On Feb 3, 2007, at 12:14 PM, Joel B. Mohler wrote:

> Here's an annoying bug in an edge case.  It appears that PARI (the  
> QQ case
> below) computes the resultant correctly for a constant polynomial  
> with itself
> and NTL (the ZZ case below) computes it incorrectly.  I'm not  
> really sure
> what the correct fix would be.  I guess it's a small bug in NTL, but I
> haven't looked at that code yet.  Should I be fixing this in NTL  
> (eek, I
> haven't touched that code!) or making a special case?
>
> sage: P=PolynomialRing(QQ,'t')
> sage: f=P(1)
> sage: f.resultant(f)
> 1
> sage: P=PolynomialRing(ZZ,'t')
> sage: f=P(1)
> sage: f.resultant(f)
> 0

If it really is a bug in NTL, you should report it to Victor Shoup  
(the author of NTL). You won't get a fix too quickly, so you might  
also want to rewrite the SAGE code to translate to PARI and then back  
to NTL. It's going to be slow, but the Z[x] class will be rewritten  
using FLINT fairly soon, so it's not a long term problem.

David


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