Sylvester matrix
[S]=sylm(a,b)
:a,b two polynomials : :S matrix :
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