Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[SylvesterMatrix], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The call sylvester(p, q, x) returns the Sylvester matrix of the polynomials p and q with respect to x.  Note that the determinant of this matrix is equal to $\mathrm{resultant}\left(p\,q\,x\right)$.

If p is of degree m in x and q is of degree n in x then the output is a square matrix of dimension $m+n$.

The polynomials p and q must be expanded in x, because the coeff function is used on p and q to determine the entries of the matrix.

The command with(linalg,sylvester) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$p≔a+bx\:$

$q≔c+dx+e{x}^2\:$

$\mathrm{sylvester}\left(p\,q\,x\right)$

$\left[\begin{array}{ccc}b& a& 0\\ 0& b& a\\ e& d& c\end{array}\right]$