Note that a and b need not be distinct.

Precondition
a and b are in {0,1,2}.
Parameters
athe element to switch with b.
bthe element to switch with a.
regina::NPerm3::NPerm3 ( int  a,
int  b,
int  c 
)
inline

Creates a permutation mapping (0,1,2) to (a,b,c) respectively.

Precondition
{a,b,c} = {0,1,2}.
Parameters
athe desired image of 0.
bthe desired image of 1.
cthe desired image of 2.
regina::NPerm3::NPerm3 ( const int *  image)
inline

Creates a permutation mapping i to image[i] for each i = 0,1,2.

Precondition
The array image contains three elements, which are 0, 1 and 2 in some order.
Python:
Not present.
Parameters
imagethe array of images.
regina::NPerm3::NPerm3 ( const NPerm3 cloneMe)
inline

Creates a permutation that is a clone of the given permutation.

Parameters
cloneMethe permutation to clone.

Member Function Documentation

int regina::NPerm3::compareWith ( const NPerm3 other) const
inline

Lexicographically compares the images of (0,1,2) under this and the given permutation.

Parameters
otherthe permutation with which to compare this.
Returns
-1 if this permutation produces a smaller image, 0 if the permutations are equal and 1 if this permutation produces a greater image.
NPerm3 regina::NPerm3::fromPermCode ( unsigned char  code)
inlinestatic

Creates a permutation from the given internal code.

Precondition
the given code is a valid permutation code; see isPermCode() for details.
Parameters
codethe internal code for the new permutation.
Returns
the permutation represented by the given internal code.
unsigned char regina::NPerm3::getPermCode ( ) const
inline

Returns the internal code representing this permutation.

Note that the internal code is sufficient to reproduce the entire permutation.

The code returned will be a valid permutation code as determined by isPermCode().

Returns
the internal code.
NPerm3 regina::NPerm3::inverse ( ) const
inline

Finds the inverse of this permutation.

Returns
the inverse of this permutation.
bool regina::NPerm3::isIdentity ( ) const
inline

Determines if this is the identity permutation.

This is true if and only if each of 0, 1 and 2 is mapped to itself.

Returns
true if and only if this is the identity permutation.
bool regina::NPerm3::isPermCode ( unsigned char  code)
inlinestatic

Determines whether the given integer is a valid internal permutation code.

Valid permutation codes can be passed to setPermCode() or fromPermCode(), and are returned by getPermCode().

Returns
true if and only if the given code is a valid internal permutation code.
bool regina::NPerm3::operator!= ( const NPerm3 other) const
inline

Determines if this differs from the given permutation.

This is true if and only if the two permutations have different images for at least one of 0, 1 or 2.

Parameters
otherthe permutation with which to compare this.
Returns
true if and only if this and the given permutation differ.
NPerm3 regina::NPerm3::operator* ( const NPerm3 q) const
inline

Returns the composition of this permutation with the given permutation.

If this permutation is p, the resulting permutation will be p o q, satisfying (p*q)[x] == p[q[x]].

Parameters
qthe permutation with which to compose this.
Returns
the composition of both permutations.
NPerm3 & regina::NPerm3::operator= ( const NPerm3 cloneMe)
inline

Sets this permutation to be equal to the given permutation.

Parameters
cloneMethe permutation whose value will be assigned to this permutation.
Returns
a reference to this permutation.
bool regina::NPerm3::operator== ( const NPerm3 other) const
inline

Determines if this is equal to the given permutation.

This is true if and only if both permutations have the same images for 0, 1 and 2.

Parameters
otherthe permutation with which to compare this.
Returns
true if and only if this and the given permutation are equal.
int regina::NPerm3::operator[] ( int  source) const
inline

Determines the image of the given integer under this permutation.

Parameters
sourcethe integer whose image we wish to find. This should be between 0 and 2 inclusive.
Returns
the image of source.
int regina::NPerm3::orderedS3Index ( ) const
inline

Returns the index of this permutation in the NPerm3::orderedS3 array.

Returns
the index i for which this permutation is equal to NPerm3::orderedS3[i]. This will be between 0 and 5 inclusive.
int regina::NPerm3::orderedSnIndex ( ) const
inline

Returns the index of this permutation in the NPerm3::orderedS3 array.

