39.8 MappedExpression

MappedExpression( expr, gens1, gens2 )

For an arithmetic expression expr in terms of gens1, MappedExpression returns the corresponding expression in terms of gens2.

gens1 may be a list of abstract generators (in this case the result is the same as the object returned by MappedWord MappedWord), or of generators of a finitely presented algebra.

    gap> a:= FreeAlgebra( Rationals, 2 );;
    gap> a:= a / [ a.1^2 - a.one, a.2^2 - a.one, (a.1*a.2)^2 - a.one ];;
    gap> matgens:= [ [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]],
    >                [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] ];;
    gap> permgens:= [ (1,4)(2,3), (1,2)(3,4) ];;
    gap> MappedExpression( a.1^2 + a.1, a.generators, matgens );
    [ [ 1, 0, 0, 1 ], [ 0, 1, 1, 0 ], [ 0, 1, 1, 0 ], [ 1, 0, 0, 1 ] ]
    gap> MappedExpression( a.1 * a.2, a.generators, permgens );
    (1,3)(2,4) 

Note that this can be done also in terms of (algebra or group) homomorphisms (see Algebra Homomorphisms).

MappedExpression may raise elements in gens2 to the zero-th power.

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