Change language to:
Français - 日本語 - Português

Please note that the recommended version of Scilab is 2023.1.0. This page might be outdated.
See the recommended documentation of this function

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`

 << simp_mode Polynomials systmat >>

 Copyright (c) 2022-2023 (Dassault Systèmes)Copyright (c) 2017-2022 (ESI Group)Copyright (c) 2011-2017 (Scilab Enterprises)Copyright (c) 1989-2012 (INRIA)Copyright (c) 1989-2007 (ENPC)with contributors Last updated:Thu Mar 03 10:59:42 CET 2011