Hello, Travis Scrimshaw wrote:
> On #15635, we are trying to decide whether we want non-associative > algebras to be included in the catalog of algebras. For a general mathematical software system such as Sage, I think it is overly restrictive to impose the rule that algebras are associative. There are too many interesting non-associative algebras (such as Lie algebras), or non-unital algebras (such as certain Hecke algebras) to make associativity part of the definition of an algebra. Moreover, it is in my opinion an unfortunate choice of terminology if non-associative algebras are not in general algebras. > The argument against including them is "most" people think of algebras > as being associative (and maybe even unital), and as such, might > surprise people when they come across the non-associativity in their > computations. Anyone has the right to think of algebras as being associative, just like many people think of vector spaces as being finite-dimensional, say. This is a bit like books or papers using the convention that all the algebras that one considers are assumed to be associative (or that vector spaces are assumed to be finite-dimensional, etc.) However, it feels wrong to elevate such conventions to definitions. > However, the community was at one point considering renaming magmatic > algebras into algebras and having to specify the associative axiom > explicitly. I would be in favour of this. When finite-dimensional algebras over a field were implemented in #12141, we explicitly included non-associative algebras. In case the user already knows that his algebra is associative, he can pass a flag "assume_associative" (default: False) to avoid a lengthy computation to check this. Peter -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
