CoCoA:Sylvester

Sylvester

the Sylvester matrix of two polynomials

Description

This function returns the Sylvester matrix of the polynomials F and G

with respect to the indeterminate X. This is the matrix used to

calculate the resultant.

Example

  Use R ::= Q[p,q,x];
  F := x^3+px-q; G := Der(F,x);
  Sylvester(F,G,x);
Mat([
  [1, 0, p, -q, 0],
  [0, 1, 0, p, -q],
  [3, 0, p, 0, 0],
  [0, 3, 0, p, 0],
  [0, 0, 3, 0, p]
])
-------------------------------
  Det(Sylvester(F,G,x)) = Resultant(F,G,x);
TRUE
-------------------------------

Syntax

Sylvester(F:POLY,G:POLY,X:INDET)

Resultant

   <type>polynomial</type>