Here is the code:
R.<q>=QQ[]
X=3*q^12 - 8*q^11 - 24*q^10 - 48*q^9 - 84*q^8 - 92*q^7 - 92*q^6 - 70*q^5 -
50*q^4 - 27*q^3 - 13*q^2 - 4*q - 1
Y=q^13 - 2*q^12 + 2*q^10 - q^9
print gcd(X,Y)
print X(1)
Here is the output:
q - 1 -510
The bug is extremely serious because it affects all computations with
rational functions. It is also quite rare, I believe. I traced it down to
the function _fmpz_poly_gcd_heuristic in FLINT. The bug is triggered when
the heuristic algorithm fails, one of the divisibility checks fails, but
still the value is returned as o.k.
The fix is easy, just one line needs to be added
if (divides) /* quotient really was exact */ { --->>>>> divides=0;
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