Regina Calculation Engine

Represents a permutation of {0,1,2,3,4}. More...
#include <maths/nperm5.h>
Public Types  
enum  { nPerms = 120, nPerms_1 = 24 } 
Public Member Functions  
NPerm5 ()  
Creates the identity permutation. More...  
NPerm5 (int a, int b)  
Creates the transposition of a and b. More...  
NPerm5 (int a, int b, int c, int d, int e)  
Creates a permutation mapping (0,1,2,3,4) to (a,b,c,d,e) respectively. More...  
NPerm5 (const int *image)  
Creates a permutation mapping i to image[i] for each i = 0,1,2,3,4. More...  
NPerm5 (int a0, int a1, int b0, int b1, int c0, int c1, int d0, int d1, int e0, int e1)  
Creates a permutation mapping (a0,b0,c0,d0,e0) to (a1,b1,c1,d1,e1) respectively. More...  
NPerm5 (const NPerm5 &cloneMe)  
Creates a permutation that is a clone of the given permutation. More...  
unsigned  getPermCode () const 
Returns the internal code representing this permutation. More...  
void  setPermCode (unsigned newCode) 
Sets this permutation to that represented by the given internal code. More...  
NPerm5 &  operator= (const NPerm5 &cloneMe) 
Sets this permutation to be equal to the given permutation. More...  
NPerm5  operator* (const NPerm5 &q) const 
Returns the composition of this permutation with the given permutation. More...  
NPerm5  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 NPerm5 &other) const 
Determines if this is equal to the given permutation. More...  
bool  operator!= (const NPerm5 &other) const 
Determines if this differs from the given permutation. More...  
int  compareWith (const NPerm5 &other) const 
Lexicographically compares the images of (0,1,2,3,4) 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...  
std::string  trunc3 () const 
Returns a string representation of this permutation with only the images of 0, 1 and 2. More...  
std::string  trunc4 () const 
Returns a string representation of this permutation with only the images of 0, 1, 2 and 3. More...  
int  S5Index () const 
Returns the index of this permutation in the NPerm5::S5 array. More...  
int  SnIndex () const 
Returns the index of this permutation in the NPerm5::S5 array. More...  
int  orderedS5Index () const 
Returns the index of this permutation in the NPerm5::orderedS5 array. More...  
int  orderedSnIndex () const 
Returns the index of this permutation in the NPerm5::orderedS5 array. More...  
Static Public Member Functions  
static NPerm5  fromPermCode (unsigned newCode) 
Creates a permutation from the given internal code. More...  
static bool  isPermCode (unsigned newCode) 
Determines whether the given integer is a valid internal permutation code. More...  
Static Public Attributes  
static const NPerm5  S5 [120] 
Contains all possible permutations of five elements. More...  
static const NPerm5 *  Sn 
A dimensionagnostic alias for NPerm5::S5. More...  
static const NPerm5  orderedS5 [120] 
Contains all possible permutations of five elements in lexicographical order. More...  
static const NPerm5 *  orderedSn 
A dimensionagnostic alias for NPerm5::orderedS5. More...  
static const unsigned  invS5 [120] 
Contains the inverses of the permutations in the array S5. More...  
static const unsigned *  invSn 
A dimensionagnostic alias for NPerm5::invS5. More...  
static const NPerm5  S4 [24] 
Contains all possible permutations of four elements. More...  
static const NPerm5 *  Sn_1 
A dimensionagnostic alias for NPerm5::S4. More...  
static const NPerm5  orderedS4 [24] 
Contains all possible permutations of four elements in lexicographical order. More...  
static const NPerm5  S3 [6] 
Contains all possible permutations of three elements. More...  
static const NPerm5  orderedS3 [6] 
Contains all possible permutations of three elements in lexicographical order. More...  
static const NPerm5  S2 [2] 
Contains all possible permutations of two elements. More...  
Friends  
std::ostream &  operator<< (std::ostream &out, const NPerm5 &p) 
Writes a string representation of the given permutation to the given output stream. More...  
Represents a permutation of {0,1,2,3,4}.
Amongst other things, such permutations are used in describing simplex gluings in 4manifold triangulations. NPerm5 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 an unsigned integer. The lowest three bits represent the image of 0, the next lowest three bits represent the image of 1 and so on.
anonymous enum 

inline 
Creates the identity permutation.

inline 
Creates the transposition of a and b.
Note that a and b need not be distinct.
a  the element to switch with b. 
b  the element to switch with a. 

inline 
Creates a permutation mapping (0,1,2,3,4) to (a,b,c,d,e) respectively.
a  the desired image of 0. 
b  the desired image of 1. 
c  the desired image of 2. 
d  the desired image of 3. 
e  the desired image of 4. 

inline 
Creates a permutation mapping i to image[i] for each i = 0,1,2,3,4.
image  the array of images. 

inline 
Creates a permutation mapping (a0,b0,c0,d0,e0) to (a1,b1,c1,d1,e1) respectively.
a0  the desired preimage of a1. 
b0  the desired preimage of b1. 
c0  the desired preimage of c1. 
d0  the desired preimage of d1. 
e0  the desired preimage of e1. 
a1  the desired image of a0. 
b1  the desired image of b0. 
c1  the desired image of c0. 
d1  the desired image of d0. 
e1  the desired image of e0. 

inline 
Creates a permutation that is a clone of the given permutation.
cloneMe  the permutation to clone. 
int regina::NPerm5::compareWith  (  const NPerm5 &  other  )  const 
Lexicographically compares the images of (0,1,2,3,4) under this and the given permutation.
other  the permutation with which to compare this. 

inlinestatic 
Creates a permutation from the given internal code.
newCode  the internal code for the new permutation. 

