40.10 Fingerprint

Fingerprint( A )
Fingerprint( A, list )

returns the fingerprint of the matrix algebra 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> m1:= PermutationMat( (1,2,3,4,5), 5, GF(2) );;
    gap> m2:= PermutationMat( (1,2)      , 5, GF(2) );;
    gap> a:= Algebra( GF(2), [ m1, m2 ] );;
    gap> Fingerprint( a );
    [ 1, 1, 1, 3, 0, 4 ] 

Let a and b be the generators of a 2-generator matix algebra. The six standard words used by Fingerprint are w_1, w_2, ldots, w_6 where [ beginarrayllllll w_1 & = & a b + a + b, & w_2 & = & w_1 + a b^2,
w_3 & = & a + b w_2, & w_4 & = & b + w_3,
w_5 & = & a b + w_4, & w_6 & = & a + w_5 endarray ]

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