On Apr 29, 10:00 am, "John Cremona" <[EMAIL PROTECTED]> wrote: > Jon's vision of lattices would include the ones I mentioned before > (f.g. but not necessarily free R-modules where R is a Dedekind Domain, > with one or more embeddings into RR^n or CC^n). > > In another direction: Jon, to what extent could your quadratic form > class be extended to binary forms of higher degree?
The quadratic forms code as it stands does not extend to higher degree forms. I think it is better to implement anew higher degree forms, depending on what functionality is desired. There are basic choices of whether to deal with a degree n form, or it's associated linear tensor, or some combinations of the two, which make the implementations different depending on the goal. In the quadratic case, I chose to store the form coefficients and not the symmetric bilinear form. This distinction becomes important in characteristic two, but is usually ignored for most applications. The more specialized routines (equivalence testing, densities, etc.) are too specialized to apply in the context you suggest. > This seems to be quite a common situation: we have some kind of > mathematical object (in this case, binary quadratic form) which has > its own very rich structure and set of specialised methods, but which > is also a special case of various *different* other objects: in this > case, quadratic forms in more variables, or higher degree binary > forms, and so on. > In these cases, it seems like the particular application should guide the choices of where to stop. Of course, it is a good idea to be as general as possible if it's no extra work. Computing with some of the other structures mentioned are interesting, and I hope that my students will work to develop these further. We'll definitely talk about this at the UGA SAGE Days in March! =) -Jon =) --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