This is a dimension-agnostic alias for orderedS3Index().

Returns
the index i for which this permutation is equal to NPerm3::orderedS3[i]. This will be between 0 and 5 inclusive.
int regina::NPerm3::preImageOf ( int  image) const
inline

Determines the preimage of the given integer under this permutation.

Parameters
imagethe integer whose preimage we wish to find. This should be between 0 and 2 inclusive.
Returns
the preimage of image.
int regina::NPerm3::S3Index ( ) const
inline

Returns the index of this permutation in the NPerm3::S3 array.

Returns
the index i for which this permutation is equal to NPerm3::S3[i]. This will be between 0 and 5 inclusive.
void regina::NPerm3::setPermCode ( unsigned char  code)
inline

Sets this permutation to that represented by the given internal code.

Precondition
the given code is a valid permutation code; see isPermCode() for details.
Parameters
codethe internal code that will determine the new value of this permutation.
int regina::NPerm3::sign ( ) const
inline

Determines the sign of this permutation.

Returns
1 if this permutation is even, or -1 if this permutation is odd.
int regina::NPerm3::SnIndex ( ) const
inline

Returns the index of this permutation in the NPerm3::S3 array.

This is a dimension-agnostic alias for S3Index().

Returns
the index i for which this permutation is equal to NPerm3::S3[i]. This will be between 0 and 5 inclusive.
std::string regina::NPerm3::str ( ) const

Returns a string representation of this permutation.

The representation will consist of three adjacent digits representing the images of 0, 1 and 2 respectively. An example of a string representation is 120.

Returns
a string representation of this permutation.
std::string regina::NPerm3::toString ( ) const
inline

A deprecated alias for str(), which returns a string representation of this permutation.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a string representation of this permutation.
std::string regina::NPerm3::trunc2 ( ) const

Returns a string representation of this permutation with only the images of 0 and 1.

The resulting string will therefore have length two.

Returns
a truncated string representation of this permutation.

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  out,
const NPerm3 p 
)
friend

Writes a string representation of the given permutation to the given output stream.

The format will be the same as is used by NPerm3::str().

Parameters
outthe output stream to which to write.
pthe permutation to write.
Returns
a reference to out.

Member Data Documentation

const unsigned regina::NPerm3::invS3[6]
static

Contains the inverses of the permutations in the array S3.

Specifically, the inverse of permutation S3[i] is the permutation S3[ invS3[i] ].

const unsigned* regina::NPerm3::invSn
static

A dimension-agnostic alias for NPerm3::invS3.

In general, for each K the class NPermK will define an alias invSn that references the list of all permutations NPermK::invSK.

const NPerm3 regina::NPerm3::orderedS3[6]
static

Contains all possible permutations of three elements in lexicographical order.

const NPerm3* regina::NPerm3::orderedSn
static

A dimension-agnostic alias for NPerm3::orderedS3.

In general, for each K the class NPermK will define an alias orderedSn that references the list of all permutations NPermK::orderedSK.

const NPerm3 regina::NPerm3::S2[2]
static

Contains all possible permutations of two elements.

In each permutation, 2 maps to 2 and 3 maps to 3.

The permutations with even indices in the array are the even permutations, and those with odd indices in the array are the odd permutations.

For all permutation classes (NPerm3, NPerm4 and so on), the S2 array stores the same permutations in the same order (but of course using different data types).

Note that these permutations are already in lexicographical order.

const NPerm3 regina::NPerm3::S3[6]
static

Contains all possible permutations of three elements.

The permutations with even indices in the array are the even permutations, and those with odd indices in the array are the odd permutations.

For all permutation classes (NPerm3, NPerm4 and so on), the S3 array stores the same permutations in the same order (but of course using different data types).

Note that these permutations are not necessarily in lexicographical order.

const NPerm3* regina::NPerm3::Sn
static

A dimension-agnostic alias for NPerm3::S3.

In general, for each K the class NPermK will define an alias Sn that references the list of all permutations NPermK::SK.

const NPerm3* regina::NPerm3::Sn_1
static

A dimension-agnostic alias for NPerm3::S2.

In general, for each K the class NPermK will define an alias Sn_1 that references the list of all permutations NPermK::S(K-1).


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

Copyright © 1999-2014, 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).