If ever there was a blocker, surely this is it!
John
---------- Forwarded message ----------
From: Anton Mellit <mel...@gmail.com>
Date: 16 February 2015 at 23:54
Subject: [sage-support] Bug in polynomial GCD (FLINT)
To: sage-supp...@googlegroups.com
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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