polresultant

Function: polresultant
Section: polynomials
C-Name: polresultant0
Prototype: GGDnD0,L,
Help: polresultant(x,y,{v},{flag=0}): resultant of the polynomials x and y,
 with respect to the main variables of x and y if v is omitted, with respect
 to the variable v otherwise. flag is optional, and can be 0: default,
 uses either the subresultant algorithm, a modular algorithm or Sylvester's
 matrix, depending on the inputs; 1 uses Sylvester's matrix (should always be
 slower than the default).
Doc: resultant of the two
 polynomials $x$ and $y$ with exact entries, with respect to the main
 variables of $x$ and $y$ if $v$ is omitted, with respect to the variable $v$
 otherwise. The algorithm assumes the base ring is a domain. If you also need
 the $u$ and $v$ such that $x*u + y*v = \text{Res}(x,y)$, use the
 \tet{polresultantext} function.

 If $\fl=0$ (default), uses the algorithm best suited to the inputs,
 either the \idx{subresultant algorithm} (Lazard/Ducos variant, generic case),
 a modular algorithm (inputs in $\Q[X]$) or Sylvester's matrix (inexact
 inputs).

 If $\fl=1$, uses the determinant of Sylvester's matrix instead; this should
 always be slower than the default.

 If $x$ or $y$ are multivariate with a huge \emph{polynomial} content, it
 is advisable to remove it before calling this function. Compare:
 \bprog
 ? a = polcyclo(7) * ((t+1)/(t+2))^100;
 ? b = polcyclo(11)* ((t+2)/(t+3))^100);
 ? polresultant(a,b);
 time = 3,833 ms.
 ? ca = content(a); cb = content(b); \
   polresultant(a/ca,b/cb)*ca^poldegree(b)*cb*poldegree(a); \\ instantaneous
 @eprog\noindent The function only removes rational denominators and does
 not compute automatically the content because it is generically small and
 potentially \emph{very} expensive (e.g. in multivariate contexts).
 The choice is yours, depending on your application.

Function: _ZX_resultant_worker
C-Name: ZX_resultant_worker
Prototype: GGGG
Section: programming/internals
Help: worker for ZX_resultant

Function: _ZX_ZXY_resultant_worker
C-Name: ZX_ZXY_resultant_worker
Prototype: GGGGG
Section: programming/internals
Help: worker for ZX_ZXY_resultant

Function: _ZXQX_resultant_worker
C-Name: ZXQX_resultant_worker
Prototype: GGGGG
Section: programming/internals
Help: worker for ZXQX_resultant