sylm

Scilab Function
Last update : April 1993

sylm - Sylvester matrix

### Calling Sequence

  `[S]=sylm(a,b)`

### Parameters

- `a,b`: two polynomials
- `S`: matrix

### Description

`sylm(a,b)` gives the Sylvester matrix associated to polynomials `a` and `b`, i.e. the matrix `S` such that:

`coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)']`.

Dimension of `S` is equal to `degree(a)+degree(b)`.

If `a` and `b` are coprime polynomials then

`rank(sylm(a,b))=degree(a)+degree(b))` and the instructions

      u = sylm(a,b) \ eye(na+nb,1)
      x = poly(u(1:nb),'z','coeff')
      y = poly(u(nb+1:na+nb),'z','coeff')

compute Bezout factors `x` and `y` of minimal degree such that `a*x+b*y = 1`