sylm

Arguments

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)