regina::NPerm Class Reference
[Triangulations]

Represents a permutation of {0,1,2,3}. More...

#include <nperm.h>

List of all members.

Public Member Functions
	NPerm ()
	Creates the identity permutation.
	NPerm (unsigned char newCode)
	Creates a permutation from the given internal code.
	NPerm (int a, int b)
	Creates the transposition of a and b.
	NPerm (int a, int b, int c, int d)
	Creates a permutation mapping (0,1,2,3) to (a,b,c,d) respectively.
	NPerm (int a0, int a1, int b0, int b1, int c0, int c1, int d0, int d1)
	Creates a permutation mapping (a0,b0,c0,d0) to (a1,b1,c1,d1) respectively.
	NPerm (const NPerm &cloneMe)
	Creates a permutation that is a clone of the given permutation.
unsigned char	getPermCode () const
	Returns the internal code representing this permutation.
void	setPermCode (unsigned char newCode)
	Sets this permutation to that represented by the given internal code.
void	setPerm (int a, int b)
	Sets this permutation to the transposition of a and b.
void	setPerm (int a, int b, int c, int d)
	Sets this permutation to that mapping (0,1,2,3) to (a,b,c,d) respectively.
NPerm &	operator= (const NPerm &cloneMe)
	Sets this permutation to be equal to the given permutation.
NPerm	operator* (const NPerm &q) const
	Returns the composition of this permutation with the given permutation.
NPerm	inverse () const
	Finds the inverse of this permutation.
int	sign () const
	Determines the sign of this permutation.
int	operator[] (int source) const
	Determines the image of the given integer under this permutation.
int	preImageOf (int image) const
	Determines the preimage of the given integer under this permutation.
bool	operator== (const NPerm &other) const
	Determines if this is equal to the given permutation.
bool	operator!= (const NPerm &other) const
	Determines if this differs from the given permutation.
int	compareWith (const NPerm &other) const
	Lexicographically compares the images of (0,1,2,3) under this and the given permutation.
bool	isIdentity () const
	Determines if this is the identity permutation.
std::string	toString () const
	Returns a string representation of this permutation.
std::string	trunc2 () const
	Returns a string representation of this permutation with only the images of 0 and 1.
std::string	trunc3 () const
	Returns a string representation of this permutation with only the images of 0, 1 and 2 included.
Static Public Member Functions
static bool	isPermCode (unsigned char newCode)
	Determines whether the given character is a valid internal permutation code.
Static Public Attributes
static const NPerm	S4 [24]
	Contains all possible permutations of four elements.
static const unsigned	invS4 [24]
	Contains the inverses of the permutations in the array S4.
static const NPerm	orderedS4 [24]
	Contains all possible permutations of four elements in lexicographical order.
static const NPerm	S3 [6]
	Contains all possible permutations of three elements.
static const unsigned	invS3 [6]
	Contains the inverses of the permutations in the array S3.
static const NPerm	orderedS3 [6]
	Contains all possible permutations of three elements in lexicographical order.
static const NPerm	S2 [2]
	Contains all possible permutations of two elements.
static const unsigned	invS2 [2]
	Contains the inverses of the permutations in the array S2.
Friends
std::ostream &	operator<< (std::ostream &out, const NPerm &p)

---

Detailed Description

Represents a permutation of {0,1,2,3}.

Such permutations are used in specifying how simplices are glued together. NPerm objects are small enough to pass about by value instead of by reference.

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 a character. The lowest two bits represent the image of 0, the next lowest two bits represent the image of 1 and so on.

Test:

Very thoroughly tested in the test suite.

---

Constructor & Destructor Documentation

regina::NPerm::NPerm

(

)

[inline]

Creates the identity permutation.

regina::NPerm::NPerm

(

unsigned char

newCode

)

[inline]

Creates a permutation from the given internal code.

Precondition:

the given code is a valid permutation code; see isPermCode() for details.

Parameters:

newCode

the internal code from which the new permutation will be created.

regina::NPerm::NPerm	(	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 {0,1,2,3}.

Parameters:

	a	the element to switch with b.
	b	the element to switch with a.

regina::NPerm::NPerm	(	int	a,
		int	b,
		int	c,
		int	d
	)			[inline]

Creates a permutation mapping (0,1,2,3) to (a,b,c,d) respectively.

Precondition:

{a,b,c,d} = {0,1,2,3}.

Parameters:

	a	the desired image of 0.
	b	the desired image of 1.
	c	the desired image of 2.
	d	the desired image of 3.

regina::NPerm::NPerm	(	int	a0,
		int	a1,
		int	b0,
		int	b1,
		int	c0,
		int	c1,
		int	d0,
		int	d1
	)			[inline]

Creates a permutation mapping (a0,b0,c0,d0) to (a1,b1,c1,d1) respectively.

Precondition:

{a0,b0,c0,d0} = {a1,b1,c1,d1} = {0,1,2,3}.

Parameters:

	a0	the desired preimage of a1.
	b0	the desired preimage of b1.
	c0	the desired preimage of c1.
	d0	the desired preimage of d1.
	a1	the desired image of a0.
	b1	the desired image of b0.
	c1	the desired image of c0.
	d1	the desired image of d0.

regina::NPerm::NPerm

(

const NPerm &

cloneMe

)

[inline]

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

Parameters:

cloneMe

the permutation to clone.

