← Back to branch summary

~ubuntu-branches/ubuntu/karmic/scilab/karmic

« back to all changes in this revision

Viewing changes to man/polynomials/sylm.cat

  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2002-03-21 16:57:43 UTC
  • Revision ID: james.westby@ubuntu.com-20020321165743-e9mv12c1tb1plztg
Tags: upstream-2.6
Import upstream version 2.6

Show diffs side-by-side

added added

removed removed

Lines of Context:
man/polynomials/sylm.cat
 
1
sylmX            Scilab Group            Scilab Function              sylmX
 
2
NAME
 
3
   sylm - Sylvester matrix
 
4
  
 
5
CALLING SEQUENCE
 
6
 [S]=sylm(a,b)
 
7
PARAMETERS
 
8
 a,b  : two polynomials
 
9
      
 
10
 S    : matrix
 
11
      
 
12
DESCRIPTION
 
13
   sylm(a,b) gives the Sylvester matrix associated to polynomials a and b,
 
14
  i.e. the matrix S such that:
 
15
  
 
16
   coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)'].
 
17
  
 
18
   Dimension of S is equal to degree(a)+degree(b).
 
19
  
 
20
   If a and b are coprime polynomials then
 
21
  
 
22
   rank(sylm(a,b))=degree(a)+degree(b)) and the instructions
 
23
  
 
24
   u = sylm(a,b) \ eye(na+nb,1)
 
25
   x = poly(u(1:nb),'z','coeff')
 
26
   y = poly(u(nb+1:na+nb),'z','coeff')
 
27
   compute Bezout factors x and y of minimal degree  such that a*x+b*y = 1  
 
28
  
 
29