Regina Calculation Engine
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Represents a permutation of {0,1,2,3}. More...
#include <maths/spec/perm4.h>
Public Types | |
typedef int | Index |
Denotes a native signed integer type large enough to count all permutations on four elements. More... | |
typedef uint8_t | Code |
Indicates the native unsigned integer type used to store the internal permutation code. More... | |
Public Member Functions | |
Perm () | |
Creates the identity permutation. More... | |
Perm (int a, int b) | |
Creates the transposition of a and b. More... | |
Perm (int a, int b, int c, int d) | |
Creates a permutation mapping (0,1,2,3) to (a,b,c,d) respectively. More... | |
Perm (const int *image) | |
Creates a permutation mapping i to image[i] for each i = 0,1,2,3. More... | |
Perm (const int *a, const int *b) | |
Creates a permutation mapping (a[0], ..., a[3]) to (b[0], ..., b[3]) respectively. More... | |
Perm (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. More... | |
Perm (const Perm< 4 > &cloneMe)=default | |
Creates a permutation that is a clone of the given permutation. More... | |
Code | permCode () const |
Returns the first-generation code representing this permutation. More... | |
Code | permCode2 () const |
Returns the second-generation code representing this permutation. More... | |
void | setPermCode (Code code) |
Sets this permutation to that represented by the given first-generation permutation code. More... | |
void | setPermCode2 (Code code) |
Sets this permutation to that represented by the given second-generation permutation code. More... | |
Perm< 4 > & | operator= (const Perm< 4 > &cloneMe)=default |
Sets this permutation to be equal to the given permutation. More... | |
Perm< 4 > | operator* (const Perm< 4 > &q) const |
Returns the composition of this permutation with the given permutation. More... | |
Perm< 4 > | inverse () const |
Finds the inverse of this permutation. More... | |
Perm< 4 > | reverse () const |
Finds the reverse 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 Perm< 4 > &other) const |
Determines if this is equal to the given permutation. More... | |
bool | operator!= (const Perm< 4 > &other) const |
Determines if this differs from the given permutation. More... | |
int | compareWith (const Perm< 4 > &other) const |
Lexicographically compares the images of (0,1,2,3) under this and the given permutation. More... | |
bool | isIdentity () const |
Determines if this is the identity permutation. More... | |
Index | index () const |
Returns the lexicographical index of this permutation. More... | |
std::string | str () const |
Returns a string representation of this permutation. More... | |
std::string | trunc (unsigned len) const |
Returns a prefix of the string representation of this permutation, containing only the images of the first len integers. 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 included. More... | |
void | clear (unsigned from) |
Resets the images of all integers from from onwards to the identity map. More... | |
int | S4Index () const |
Returns the index of this permutation in the Perm<4>::S4 array. More... | |
int | SnIndex () const |
Returns the index of this permutation in the Perm<4>::S4 array. More... | |
REGINA_INLINE_REQUIRED int | orderedS4Index () const |
Returns the index of this permutation in the Perm<4>::orderedS4 array. More... | |
int | orderedSnIndex () const |
Returns the index of this permutation in the Perm<4>::orderedS4 array. More... | |
Static Public Member Functions | |
static Perm< 4 > | fromPermCode (Code code) |
Creates a permutation from the given first-generation permutation code. More... | |
static Perm< 4 > | fromPermCode2 (Code code) |
Creates a permutation from the given second-generation permutation code. More... | |
static bool | isPermCode (Code code) |
Determines whether the given character is a valid first-generation permutation code. More... | |
static bool | isPermCode2 (Code code) |
Determines whether the given character is a valid second-generation permutation code. More... | |
static Perm | atIndex (Index i) |
Returns the ith permutation on four elements, where permutations are numbered lexicographically beginning at 0. More... | |
static Perm | rand (bool even=false) |
Returns a random permutation on four elements. More... | |
template<int k> | |
static Perm< 4 > | extend (Perm< k > p) |
Extends a k-element permutation to a 4-element permutation, where 2 ≤ k < 4. More... | |
template<int k> | |
static Perm< 4 > | contract (Perm< k > p) |
Restricts a k-element permutation to an 4-element permutation, where k > 4. More... | |
Static Public Attributes | |
static const Index | nPerms = 24 |
The total number of permutations on four elements. More... | |
static const Index | nPerms_1 = 6 |
The total number of permutations on three elements. More... | |
static const Perm< 4 > | S4 [24] |
Contains all possible permutations of four elements. More... | |
static const Perm< 4 > * | Sn |
A dimension-agnostic alias for Perm<4>::S4. More... | |
static const unsigned | invS4 [24] |
Contains the inverses of the permutations in the array S4. More... | |
static const unsigned * | invSn |
A dimension-agnostic alias for Perm<4>::invS4. More... | |
static const Perm< 4 > | orderedS4 [24] |
Contains all possible permutations of four elements in lexicographical order. More... | |
static const Perm< 4 > * | orderedSn |
A dimension-agnostic alias for Perm<4>::orderedS4. More... | |
static const Perm< 4 > | S3 [6] |
Contains all possible permutations of three elements. More... | |
static const Perm< 4 > * | Sn_1 |
A dimension-agnostic alias for Perm<4>::S3. More... | |
static const Perm< 4 > | orderedS3 [6] |
Contains all possible permutations of three elements in lexicographical order. More... | |
static const Perm< 4 > | S2 [2] |
Contains all possible permutations of two elements. More... | |
Represents a permutation of {0,1,2,3}.
This is a specialisation of the generic Perm template: it is highly optimised, and also offers some additional functionality. Amongst other things, this permutation class is used to specify how simplices of a 3-manifold triangulation are glued together.
As with all Perm template classes, these objects are small enough to pass about by value instead of by reference. Moreover, Perm<4> is extremely fast to work with.
Each permutation has an internal code, which is a single native integer that is sufficient to reconstruct the permutation. Thus the internal code may be a useful means for passing permutation objects to and from the engine. For Perm<4>, the internal permutation codes have changed as of Regina 4.6.1:
It is highly recommended that, if you need to work with permutation codes at all, you use second-generation codes where possible. This is because the first-generation routines incur additional overhead in converting back and forth between the second-generation codes (which are used internally by Perm<4>).
To use this class, simply include the main permutation header maths/perm.h.