#include <nperm.h>
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. | |
Static Public Member Functions | |
static bool | isPermCode (unsigned char newCode) |
Determines whether the given character is a valid internal permutation code. | |
Friends | |
std::ostream & | operator<< (std::ostream &out, const NPerm &p) |
Writes a string representation of the given permutation to the given output stream. |
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.
regina::NPerm::NPerm | ( | ) | [inline] |
Creates the identity permutation.
regina::NPerm::NPerm | ( | unsigned char | newCode | ) | [inline] |
Creates a permutation from the given internal code.
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.
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.
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.
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.
cloneMe | the permutation to clone. |
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().
void regina::NPerm::setPermCode | ( | unsigned char | newCode | ) | [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. |
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().
true
if and only if the given code is a valid internal permutation code. 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.
a | the element to switch with b. | |
b | the element to switch with a. |
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.
a | the desired image of 0. | |
b | the desired image of 1. | |
c | the desired image of 2. | |
d | the desired image of 3. |
Sets this permutation to be equal to the given permutation.
cloneMe | the permutation whose value will be assigned to this permutation. |
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. |
NPerm regina::NPerm::inverse | ( | ) | const [inline] |
Finds the inverse of this permutation.
int regina::NPerm::sign | ( | ) | const |
Determines the sign of this permutation.
int regina::NPerm::operator[] | ( | int | source | ) | const [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 3 inclusive. |
int regina::NPerm::preImageOf | ( | int | image | ) | const [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 3 inclusive. |
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.
other | the permutation with which to compare this. |
true
if and only if this and the given permutation are equal. 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.
other | the permutation with which to compare this. |
true
if and only if this and the given permutation differ. int regina::NPerm::compareWith | ( | const NPerm & | other | ) | const |
Lexicographically compares the images of (0,1,2,3) under this and the given permutation.
other | the permutation with which to compare this. |
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.
true
if and only if this is the identity permutation. 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
.
std::ostream& operator<< | ( | std::ostream & | out, | |
const NPerm & | 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 NPerm::toString().
out | the output stream to which to write. | |
p | the permutation to write. |