68.22 MeatAxe Object Records

MeatAxe matrix records

A MeatAxe matrix in GAP is a record that has necessarily the components

isMeatAxeMat:

always true,

isMatrix:

always true,

domain:

the record MeatAxeMatrices,

file :

the name of the file that contains the matrix in MeatAxe format,

field:

the (finite) field the matrix is viewed over,

dimensions:

list containing the numbers of rows and columns,

operations:

the record MeatAxeMatOps.

Optional components are

structure:

algebra or group that contains the matrix,

abstract:

an element of a free algebra (see FreeAlgebra) representing the construction of the matrix in terms of generators.

Furthermore the record is used to store information whenever it is computed, e.g., the rank, the multiplicative order, and the inverse of a MeatAxe matrix.

MeatAxe permutation records

A MeatAxe permutation in GAP is a record that has necessarily the components

isMeatAxePerm:

always true,

isPermutation:

always true,

domain:

the record MeatAxePermutations,

file:

the name of the file that contains the permutation in MeatAxe format,

maxpoint:

an integer n that means that the permutation acts on the point set [ 1 .. n ]

operations:

the record MeatAxePermOps.

Optional components are

structure:

group that contains the permutation, and

abstract:

an element of a free algebra (see FreeAlgebra) representing the construction of the permutation in terms of generators.

Furthermore the record is used to store information whenever it is computed, e.g., the multiplicative order, and the inverse of a MeatAxe permutation.

MeatAxe

MeatAxe is a record that contains information about the usage of the MeatAxe with GAP. Currently it has the following components.

PATH:

the path name of the directory that contains the MeatAxe executables ,

fields:

a list where position i is bound if and only if the field of order i has already been constructed by the maketab command; in this case it contains the name of the pxxx.zzz file,

files:

a list of all file names that were constructed by calls to MeatAxe (for allowing to make clean),

dirs:

a list of all directory names that were constructed by calls to MeatAxe (for allowing to make clean),

gennames:

list of strings that are used as generator names in abstract components of MeatAxe matrices,

alpha:

alphabet over which gennames entries are formed,

direc:

directory that contains all the files that are constructed using MeatAxe functions,

EXEC :

function of arbitrary many string arguments that calls Exec for the concatenation of these arguments in the directory MeatAxe.direc.

Maketab:

function that produces field information files,

SetDirecory:

function that sets the direc component,

TmpName:

function of zero arguments that produces file names in the directory MeatAxe.direc,

Unbind:

function to delete files (see MeatAxe.Unbind).

Furthermore some components are bound intermediately when MeatAxe output files are read. So you should better not use the MeatAxe record to store your own objects.

Field information

The correspondence between the MeatAxe numbering and the GAP numbering of the elements of a finite field F is given by the function FFList (see FFList). The element of F corresponding to MeatAxe number n is FFList( F )[ n+1 ], and the MeatAxe number of the field element z is Position( FFList( F ), z ) -1.

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