Thanks, Nils and John, for the helpful comments. I see "lift" as worse than ambiguous - on tab-completion it does not suggest to me any possibility of doing what it does. I cannot even recall quite how I found it.
But I agree that the terms "preimage" and "inverse image" should return a full set, no matter what. As Nils notes, in the setting of modules, the set of preimages is a coset. The quotient by the kernel is available in Sage, though somewhat obfuscated by returning a new module along with mappings to translate back to the setting of the original module. However, the function in question, which returns just one element, is giving a representative of this coset. So how about "preimage_representative"? Says precisely (mathematically) what it is, reasonably obvious on tab-completion, and less clunky than "inverse_image_an_element". I'm finding this function useful, just as implemented. It would be an improvement to have something like inverse_image() give back the full set in some useful form. For what it is worth, the full set that is a preimage of a single codomain element appears to be called a "fiber" in some settings. Rob -- 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