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().

inline 
Finds the inverse of this permutation.

inline 
Determines if this is the identity permutation.
This is true if and only if each of 0, 1, 2, 3 and 4 is mapped to itself.
true
if and only if this is the identity permutation.

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

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, 3 or 4.
other  the permutation with which to compare this. 
true
if and only if this and the given permutation differ. 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]]
.
q  the permutation with which to compose this. 
Sets this permutation to be equal to the given permutation.
cloneMe  the permutation whose value will be assigned to this permutation. 

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, 3 and 4.
other  the permutation with which to compare this. 
true
if and only if this and the given permutation are equal.

inline 
Determines the image of the given integer under this permutation.
source  the integer whose image we wish to find. This should be between 0 and 4 inclusive. 
int regina::NPerm5::orderedS5Index  (  )  const 
Returns the index of this permutation in the NPerm5::orderedS5 array.

inline 
Returns the index of this permutation in the NPerm5::orderedS5 array.
This is a dimensionagnostic alias for orderedS5Index().

inline 
Determines the preimage of the given integer under this permutation.
image  the integer whose preimage we wish to find. This should be between 0 and 4 inclusive. 
int regina::NPerm5::S5Index  (  )  const 
Returns the index of this permutation in the NPerm5::S5 array.

inline 
Sets this permutation to that represented by the given internal code.
newCode  the internal code that will determine the new value of this permutation. 
int regina::NPerm5::sign  (  )  const 
Determines the sign of this permutation.

inline 
Returns the index of this permutation in the NPerm5::S5 array.
This is a dimensionagnostic alias for S5Index().
std::string regina::NPerm5::str  (  )  const 
Returns a string representation of this permutation.
The representation will consist of five adjacent digits representing the images of 0, 1, 2, 3 and 4 respectively. An example of a string representation is 30421
.

inline 
A deprecated alias for str(), which returns a string representation of this permutation.
std::string regina::NPerm5::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.
std::string regina::NPerm5::trunc3  (  )  const 
Returns a string representation of this permutation with only the images of 0, 1 and 2.
The resulting string will therefore have length three.
std::string regina::NPerm5::trunc4  (  )  const 
Returns a string representation of this permutation with only the images of 0, 1, 2 and 3.
The resulting string will therefore have length four.

friend 
Writes a string representation of the given permutation to the given output stream.
The format will be the same as is used by NPerm5::str().
out  the output stream to which to write. 
p  the permutation to write. 

static 
Contains the inverses of the permutations in the array S5.
Specifically, the inverse of permutation S5[i]
is the permutation S5[ invS5[i] ]
.

static 
A dimensionagnostic alias for NPerm5::invS5.
In general, for each K the class NPermK will define an alias invSn that references the list of all permutations NPermK::invSK.

static 
Contains all possible permutations of three elements in lexicographical order.
In each permutation, 3 maps to 3 and 4 maps to 4.

static 
Contains all possible permutations of four elements in lexicographical order.
In each permutation, 4 maps to 4.

static 
Contains all possible permutations of five elements in lexicographical order.

static 
A dimensionagnostic alias for NPerm5::orderedS5.
In general, for each K the class NPermK will define an alias orderedSn that references the list of all permutations NPermK::orderedSK.

static 
Contains all possible permutations of two elements.
In each permutation, 2 maps to 2, 3 maps to 3, and 4 maps to 4.
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 (NPerm4, NPerm5 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.

static 
Contains all possible permutations of three elements.
In each permutation, 3 maps to 3 and 4 maps to 4.
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 (NPerm4, NPerm5 and so on), the S3 array stores the same permutations in the same order (but of course using different data types).
Note that the permutations are not necessarily in lexicographical order. For the corresponding inverse array, see NPerm3::invS3.

static 
Contains all possible permutations of four elements.
In each permutation, 4 maps to 4.
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 (NPerm4, NPerm5 and so on), the S4 array stores the same permutations in the same order (but of course using different data types).
Note that the permutations are not necessarily in lexicographical order. For the corresponding inverse array, see NPerm4::invS4.

static 
Contains all possible permutations of five 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.

static 
A dimensionagnostic alias for NPerm5::S5.
In general, for each K the class NPermK will define an alias Sn that references the list of all permutations NPermK::SK.

static 
A dimensionagnostic alias for NPerm5::S4.
In general, for each K the class NPermK will define an alias Sn_1 that references the list of all permutations NPermK::S(K1).