UnitalSubalgebra( A, gens )
returns the unital subalgebra of the algebra A generated by the elements in the list gens. If A is not (known to be) unital then first it is checked that A really contains the zero-th power of elements.
gap> a:= [ [ 1, 0 ], [ 0, 0 ] ];; gap> b:= [ [ 0, 0 ], [ 0, 1 ] ] ;; gap> alg:= Algebra( Rationals, [ a, b ] );; gap> alg.name:= "alg";; gap> s:= Subalgebra( alg, [ a ] ); Subalgebra( alg, [ [ [ 1, 0 ], [ 0, 0 ] ] ] ) gap> s = alg; false gap> s:= UnitalSubalgebra( alg, [ a ] ); UnitalSubalgebra( alg, [ [ [ 1, 0 ], [ 0, 0 ] ] ] ) gap> s = alg; true
AsUnitalSubalgebra are the only functions in which the name
Subalgebra does not refer to the mathematical terms subalgebra and
superalgebra but to the implementation of algebras as subalgebras and
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