polresultantext

Function: polresultantext
Section: polynomials
C-Name: polresultantext0
Prototype: GGDn
Help: polresultantext(A,B,{v}): return [U,V,R] such that
 R=polresultant(A,B,v) and U*A+V*B = R, where A and B are polynomials.
Doc: finds polynomials $U$ and $V$ such that $A*U + B*V = R$, where $R$ is
 the resultant of $U$ and $V$ with respect to the main variables of $A$ and
 $B$ if $v$ is omitted, and with respect to $v$ otherwise. Returns the row
 vector $[U,V,R]$. The algorithm used (subresultant) assumes that the base
 ring is a domain.
 \bprog
 ? A = x*y; B = (x+y)^2;
 ? [U,V,R] = polresultantext(A, B)
 %2 = [-y*x - 2*y^2, y^2, y^4]
 ? A*U + B*V
 %3 = y^4
 ? [U,V,R] = polresultantext(A, B, y)
 %4 = [-2*x^2 - y*x, x^2, x^4]
 ? A*U+B*V
 %5 = x^4
 @eprog
Variant: Also available is
 \fun{GEN}{polresultantext}{GEN x, GEN y}.