sylvester

sylvester

the Sylvester matrix of two polynomials

Syntax

sylvester(F: RINGELEM, G: RINGELEM, X: RINGELEM): MAT

Description

(sorry Sylvester for the lower-case: here we follow the naming convention single name goes lower-case)

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 ::= QQ[p,q,x];
/**/  F := x^3+p*x-q;  G := deriv(F, x);
/**/  sylvester(F, G, x);
matrix( /*RingWithID(36, "QQ[p,q,x]")*/
 [[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

See Also

resultant