On 1 mar, 20:46, Pierre <pierre.guil...@gmail.com> wrote: > oooh wait wait wait. I've said something totally confusing. > > My previous two posts apply to rational fractions... for which indeed, > the numerator method gives the 'correct' answer ! The issue I raised > in my original post is the 'funny' behaviour when you ask for the > numerator of something in QQ[x] -- which, come to think of it, is > mathematically a little unsound. I just totally assumed this should > give the same answer as coercing into the field of rational fractions > and then applying numerator(), but it doesn't. You (Robert) assumed > something absolutely different. > > (Now i still think it would be less surprising is sage acted as i > suggested, but i don't have strong feelings about it anymore :) ) > > so in any case, having realized this, i have found an ugly fix : > > sage: N= P.parent().fraction_field()(P).numerator() # gives what i > want !! always work !
Yes, this is intentional, I think that it is used somewhere for number theory. As pointed out, there is no good definition for numerator of an element in QQ[x]. The current implementation for polynomial rings K[x1,..,xn] is as following: -For the denominator: if there is a denominator function for the coefficients and these denominators have a lcm function, then return the lcm of the coefficients. This is an element of K, not K[x1,...,xn] -If the previous computation fails, then return K(1) not K[x1,...,xn] (1) The numerator is the original polynomial times its denominator. This is always in K[x1,..,xn] It has its drawbacks, as you have found. In particular, the numerator of an element in QQ[x] is not necessarily the same as the numerator of the same element in QQ(x). It has its advantages though. If you try this: sage: K=QQ['x'] sage: L=K.fraction_field()['y'] sage: f=L.random_element() sage: f.numerator() sage: QQ['x','y'](f.numerator()) f lives in Q(x)[y], but its numerator can be coerced to Q[x,y] wich is nice for some computations. So, in fact, it depends much on what are you computing. -- 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 URL: http://www.sagemath.org
