Regina Calculation Engine
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Represents a permutation of {0,1,2}. More...
#include <maths/nperm3.h>
Public Types | |
enum | { nPerms = 6, nPerms_1 = 2 } |
enum | { code012 = 0, code021 = 1, code120 = 2, code102 = 3, code201 = 4, code210 = 5 } |
Public Member Functions | |
NPerm3 () | |
Creates the identity permutation. More... | |
NPerm3 (int a, int b) | |
Creates the transposition of a and b. More... | |
NPerm3 (int a, int b, int c) | |
Creates a permutation mapping (0,1,2) to (a,b,c) respectively. More... | |
NPerm3 (const int *image) | |
Creates a permutation mapping i to image[i] for each i = 0,1,2. More... | |
NPerm3 (const NPerm3 &cloneMe) | |
Creates a permutation that is a clone of the given permutation. More... | |
unsigned char | getPermCode () const |
Returns the internal code representing this permutation. More... | |
void | setPermCode (unsigned char code) |
Sets this permutation to that represented by the given internal code. More... | |
NPerm3 & | operator= (const NPerm3 &cloneMe) |
Sets this permutation to be equal to the given permutation. More... | |
NPerm3 | operator* (const NPerm3 &q) const |
Returns the composition of this permutation with the given permutation. More... | |
NPerm3 | 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 NPerm3 &other) const |
Determines if this is equal to the given permutation. More... | |
bool | operator!= (const NPerm3 &other) const |
Determines if this differs from the given permutation. More... | |
int | compareWith (const NPerm3 &other) const |
Lexicographically compares the images of (0,1,2) 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... | |
int | S3Index () const |
Returns the index of this permutation in the NPerm3::S3 array. More... | |
int | SnIndex () const |
Returns the index of this permutation in the NPerm3::S3 array. More... | |
int | orderedS3Index () const |
Returns the index of this permutation in the NPerm3::orderedS3 array. More... | |
int | orderedSnIndex () const |
Returns the index of this permutation in the NPerm3::orderedS3 array. More... | |
Static Public Member Functions | |
static NPerm3 | fromPermCode (unsigned char code) |
Creates a permutation from the given internal code. More... | |
static bool | isPermCode (unsigned char code) |
Determines whether the given integer is a valid internal permutation code. More... | |
Static Public Attributes | |
static const NPerm3 | S3 [6] |
Contains all possible permutations of three elements. More... | |
static const NPerm3 * | Sn |
A dimension-agnostic alias for NPerm3::S3. More... | |
static const unsigned | invS3 [6] |
Contains the inverses of the permutations in the array S3. More... | |
static const unsigned * | invSn |
A dimension-agnostic alias for NPerm3::invS3. More... | |
static const NPerm3 | orderedS3 [6] |
Contains all possible permutations of three elements in lexicographical order. More... | |
static const NPerm3 * | orderedSn |
A dimension-agnostic alias for NPerm3::orderedS3. More... | |
static const NPerm3 | S2 [2] |
Contains all possible permutations of two elements. More... | |
static const NPerm3 * | Sn_1 |
A dimension-agnostic alias for NPerm3::S2. More... | |
Friends | |
std::ostream & | operator<< (std::ostream &out, const NPerm3 &p) |
Writes a string representation of the given permutation to the given output stream. More... | |
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 and NPerm5. On the other hand, this class does not offer quite as rich an interface as the others.
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Creates the identity permutation.
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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. |
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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. |
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Creates a permutation mapping i to image[i] for each i = 0,1,2.
image | the array of images. |
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Creates a permutation that is a clone of the given permutation.
cloneMe | the permutation to clone. |
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Lexicographically compares the images of (0,1,2) under this and the given permutation.
other | the permutation with which to compare this. |
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inlinestatic |
Creates a permutation from the given internal code.
code | the internal code for the new permutation. |
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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().
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Finds the inverse of this permutation.
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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.
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inlinestatic |
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.
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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. |
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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.
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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. |
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Returns the index of this permutation in the NPerm3::orderedS3 array.
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Returns the index of this permutation in the NPerm3::orderedS3 array.
This is a dimension-agnostic alias for orderedS3Index().
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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. |
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Returns the index of this permutation in the NPerm3::S3 array.
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Sets this permutation to that represented by the given internal code.
code | the internal code that will determine the new value of this permutation. |
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Determines the sign of this permutation.
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Returns the index of this permutation in the NPerm3::S3 array.
This is a dimension-agnostic alias for S3Index().
std::string regina::NPerm3::str | ( | ) | 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
.
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A deprecated alias for str(), which returns a string representation of this permutation.
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.
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Writes a string representation of the given permutation to the given output stream.
The format will be the same as is used by NPerm3::str().
out | the output stream to which to write. |
p | the permutation to write. |
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Contains the inverses of the permutations in the array S3.
Specifically, the inverse of permutation S3[i]
is the permutation S3[ invS3[i] ]
.
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A dimension-agnostic alias for NPerm3::invS3.
In general, for each K the class NPermK will define an alias invSn that references the list of all permutations NPermK::invSK.
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Contains all possible permutations of three elements in lexicographical order.
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A dimension-agnostic alias for NPerm3::orderedS3.
In general, for each K the class NPermK will define an alias orderedSn that references the list of all permutations NPermK::orderedSK.
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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.
For all permutation classes (NPerm3, NPerm4 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.
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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.
For all permutation classes (NPerm3, NPerm4 and so on), the S3 array stores the same permutations in the same order (but of course using different data types).
Note that these permutations are not necessarily in lexicographical order.
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A dimension-agnostic alias for NPerm3::S3.
In general, for each K the class NPermK will define an alias Sn that references the list of all permutations NPermK::SK.
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A dimension-agnostic alias for NPerm3::S2.
In general, for each K the class NPermK will define an alias Sn_1 that references the list of all permutations NPermK::S(K-1).