41.14 IsEquivalent for Row Modules

IsEquivalent( M1, M2 )

Let M1 and M2 be modules acted on by rings R_1 and R_2, respectively, such that mapping the generators of R_1 to the generators of R_2 defines a ring homomorphism. Furthermore let at least one of M1, M2 be irreducible. Then IsEquivalent( M1, M2 ) returns true if the actions on M1 and M2 are equivalent, and false otherwise.

    gap> rand:= RandomInvertableMat( 3, GF(2) );;
    gap> b:= UnitalAlgebra( GF(2), List( a.generators, x -> x^rand ) );;
    gap> m:= NaturalModule( b );;
    gap> IsEquivalent( nat / FixedSubmodule( nat ),
    >                  m / FixedSubmodule( m ) );
    true 

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