38.12 AsUnitalAlgebra

AsUnitalAlgebra( D )
AsUnitalAlgebra( F, D )

Let D be a domain. AsUnitalAlgebra returns a unital algebra A over the field F such that the set of elements of D is the same as the set of elements of A if this is possible. If D is an algebra the argument F may be omitted, the coefficients field of D is taken as coefficients field of F in this case.

If D is a list of algebra elements these elements must form a unital algebra. Otherwise an error is signalled.

    gap> a:= [ [ 1, 0 ], [ 0, 0 ] ] * Z(2);;
    gap> AsUnitalAlgebra( GF(2), [ a, a^0, 0*a, a^0-a ] );
    UnitalAlgebra( GF(2), [ [ [ 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0 ] ],
      [ [ Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2) ] ] ] ) 

Note that this function returns a parent algebra or a subalgebra of a parent algebra depending on D. In order to convert a subalgebra into a parent algebra you must use Algebra or UnitalAlgebra (see Algebra, UnitalAlgebra).

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