Vincent Delecroix wrote: > That does not prevent us to normalize for let say: __repr__() , > numerator(), denominator(). Is there any reasonable rule to choose > when to and when not to normalize? For QQ itself, GMP does normalize > all the time.
Just to be certain that we are talking about the same thing: Currently, elements of fraction fields are always reduced (except over inexact rings) in the sense of dividing out by the gcd of the numerator and the denominator. But no further normalization is done, and in particular, when the numerator and denominator are polynomials, their contents or leading coefficients are not normalized. There is a ticket needing review that proposes to normalize the leading coefficient of the denominator to one: https://trac.sagemath.org/ticket/16268 Actually, I first tried implementing a version that would systematically clear denominators inside the numerator and denominator of the fraction, but I didn't manage to make it reasonably fast, even with a dedicated class for polynomials over fraction fields (with a single denominator, similar to the representation of polynomials over ℚ). While I'm not saying it can't be done, in the short term, the version at #16268 is a lot simpler and already fixes a number of issues! Regarding your question: Having a variant of numerator()/denominator() that works recursively would definitely be useful, and yes, it may be nice to use it in __repr__(). At the same time, I think we do want to keep programmatic access to the “true” numerator and denominator as defined in the data structure. In case you want to experiment with the idea, here is a (perhaps a bit naive, improvements welcome!) implementation of something similar that I needed for something I'm working on. It is intended to be used with #16268 and #23909. def _my_lcm(elts): # non monic l = ZZ.one() for p in elts: l *= (p//p.gcd(l)) return l def _clear_denominators_1(elt, dom): num, den = elt.numerator(), elt.denominator() base = dom.base_ring() if isinstance(base, FractionField_generic): numnum, numden = clear_denominators(num, base) dennum, denden = clear_denominators(den, base) newdom = dom.change_ring(base.ring()) numnum = newdom(numnum) dennum = newdom(dennum) gnum = numnum.gcd(dennum) numnum, dennum = numnum//gnum, dennum//gnum gden = numden.gcd(denden) numden, denden = numden//gden, denden//gden return (numnum, numden, dennum, denden) else: return (num, dom.one(), den, dom.one()) def clear_denominators(elts, dom=None): r""" Recursively clear denominators in a list (or other iterable) of elements. Typically intended for elements of fields like QQ(x)(y). """ if not elts: return elts, dom.one() if dom is None: dom = elts[0].parent() if isinstance(dom, FractionField_generic): ring = dom.ring() split = [_clear_denominators_1(elt, ring) for elt in elts] lcmnum = _my_lcm((dennum for _, _, dennum, _ in split)) lcmden = _my_lcm((numden for _, numden, _, _ in split)) num = [(denden*(lcmden//numden))*(numnum*(lcmnum//dennum)) for (numnum, numden, dennum, denden) in split] den = lcmden*lcmnum g = gcd(num + [den]) # XXX: can we be more specific here? num = [p//g for p in num] den = den//g else: num, den = elts, dom.one() # assert all(b/den == a for a, b in zip(elts, num)) # assert gcd(num + [den]).is_one() return num, den -- Marc -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
