When I first tried Ben's OP code, it worked as there. Then when trying
Nil's code, I get the same output as Ben, but when I immediate after run
sage: D2 / D1
...Same traceback as above...
ZeroDivisionError: fraction field element division by zero
Now in a fresh Sage session, I immediately get the zero division error for
D2 / D1, but then running Nil's code, I now get:
sage: Kp = parent(1/D1)
sage: r = Kp(D2)
sage: s = Kp(1/D1)
sage: r.numerator().gcd(s.denominator())
a*x^3 + (-a)*x^2*y + (-a^2 + 3*a - 1)*x*y^2 + (2*a^2 - 3*a + 1)*y^3
sage: r * s
ZeroDivisionError
sage: r.numerator().gcd(s.denominator())
0
So I think Nil's correctly identified the main symptom, but Ben's diagnosis
is almost correct. It is not something being cached but an internal
property being changed in some place where it believes it is safe to mutate
it. I have created a new issue
https://github.com/sagemath/sage/issues/35886 and put some additional
observations.
Best,
Travis
On Wednesday, June 28, 2023 at 1:42:35 AM UTC+9 Ben Hutz wrote:
> I'm not getting 0 with that code:
>
> sage: K. = Frac(QQ['a'])
> sage: P. = ProjectiveSpace(K, 1)
> sage: D2=-x^5 + (-3*a^2 + 7*a - 2)/a*x^4*y + (6*a^2 - 12*a + 4)/a*x^3*y^2
> + (3*a^4 - 19*a^3 + 29*a^2 - 14*a + 2)/(a^2)*x^2*y^3 + (-8*a^4 + 30*a^3 -
> 37*a^2 + 18*a - 3)/(a^2)*x*y^4 + (4*a^4 - 12*a^3 + 13*a^2 - 6*a +
> 1)/(a^2)*y^5
> sage: D1=-x^3 + x^2*y + (a^2 - 3*a + 1)/a*x*y^2 + (-2*a^2 + 3*a - 1)/a*y^3
>
> sage: K=parent(1/D2)
> sage: r=K(D1)
> sage: s=K(1/D2)
> sage: r.numerator().gcd(s.denominator())
> a*x^3 + (-a)*x^2*y + (-a^2 + 3*a - 1)*x*y^2 + (2*a^2 - 3*a + 1)*y^3
>
>
> However, if I run
> sage: K. = Frac(QQ['a'])
> sage: P. = ProjectiveSpace(K, 1)
> sage: f = x^2 + (a + 1/a - 3)*x*y - (2*a + 1/a - 3)*y^2
> sage: phi = DynamicalSystem_projective([f,x^2])
> sage: phi.dynatomic_polynomial(2)
> 0
>
> and *then* run the code I get zero.
>
> sage: K. = Frac(QQ['a'])
> sage: P. = ProjectiveSpace(K, 1)
> sage: D2=-x^5 + (-3*a^2 + 7*a - 2)/a*x^4*y + (6*a^2 - 12*a + 4)/a*x^3*y^2
> + (3*a^4 - 19*a^3 + 29*a^2 - 14*a + 2)/(a^2)*x^2*y^3 + (-8*a^4 + 30*a^3 -
> 37*a^2 + 18*a - 3)/(a^2)*x*y^4 + (4*a^4 - 12*a^3 + 13*a^2 - 6*a +
> 1)/(a^2)*y^5
> sage: D1=-x^3 + x^2*y + (a^2 - 3*a + 1)/a*x*y^2 + (-2*a^2 + 3*a - 1)/a*y^3
>
> sage: K=parent(1/D2)
> sage: r=K(D1)
> sage: s=K(1/D2)
> sage: r.numerator().gcd(s.denominator())
> 0
>
>
> So I still find that weird. Is there something being oddly cached?
> On Monday, June 26, 2023 at 4:04:18 PM UTC-5 Nils Bruin wrote:
>
>> With your data, we get:
>>
>> sage: K=parent(1/D2)
>> sage: r=K(D1)
>> sage: s=K(1/D2)
>> sage: r.numerator().gcd(s.denominator())
>> 0
>>
>> and I think that's the zero which leads to the division-by-zero error. Of
>> course, a 0 returned as gcd is just a bug. It doesn't look like the
>> coercion framework is really involved here.
>>
>>
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