#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. | |
void | 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 | |
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.
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Creates the identity permutation.
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Creates a permutation from the given internal code.
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Creates the transposition of a and b. Note that a and b need not be distinct.
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Creates a permutation mapping (0,1,2,3) to (a,b,c,d) respectively.
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Creates a permutation mapping (a0,b0,c0,d0) to (a1,b1,c1,d1) respectively.
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Creates a permutation that is a clone of the given permutation.
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Lexicographically compares the images of (0,1,2,3) under this and the given 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, 2 and 3 is mapped to itself.
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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().
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Returns the composition of this permutation with the given permutation.
If this permutation is p, the resulting permutation will be p o q, satisfying
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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, 2 or 3.
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Sets this permutation to be equal to the given 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, 2 and 3.
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Determines the image of the given integer under this permutation.
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Determines the preimage of the given integer under this permutation.
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Sets this permutation to that mapping (0,1,2,3) to (a,b,c,d) respectively.
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Sets this permutation to the transposition of a and b. Note that a and b need not be distinct.
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Sets this permutation to that represented by the given internal code.
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Determines the sign of this permutation.
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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
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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 NPerm::toString().
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