Regina Calculation Engine
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Represents a permutation of {0,1,2}. More...
#include <maths/nperm3.h>
Public Types | |
enum | { code012 = 0, code021 = 1, code120 = 2, code102 = 3, code201 = 4, code210 = 5 } |
Public Member Functions | |
NPerm3 () | |
Creates the identity permutation. | |
NPerm3 (int a, int b, int c) | |
Creates a permutation mapping (0,1,2) to (a,b,c) respectively. | |
NPerm3 (const NPerm3 &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 code) |
Sets this permutation to that represented by the given internal code. | |
NPerm3 & | operator= (const NPerm3 &cloneMe) |
Sets this permutation to be equal to the given permutation. | |
NPerm3 | operator* (const NPerm3 &q) const |
Returns the composition of this permutation with the given permutation. | |
NPerm3 | 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 NPerm3 &other) const |
Determines if this is equal to the given permutation. | |
bool | operator!= (const NPerm3 &other) const |
Determines if this differs from 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. | |
int | S3Index () const |
Returns the index of this permutation in the NPerm3::S3 array. | |
int | orderedS3Index () const |
Returns the index of this permutation in the NPerm3::orderedS3 array. | |
Static Public Member Functions | |
static NPerm3 | fromPermCode (unsigned char code) |
Creates a permutation from the given internal code. | |
static bool | isPermCode (unsigned char code) |
Determines whether the given integer is a valid internal permutation code. | |
Static Public Attributes | |
static const NPerm3 | S3 [6] |
Contains all possible permutations of three elements. | |
static const int | invS3 [6] |
Contains the inverses of the permutations in the array S3. | |
static const NPerm3 | orderedS3 [6] |
Contains all possible permutations of three elements in lexicographical order. | |
Friends | |
std::ostream & | operator<< (std::ostream &out, const NPerm3 &p) |
Writes a string representation of the given permutation to the given output stream. |
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. On the other hand, this class does not offer quite as rich an interface.
anonymous enum |
regina::NPerm3::NPerm3 | ( | ) | [inline] |
Creates the identity permutation.
regina::NPerm3::NPerm3 | ( | int | a, |
int | b, | ||
int | c | ||
) | [inline] |
Creates a permutation mapping (0,1,2) to (a,b,c) respectively.
a | the desired image of 0. |
b | the desired image of 1. |
c | the desired image of 2. |
regina::NPerm3::NPerm3 | ( | const NPerm3 & | cloneMe | ) | [inline] |
Creates a permutation that is a clone of the given permutation.
cloneMe | the permutation to clone. |
NPerm3 regina::NPerm3::fromPermCode | ( | unsigned char | code | ) | [inline, static] |
Creates a permutation from the given internal code.
code | the internal code for the new permutation. |
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().
NPerm3 regina::NPerm3::inverse | ( | ) | const [inline] |
Finds 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.
true
if and only if this is the identity permutation. bool regina::NPerm3::isPermCode | ( | unsigned char | code | ) | [inline, 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. 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.
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. |
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.
other | the permutation with which to compare this. |
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.
source | the integer whose image we wish to find. This should be between 0 and 2 inclusive. |
int regina::NPerm3::orderedS3Index | ( | ) | const [inline] |
Returns the index of this permutation in the NPerm3::orderedS3 array.
int regina::NPerm3::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 2 inclusive. |
int regina::NPerm3::S3Index | ( | ) | const [inline] |
Returns the index of this permutation in the NPerm3::S3 array.
void regina::NPerm3::setPermCode | ( | unsigned char | code | ) | [inline] |
Sets this permutation to that represented by the given internal code.
code | the internal code that will determine the new value of this permutation. |
int regina::NPerm3::sign | ( | ) | const [inline] |
Determines the sign of this permutation.
std::string regina::NPerm3::toString | ( | ) | 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
.
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.
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::toString().
out | the output stream to which to write. |
p | the permutation to write. |
const int 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 NPerm3 regina::NPerm3::orderedS3[6] [static] |
Contains all possible permutations of three elements 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.
This array contains the same permutations in the same order as the corresponding array NPerm4::S3 (though of course this array stores NPerm3 objects instead of NPerm4 objects).
Note that these permutations are not necessarily in lexicographical order.