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.TH sylmX 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
sylm - Sylvester matrix
.SH CALLING SEQUENCE
.nf
[S]=sylm(a,b)
.fi
.SH PARAMETERS
.TP
a,b
: two polynomials
.TP
S
: matrix
.SH DESCRIPTION
\fVsylm(a,b)\fR gives the Sylvester matrix associated to polynomials
\fVa\fR and \fVb\fR, i.e. the matrix \fVS\fR such that:
.LP
\fVcoeff( a*x + b*y )' = S * [coeff(x)';coeff(y)']\fR.
.LP
Dimension of \fVS\fR is equal to \fVdegree(a)+degree(b)\fR.
.LP
If \fVa\fR and \fVb\fR are coprime polynomials then
.LP
\fVrank(sylm(a,b))=degree(a)+degree(b))\fR and the instructions
.nf
u = sylm(a,b) \\ eye(na+nb,1)
x = poly(u(1:nb),'z','coeff')
y = poly(u(nb+1:na+nb),'z','coeff')
.fi
compute Bezout factors \fVx\fR and \fVy\fR of minimal degree
such that \fVa*x+b*y = 1\fR
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