# 68.16 Functions for MeatAxe Matrix Algebras

The following functions are overlaid in the operations record of MeatAxe matrix algebras.

`Fingerprint( A )`

`Fingerprint( A, list )` :

returns the fingerprint of A, i.e., a list of nullities of six ``standard'' words in A (for 2-generator algebras only) or of the words with numbers in list.

```    gap> f:= GF(2);;
gap> a:= UnitalAlgebra( f, [ MeatAxeMat( (1,2,3,4,5), f, [5,5] ),
>                            MeatAxeMat( (1,2)      , f, [5,5] ) ] );;
gap> Fingerprint( a );
[ 1, 1, 1, 3, 0, 1 ] ```

`Module( matalg, gens )` :

returns the module generated by the rows of the MeatAxe matrix gens, and acted on by the MeatAxe matrix algebra matalg. Such a module will usually contain the vectors of a basis in the `base` component.

`NaturalModule( matalg )` :

returns the n-dimensional space acted on by the MeatAxe matrix algebra matalg which consists of n times n MeatAxe matrices.

`Operation( A, M )` :

Let M be a MeatAxe module acted on by the MeatAxe matrix algebra A. `Operation( A, M )` returns a MeatAxe matrix algebra of n times n matrices (where n is the dimension of M), with action on its natural module equivalent to that of A on M.
Note: If M is a quotient module, it must be a quotient of the entire space.

`RandomOrders( A )` :

returns a list with the orders of 120 random elements of the MeatAxe matrix algebra A, provided that the generators of A are invertible.

It should be noted that no set theoretic functions (such as `Size`) and vector space functions (such as `Base`) are provided for MeatAxe matrix algebras, and also algebra functions (such as `Centre`) will not work.

GAP 3.4.4
April 1997