On Jan 19, 7:50 pm, William Stein <wst...@gmail.com> wrote: > 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.
I don't remember any features in Singular that would let you handle relative extensions in any reasonable way; I think it only deals with aboslute fields. > 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. Currently, QQbar always computes absolute fields internally; being able to get elements of QQbar in terms of relative extensions would require a major rewrite of QQbar, unless there's some sort of trick I'm not thinking of. Such a rewrite could be a good thing, but I probably won't do it. I'd be happy to answer questions, etc., if somebody else wanted to try, though. Carl --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
