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sylvester

the Sylvester matrix of two polynomials

Syntax
sylvester(F:POLY, G:POLY, X:INDET)

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