Re: polresultant disagrees with sage, maxima and magma

[Andreas Enge <andreas.enge@inria.fr>]

On Thu, Sep 20, 2012 at 04:09:07PM +0300, Georgi Guninski wrote:
> I don't claim this is a bug in pari, more like a bug in the
> mentioned CAS.
> 
> ? p1=x2*(x3-x4);p2=x2*(x3-2*x4);polresultant(p1,p2,x1)
> %1 = 0
> 
> Since p1 and p2 certainly have common roots I expect the resultant
> w.r.t. x1 (not present in p1 or p2) to be able to vanish.

As a polynomial in x1, both polynomials are constant and non-zero and so do
not have roots. The correct result should be 1.

Also interesting:
? polresultant(x,y,z)
%1 = x
? polresultant(y,x,z)
%2 = x

And:
? polresultant(x,y,x)
%7 = y

All of these should be 1, if I understand resultants correctly.

Andreas