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Scilab help >> Polynomials > sylm

# sylm

Sylvester matrix

### Calling Sequence

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

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`

### Examples

```x = poly(0,"x")
y = poly ([1, 2, 3], "x","coeff");
sylm(x,y)```