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Aide de Scilab >> Polynômes > sylm

sylm

matrice de Sylvester

Séquence d'appel

[S]=sylm(a,b)

Paramètres

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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Last updated:
Thu Oct 02 13:54:32 CEST 2014