39.2 FreeAlgebra

FreeAlgebra( F, rank )
FreeAlgebra( F, rank, name )
FreeAlgebra( F, name1, name2, ... )

return a free algebra with ground field F. In the first two forms an algebra on rank free generators is returned, their names will be name.1, ldots, name.rank, the default for name is the string "a".

    gap> a:= FreeAlgebra( GF(2), 2 );
    UnitalAlgebra( GF(2), [ a.1, a.2 ] )
    gap> b:= FreeAlgebra( Rationals, "x", "y" );
    UnitalAlgebra( Rationals, [ x, y ] )
    gap> x:= b.1;
    x 

Finitely presented algebras are constructed from free algebras via factoring by a suitable ideal (see Operators for Finitely Presented Algebras).

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