MeatAxe
2.4
Programs for working with modular representations

In the MeatAxe, a permutation of degree n operates on {0,1,...,n1} and is represented by a Perm_t structure. However, in the textual representation produced by PermPrint() or by the zpr program, the points are numbered from 1...n.
Only permutations of equal degree can be multiplied. This can be confusing because the textual representation produced by PermPrint() does not include the degree, and fixed points are always suppressed. For example "(3 4)(5 6 7)" could be interpreted as a permutation of degree 8 or any higher degree. All these permutations are in some natural way equal to each other, but they are different and incompatible in the MeatAxe.
Permutations are usually created with PermAlloc() or read from a file with PermRead(). When a permutation is no longer used, the application must release the associated memory by calling PermFree().
Data Structures  
class  Perm_t 
A Permutation. More...  
Functions  
int  PermCompare (const Perm_t *a, const Perm_t *b) 
Compare two permutations. More...  
int  PermIsValid (const Perm_t *p) 
Check a permutation. More...  
Perm_t *  PermAlloc (int deg) 
Allocate a permutation This function creates a permutation of the specified degree. More...  
int  PermFree (Perm_t *p) 
Free a permutation. More...  
Perm_t *  PermDup (const Perm_t *src) 
Duplicate a permutation. More...  
Perm_t *  PermInverse (const Perm_t *src) 
Inverse of a permutation This function calulates the inverse of a permutation. More...  
Perm_t *  PermMul (Perm_t *dest, const Perm_t *src) 
Multiply permutations. More...  
int  PermOrder (const Perm_t *perm) 
Order of a permutation. More...  
void  PermPrint (const char *name, const Perm_t *perm) 
Print a permutation This function prints a permutation on the standard output using cycle notation. More...  
Perm_t *  PermPower (const Perm_t *p, int n) 
Power of a permutation This function calculates the nth power of a permutation. More...  
Perm_t *  PermRead (FILE *f) 
Read a Permutation from a File. More...  
Perm_t *  PermLoad (const char *fn) 
Read a permutation. More...  
int  PermWrite (const Perm_t *perm, FILE *f) 
Write a Permutation to a File. More...  
int  PermSave (const Perm_t *perm, const char *fn) 
Write a Permutation to a File. More...  
Perm_t* PermAlloc  (  int  deg  ) 
Allocate a permutation This function creates a permutation of the specified degree.
The new permutation is initialized to the identity.
deg  Degree. 
Compare two permutations.
This function compares two permutations. If the permutations are equal, the return value is 0. Otherwise the return value is positive if a is "greater" than b, and negative if a is "less" than b. The ordering of permutations is defined as follows. If the permutations have different degrees, the permutations with the smaller degree is smaller. Otherwise, the result of the comparison is unspecified.
Note that the return value 1 does not necessarily mean that an error occured.
a  Pointer to the first permutation. 
b  Pointer to the second permutation. 
Duplicate a permutation.
This function creates a copy of an existing permutation.
src  Pointer to the permutation. 
int PermFree  (  Perm_t *  p  ) 
Inverse of a permutation This function calulates the inverse of a permutation.
src  Pointer to the permutation. 
int PermIsValid  (  const Perm_t *  p  ) 
Check a permutation.
This function checks if the argument is a pointer to a valid permutation. If the permutation is o.k., the function returns 1. Otherwise, an error is signalled and, if the error handler does not terminate the program, the function returns 0.
Perm_t* PermLoad  (  const char *  fn  ) 
Read a permutation.
This function opens a file, reads a single permutation, and closes the file. The return value is a pointer to the permutation or 0 on error. If the file contains more than one permutation, only the first one is read. If a permutation was successfully read, the function returns a pointer to a newly created Perm_t object. The caller is responsible for deleting this object as soon as the permutation is no longer needed.
fn  File name. 
Multiply permutations.
This function multiplies dest from the right by src. Both permutations must have the same degree.
dest  Pointer to the first permutation. 
src  Pointer to the second permutation. 
int PermOrder  (  const Perm_t *  perm  ) 
Order of a permutation.
perm  Pointer to the permutation. 
Power of a permutation This function calculates the nth power of a permutation.
It allocates a new permutation, leaving the original permutation intact. The caller is responsible for deleting the result when it is no longer needed.
p  Pointer to the permutation. 
n  Exponent. Must be greather than or equal to 0. 
void PermPrint  (  const char *  name, 
const Perm_t *  perm  
) 
Print a permutation This function prints a permutation on the standard output using cycle notation.
If name is not 0, the name followed by an equal sign is printed before the permutation. For example, the statement PermPrint("Perm",P);
could produce the following output:
Perm=(1 9)(2 3 6)(4 5 7)
Fixed points are always suppressed in the output.
name  Name to print before the permutation or 0. 
perm  Pointer to the permutation. 
Perm_t* PermRead  (  FILE *  f  ) 
Read a Permutation from a File.
This function reads a permutation from a file. f must be a pointer to an open file with read permission. If a permutation was successfully read, the function returns a pointer to a newly created Perm_t object. The caller is responsible for deleting this object as soon as the permutation is no longer needed.
f  File to read from. 
int PermSave  (  const Perm_t *  perm, 
const char *  fn  
) 
Write a Permutation to a File.
This function creates a file, writes a single permutation to the file and closes the file. If a file with the specified name already exists, its contents are destroyed.
perm  Permutation to write. 
fn  File name. 