I can confirm this is definitely a bug in flint. And the fix is absolutely
correct. Thanks to Anton Mellit for not only figuring out which library was
at fault, but actually tracing it to an individual line of C code!!
It is a rare corner case, but very serious.
I will issue a patch release with the fix as soon as possible.
Bill.
On Tuesday, 17 February 2015 10:06:11 UTC+1, John Cremona wrote:
>
> If ever there was a blocker, surely this is it!
>
> John
>
>
> ---------- Forwarded message ----------
> From: Anton Mellit <mel...@gmail.com <javascript:>>
> Date: 16 February 2015 at 23:54
> Subject: [sage-support] Bug in polynomial GCD (FLINT)
> To: sage-s...@googlegroups.com <javascript:>
>
>
> 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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