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.

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