A simple way to fix the OP is to set FractionFieldElement.__hash__ to return 0 always.
Though, if we want to keep x == y implies hash(x) == hash(y) through injective coercions then we are in trouble because of fraction fields. One could introduce a framework for canonical representatives of fraction field elements... but it looks like a can of worms. Vincent On Tue, 22 Apr 2025 at 19:06, Nils Bruin <nbr...@sfu.ca> wrote: > > Good find! Indeed, the fraction field of ZZ[x,y] is equally broken. It's just > less pronounced because there are fewer units: > > sage: K.<x,y>=ZZ[] > sage: (-x)/(-y) > (-x)/(-y) > sage: (-x)/(-y) == x/y > True > sage: hash((x)/(y)) > -8752216344059172460 > sage: hash((-x)/(-y)) > -8752216196772797820 > > That hash is bad in other ways too: n^d is symmetric and generally looks > quite likely to generate hash collisions (although that depends a bit on how > garbled the hashes of the numerator and denominator are) > > On Tuesday, 22 April 2025 at 01:35:31 UTC-7 axio...@yahoo.de wrote: >> >> I would think that the method `__hash__` of FractionFieldElement in >> fraction_field_element.pyx is broken, since >> >> sage: f1 = x/y >> sage: f2 = (2*x)/(2*y) >> sage: f1 == f2 >> True >> sage: hash(f1) >> -284264079394034550 >> sage: hash(f2) >> -284264773958195866 >> >> In `__hash__`, we do the following: >> >> if self._parent.is_exact(): >> ... >> self.reduce() >> # Same algorithm as for elements of QQ >> n = hash(self._numerator) >> d = hash(self._denominator) >> if d == 1: >> return n >> else: >> return n ^ d >> >> The problem is that `self.reduce()` doesn't have any effect: it divides out >> the gcd of numerator and denominator, which is 1, since QQ is a field. >> (Over ZZ it is 2, which is the reason why it works) >> >> I don't know how to fix this properly. Can we define a sensible hash >> generically for FractionFieldElement at all? >> >> Partially, this might also be my fault from >> https://github.com/sagemath/sage/pull/38924 >> >> There are other tickets that thought about this, e.g., >> https://github.com/sagemath/sage/issues/16268 >> >> :-( >> >> Martin >> >> On Wednesday, 16 April 2025 at 17:48:47 UTC+2 Nils Bruin wrote: >>> >>> On Wednesday, 16 April 2025 at 04:55:39 UTC-7 Peter Mueller wrote: >>> >>> The following code >>> >>> K.<x, y> = QQ[] >>> K = K.fraction_field() >>> print(len({x/y, (2*x)/(2*y)})) >>> >>> gives the answer 2, even though the two elements of course are the same! Is >>> this a bug or a feature for a reason I cannot guess? Same on the SageMath >>> Cell. >>> >>> >>> I don't think it's a feature but it might be that you're hitting general >>> code that can't do much more than it does. In that case we should probably >>> have a specialization that deals with that particular situation. >>> >>> In your case, we can just force the denominator to be monic. It can make >>> for less nice representations because it might cause fractional >>> coefficients in the numerator and denominator: >>> >>> f.numerator()/(c:=f.denominator().leading_coefficient())/(f.denominator()/c) >>> >>> For this standardization, we need that there's a monomial ordering (which >>> would generally be met) and that the leading coefficient is a unit (true >>> over a field). It's the last one that is generally problematic. In >>> ZZ["x,y"].fraction_field(), you'd already need a different approach and >>> over domains with more complicated unit groups and/or without unique >>> factorization, normalizing the denominator is going to be very expensive. >>> Note that it doesn't affect the ability to compute in the field of >>> fractions: equality testing is still easy. It's just the normal form that's >>> hard (and which is necessary to get to a well-defined hash). >>> >>> Funniliy enough: >>> >>> K.<x, y> = ZZ[] >>> >>> K = K.fraction_field() >>> print(len({x/y, (2*x)/(2*y)})) >>> >>> so it seems that the extra work was already done in that case. And that's >>> also the representation in which you'll avoid denominators in the >>> denominator! So probably it's better to switch to that representation. If >>> you need polynomials you can use >>> >>> QQ['x,y'](f) >>> >>> when the denominator has degree 0. >>> > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion visit > https://groups.google.com/d/msgid/sage-support/43c4110d-3238-4039-b47f-4c593e453338n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-support/CAGEwAAnRbDoiE0xESsD_dEUBTDWQMOHohc_vv8G7afUenbTgFg%40mail.gmail.com.
