Derivative computation does not finish over finite field.

[pogudingleb]

The following code

using Nemo

R, (l1, l2, l3, a1, a2, a3, b1, b2, b3, g1, g2, g3) = polynomial_ring(Nemo.GF(2^31 - 1), ["l1", "l2", "l3", "a1", "a2", "a3", "b1", "b2", "b3", "g1", "g2", "g3"])

f =  (-a1*b1^2*g2^2 - a1*b1^2*g3^2 - a1*b1*b2*g1*g2 - a1*b1*b3*g1*g3 + a1*b2^2*g3^2 + 2*a1*b2*b3*g2*g3 + a1*b3^2*g2^2 + a2*b1^2*g3^2 - a2*b1*b2*g1*g2 + 2*a2*b1*b3*g1*g3 - a2*b2^2*g1^2 - a2*b2^2*g3^2 - a2*b2*b3*g2*g3 + a2*b3^2*g1^2 + a3*b1^2*g2^2 + 2*a3*b1*b2*g1*g2 - a3*b1*b3*g1*g3 + a3*b2^2*g1^2 - a3*b2*b3*g2*g3 - a3*b3^2*g1^2 - a3*b3^2*g2^2)//(l1*a2*b1*g2*g3 + l1*a2*b2*g1*g3 + l1*a2*b3*g1*g2 - l1*a3*b1*g2*g3 - l1*a3*b2*g1*g3 - l1*a3*b3*g1*g2 - l2*a1*b1*g2*g3 - l2*a1*b2*g1*g3 - l2*a1*b3*g1*g2 + l2*a3*b1*g2*g3 + l2*a3*b2*g1*g3 + l2*a3*b3*g1*g2 + l3*a1*b1*g2*g3 + l3*a1*b2*g1*g3 + l3*a1*b3*g1*g2 - l3*a2*b1*g2*g3 - l3*a2*b2*g1*g3 - l3*a2*b3*g1*g2)

derivative(f, b1)

does not finish in an hour (also with Native.GF instead of GF). The calculation finishes quickly over QQ.
I have reproduced this problem with Nemo 0.54.1 on Julia 1.10.8 and with Nemo 0.49.5 with Julia 1.11.7.

Thank you in advance!

[thofma]

From a quick look at it, the following gcd computation does not finish:

julia> h = (derivative(numerator(f), 7)*denominator(f) - numerator(f)*derivative(denominator(f), 7));

julia> g = denominator(f)^2;

julia> gcd(h, g)
# does not finish

[thofma]

I opened flintlib/flint#2581 to track this in flint. There is not much we can do here.