On Feb 14, 7:27 am, Ben Hutz <[email protected]> wrote:
> R.<x,y,c>=PolynomialRing(QQbar,3)
> Y=(x^4*y + 2*c*x^2*y^3 - x*y^4 + (c^2 + c)*y^5)/(x^2*y - x*y^2 +c*y^3)

In addition, this doesn't simplify, whereas over QQ sage recognizes
the denominator divides the numerator (you still get a fraction field
element, though). That's probably because we only have basic
multivariate polynomial arithmetic over QQbar (no gcds/groebner
bases).

Incidentally,

sage: R.<x,y,z>=QQ[]
sage: K=FractionField(R)
sage: hash(R.0),hash(K.0)
(15360174650385711, 15360174650385711)

so there the discrepancy in hash values does not occur.

The practical solution to your problem is probably to only use QQbar
where you really need to.

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