One further example perhaps, to be more convincing : sage: N= (2*x).numerator() sage: N.prime_divisors() [2, x] sage: [valuation(N, p) for p in prime_divisors(N)] # innocent- looking piece of code
... ArithmeticError: The polynomial, p, must have positive degree. I do think the innocent piece of code above ought to work. p. On 1 mar, 20:25, Pierre <[email protected]> wrote: > hmm it's not mathematical, it's just that IMHO n should belong to > QQ[x], not ZZ[x]. I do see your point though, in that the coefficients > should be mathematical integers (or "may as well be"). And I do see > now that it is intentional. > > Think about it : if i wanted to use your metaphor, over QQ the > numerator of a fraction ought to be in ZZ, not in NN, even if it is > positive ! and it should not be in the group {1 ; -1} with two > elements even if it is equal to 1... I guess i'm trying to say that > when k= R.fraction_field(), and when x is in k, then x.numerator() > should be in R. Not in some subset of R. You may well disagree and say > that we can take a convention for numerators such that they always lie > in some subset of R, but I don't think it's a good idea. > > Also think about my nightmare when i ask for the prime divisors of the > numerator of a fraction, expecting polynomials, and getting things > like 2 and 3... I know I can use numerator().change_ring(QQ) but then > my code wouldn't be as general (if I apply 'numerator' to something in > QQ, i find an element of ZZ which doesn't have a change_ring() > method... etc). > > pierre > > On 1 mar, 19:37, Robert Bradshaw <[email protected]> wrote: > > > On Mar 1, 2010, at 7:50 AM, Pierre wrote: > > > > hi all, > > > > is this a bug or intentional ? > > > > sage: x= QQ['x'].gen() > > > sage: n= x.numerator() > > > sage: x.parent() > > > Q[x] > > > sage: n.parent() > > > Z[x] > > > > what about this Z popping out of nowhere ? (well...) It's certainly > > > making my like (a little) more complicated (i have a more involved > > > example of course, and i proceed to look for prime divisors of the > > > numerator). > > > This is just the general definition of numerator and denominator > > extended from Q to Q[x]. I don't see any other definition of numerator > > that would make more sense here... > > > - Robert -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
