On Mon, Jan 19, 2009 at 4:46 PM, Alex Raichev <tortoise.s...@gmail.com> wrote: > > Hi everyone: > > I'm applying for a grant from the New Zealand government to fund some > Sage development in the area of computational algebraic and analytic > geometry. For part of the application i need to report on the 'state > of the field'. Part of my response to this will be to mention that > Sage doesn't have an implementation of factorization, ideal, and > variety calculations over QQbar. To double-check, is this true? > Related to that, do any major computer algebra systems (Singular > included) have such implementations? > > Alex
Any commutative algebra computer computation over QQbar can be reduced to a computation over a specific absolute number field, since there are only finitely many symbols in the input to the calculation. Singular, etc., fully supports doing commutative algebra over absolute number fields. I think Singular doesn't explicitly support relative extensions, but might be able to do them anyways by just throwing in more variables. So if you're asking whether computer algebra systems such as Singular, Macaulay 2, Magma, etc., implement commutative algebra over QQbar the answer is formally "yes", in that there is a direct translation of any problem over QQbar into a problem they are designed to solve. Sage and probably the other systems are probably VERY awkward for actually doing computations over QQbar. There's a lot of bookkeeping and stuff that one would have to do, and conceptually it would be painful. Also, being able to do relative extensions is critical, since e.g., your coefficients could be the square roots of the primes up to 1000, and as an absolute field they would generate an extension of degre 2^168, which is too big. So, I'm curious, did you envision your proposal to be to automate all bookkeeping in translating between QQbar (as presented to the user) and numbers fields (as fed to the backend Singular)? I think this would be very nice and useful. - William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
