[GAP Forum] Degree and Generators

[Willem De Graaf]

Dear Markus,

You asked:

>Hello everyone. I have two questions.
>
>First, how do I find out what algebra
>a given element is an element of?
>
>For example, if I do
>gap> A:=AlgebraByStructureConstants(...
>gap> a:=GeneratorsOfAlgebra(A)[1]
>then what can I call, knowing 'a', that
>will return 'A'? Perhaps something along
>the lines of IAmAnElementOf(a)?
>
>  
>
In the case of structure constant algebras this is possible, because a link
to the algebra is stored in the family of the element. In your case you 
can access
it by

FamilyObj( a )!.fullSCAlgebra;

>What I really want is to call Grading(A)
>so I can find out what degree 'a' is
>(after having set up Grading(A).hom_components).
>Is this information available 
>via some other method, given only 'a'?
>
>  
>
Currently there is no standard method in GAP for this. You would have
to write a little function that finds out in which homogeneous component
your element a lies.

>Second, how do I cause the generators of 'A'
>above to be available via the names A.1, A.2, etc?
>This isn't essential, but is certainly makes
>algebra more pleasant :)
>  
>
This is unfortunately not possible.

Hope this helps; if you have more questions, please ask.

All the best,

Willem de Graaf