Am 17.11.2011 um 13:43 schrieb Stefan Kohl: [...]
> Regarding `IsAlgebraWithOne': the Is<something> operations check for > membership > in GAP categories. (sorry for the nitpicking, but: this actually refers to* mathematical* categories; GAP categories are something different). > -- So for example, mathematically a group may be 'regarded' > as the set of its elements (apply the forgetful functor from the category of > groups to the category of sets). Exactly. For those who are not so familiar with categories, an important place where this makes a difference is homomorphisms: In the category of algebras with one, a homomorphism will always map one to one. In the category of Algebra, one could be mapped to anything, e.g. zero. > Anyway, `IsSet' returns 'false' when applied > to a group. Rather, to transform a domain to a domain with the same elements > in another category, there are operations As<something>. So for example you > can transform a group to a set by applying `AsSet', and you can transform > a suitable domain to an algebra with one by applying `AsAlgebraWithOne'. > However, in your particular case, there is presently no suitable method for > `AsAlgebraWithOne' available. Of course you may add one, if you like. Actually, there is one, and it takes two parameters, like this: gap> S2 := AsAlgebraWithOne( Rationals, S ); <algebra-with-one of dimension 81 over Rationals> Cheers, Max _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