---

Member Function Documentation

int regina::NPerm::compareWith

(

const NPerm &

other

)

const

Lexicographically compares the images of (0,1,2,3) under this and the given permutation.

Parameters:

other

the 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.

unsigned char regina::NPerm::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.

NPerm regina::NPerm::inverse

(

)

const [inline]

Finds the inverse of this permutation.

Returns:

the inverse of this permutation.

bool regina::NPerm::isIdentity

(

)

const [inline]

Determines if this is the identity permutation.

This is true if and only if each of 0, 1, 2 and 3 is mapped to itself.

Returns:

true if and only if this is the identity permutation.

static bool regina::NPerm::isPermCode

(

unsigned char

newCode

)

[static]

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

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

Returns:

true if and only if the given code is a valid internal permutation code.

bool regina::NPerm::operator!=

(

const NPerm &

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, 2 or 3.

Parameters:

other

the permutation with which to compare this.

Returns:

true if and only if this and the given permutation differ.

NPerm regina::NPerm::operator*

(

const NPerm &

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:

q

the permutation with which to compose this.

Returns:

the composition of both permutations.

NPerm & regina::NPerm::operator=

(

const NPerm &

cloneMe

)

[inline]

Sets this permutation to be equal to the given permutation.

Parameters:

cloneMe

the permutation whose value will be assigned to this permutation.

Returns:

a reference to this permutation.

bool regina::NPerm::operator==

(

const NPerm &

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, 2 and 3.

Parameters:

other

the permutation with which to compare this.

Returns:

true if and only if this and the given permutation are equal.

int regina::NPerm::operator[]

(

int

source

)

const [inline]

Determines the image of the given integer under this permutation.

Parameters:

source

the integer whose image we wish to find. This should be between 0 and 3 inclusive.

Returns:

the image of source.

int regina::NPerm::preImageOf

(

int

image

)

const [inline]

Determines the preimage of the given integer under this permutation.

Parameters:

image

the integer whose preimage we wish to find. This should be between 0 and 3 inclusive.

Returns:

the preimage of image.

void regina::NPerm::setPerm	(	int	a,
		int	b,
		int	c,
		int	d
	)			[inline]

Sets this permutation to that mapping (0,1,2,3) to (a,b,c,d) respectively.

Precondition:

{a,b,c,d} = {0,1,2,3}.

Deprecated:

This routine is largely unnecessary, since NPerm objects are tiny and cheap. Just use the assignment operator instead. This routine will eventually be removed entirely in a future version of Regina.

Parameters:

	a	the desired image of 0.
	b	the desired image of 1.
	c	the desired image of 2.
	d	the desired image of 3.

void regina::NPerm::setPerm	(	int	a,
		int	b
	)			[inline]

Sets this permutation to the transposition of a and b.

Note that a and b need not be distinct.

Precondition:

a and b are in {0,1,2,3}.

Deprecated:

This routine is largely unnecessary, since NPerm objects are tiny and cheap. Just use the assignment operator instead. This routine will eventually be removed entirely in a future version of Regina.

Parameters:

	a	the element to switch with b.
	b	the element to switch with a.

void regina::NPerm::setPermCode

(

unsigned char

newCode

)

[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:

newCode

the internal code that will determine the new value of this permutation.

int regina::NPerm::sign

(

)

const

Determines the sign of this permutation.

Returns:

1 if this permutation is even, or -1 if this permutation is odd.

std::string regina::NPerm::toString

(

)

const

Returns a string representation of this permutation.

The representation will consist of four adjacent digits representing the images of 0, 1, 2 and 3 respectively. An example of a string representation is 1302.

Returns:

a string representation of this permutation.

std::string regina::NPerm::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.

std::string regina::NPerm::trunc3

(

)

const

Returns a string representation of this permutation with only the images of 0, 1 and 2 included.

The resulting string will therefore have length three.

Returns:

a truncated string representation of this permutation.

---

Member Data Documentation

const unsigned regina::NPerm::invS2[2] [static]

Contains the inverses of the permutations in the array S2.

Specifically, the inverse of permutation S2[i] is the permutation S2[ invS2[i] ].

const unsigned regina::NPerm::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::NPerm::invS4[24] [static]

Contains the inverses of the permutations in the array S4.

Specifically, the inverse of permutation S4[i] is the permutation S4[ invS4[i] ].

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

Contains all possible permutations of three elements in lexicographical order.

In each permutation, 3 maps to 3.

const NPerm regina::NPerm::orderedS4[24] [static]

Contains all possible permutations of four elements in lexicographical order.

const NPerm regina::NPerm::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.

Note that the permutations are also in lexicographical order.

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

Contains all possible permutations of three elements.

In each permutation, 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.

Note that the permutations are not necessarily in lexicographical order.

const NPerm regina::NPerm::S4[24] [static]

Contains all possible permutations of four 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.

Note that the permutations are not necessarily in lexicographical order.

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

• nperm.h