On Wednesday, July 13, 2011 12:29:39 PM UTC-7, Rob Beezer wrote: > > Thanks, Minh. That's the way I see it as well, though as usual you > are more eloquent. > > So this is really a two-part question. Should lift() for free > module morphisms be deprecated? > > If so, in favor of > > (a) a simple renaming, as perhaps "pre_image()" > > OR > > (b) make the existing inverse_image() method more capable: > submodule in, submodule out plus element in, element out. >
I think of "preimage" and "inverse image" as synonyms, both meaning (as Nils says for inverse image) the set of elements in the domain mapping to the given element of, or subset of, the codomain. As such, I think both terms have a precise mathematical meaning, and neither one will assign single elements to single elements: they assign a subset of the domain to a single element of the codomain. For the given situation, I think that the word "lift" is ambiguous, but it may be the best choice. Since it's ambiguous, it can handle the fact that f.lift(x) need not be mathematically well-defined; f.lift(x) is just some element from the preimage of x under f. It's much better to use "lift" than to misuse "inverse_image". Are there any other good candidates? "inverse_image_an_element" is accurate but clunky. I don't think "pullback" would be appropriate. I think extending the inverse_image() method is a good idea (just to singletons or to subsets?), and it should also be extended for morphisms of finitely generated modules over PIDs. -- John -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
