On Thursday, September 20, 2012 1:05:56 PM UTC+2, Georgi Guninski wrote:
>
> pari disagrees with sage and maxima agrees with it. 
>
> which way is it? 
>
> maxima session: 
> (%i12) p1:(x2)*(x3-x4);p2:x2*(x3-2*x4); 
> (%i14) resultant(p1,p2,x1); 
> (%o14)                                 1 
>

In this case, there is no evaluation of x1 in the algbebraic closure of 
QQ(x2,x3,x4) that makes both polynomials zero.
 

> (%i15) resultant(p1,p2,x2); 
> (%o15)                                 0
>

In this case, there is a common root in the algebraic closure of 
QQ(x1,x3,x4), namely x2=0

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