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Polynomial coefficient vector derived from sub-polynomial factors

Feng Cheng Chang (view profile)

25 Apr 2009 (Updated )

A polynomial coefficient vector is derived from several powered polynomial factors.

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Description

For given
p(x) = PROD[i=1,m]{SUM[j=2,n+2]{(A(i,j)*x^(j-2))^A(i,1)}}
we shall get
p(x) = SUM[s=1,N+1]{p(s)^(N+1-s)}

For example
If
p(x) = (x-4)^5 * (3x^6-7x^3+5x+2)^2 * (x^3+8)^3 * x^2
or
A = [ 5 -4 1 0 0 0 0 0
2 2 5 0 -7 0 0 3
3 8 0 0 1 0 0 0
1 0 0 1 0 0 0 0 ]
then from
p = polyget(A)
we get
p = [ 9 -180 1440 -5586 .... -7864320 -209715 0 0 ]
or
p(x) = 9x^28-180x^27+1440x^26-5586x^25+ ... -7864320x^3-2097152x^2.

This routine is mainly to be used for creating test polynomials to
(a) determine the polynomial GCD of a pair of polynomials,
(b) find the roots with muliplicities of a given polynomial.

References in MATLAB Central:
(1) "GCD of polynomials,"
File ID 20859, 12 Apr 2009
(2) "Factorization of a polynomial with multiple roots,"
File ID: 20867, 27 Jul 2008
(3) "Multiple-roots polynomial solved by partial fraction expansion,"
File ID: 22375, 10 Dec 2008

F C Chang 04/25/09

Acknowledgements

This file inspired Solving Multiple Root Polynomials and Polynomials With Multiple Roots Solved.

MATLAB release MATLAB 6.5 (R13)