Re: polresultant disagrees with sage, maxima and magma

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Thu, Sep 20, 2012 at 03:26:57PM +0200, Andreas Enge wrote:
> 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.

If x1 has highest priority then indeed the computation is done in
Q(x2,x3,x4)[x1] and indeed the result is 1.

x1;p1=x2*(x3-x4);p2=x2*(x3-2*x4);polresultant(p1,p2,x1)
%1 = 1

Cheers,
Bill.