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Aide de Scilab >> Polynômes > sylm

# sylm

matrice de Sylvester

### Séquence d'appel

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

a,b

deux polynômes

S

matrice

### Description

`sylm(a,b)` renvoie la matrice de Sylvester associée aux polynômes `a` et `b`, i.e. la matrice `S` telle que :

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

La dimension de `S` est égale à `degree(a)+degree(b)`.

Si `a` et `b` sont premiers entre eux alors

`rank(sylm(a,b))=degree(a)+degree(b))` et les 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')```

calculent les facteurs de Bezout `x` ainsi que `y` de degré minimum tels que `a*x+b*y = 1`

### Exemples

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