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Polynomial coefficient vector derived from sub-polynomial factors

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Polynomial coefficient vector derived from sub-polynomial factors

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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)
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Updates
27 Apr 2009

Correct typo in m-file

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