> 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.
That's exactly what i was thinking of. I know such functionality
would help me with my work. For instance, in factorization, ideal, or
variety calculations, i could simply say to Sage, "I want to work over
QQbar. You figure out the number fields required." It's that ease of
use, as exemplified by Carl's 'variety(ring=QQbar)' command, that i
would like.
> sage: K.<x, y> = PolynomialRing(QQ, 2, order='lex')
> sage: I = Ideal([ x*y - 1, (x-2)^2 + (y-1)^2 - 1])
> sage: I = Ideal(I.groebner_basis())
> sage: I.variety(ring=QQbar)
> [{ y: 0.3194484597356763? - 1.633170240915238?*I, x:
> 0.11535382288068429? + 0.5897428050222055?*I}, {y: 0.3194484597356763?
> + 1.633170240915238?*I, x: 0.11535382288068429? - 0.5897428050222055?
> *I}, {y: 0.3611030805286474?, x: 2.769292354238632?}, {y: 1, x: 1}]
(By the way, there's a Singular bug in the 'variety()' command; see
http://sagetrac.org/sage_trac/ticket/4622 .) The point of my email
was to check if something like this has already been done in Sage or
some other math software system. If not and if i get a grant (time
and money), then i'd like to extend Carl's work which, as he
mentioned, might require a major rewrite of QQbar.
Alex
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