sylm
====

Sylvester matrix



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [S]=sylm(a,b)




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`