(octave.info)Miscellaneous Functions

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28.6 Miscellaneous Functions
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 -- : poly (A)
 -- : poly (X)
     If A is a square N-by-N matrix, ‘poly (A)’ is the row vector of the
     coefficients of ‘det (z * eye (N) - A)’, the characteristic
     polynomial of A.

     For example, the following code finds the eigenvalues of A which
     are the roots of ‘poly (A)’.

          roots (poly (eye (3)))
              ⇒ 1.00001 + 0.00001i
                 1.00001 - 0.00001i
                 0.99999 + 0.00000i

     In fact, all three eigenvalues are exactly 1 which emphasizes that
     for numerical performance the ‘eig’ function should be used to
     compute eigenvalues.

     If X is a vector, ‘poly (X)’ is a vector of the coefficients of the
     polynomial whose roots are the elements of X.  That is, if C is a
     polynomial, then the elements of ‘D = roots (poly (C))’ are
     contained in C.  The vectors C and D are not identical, however,
     due to sorting and numerical errors.

     See also: Note: roots, Note: eig.

 -- : polyout (C)
 -- : polyout (C, X)
 -- : STR = polyout (...)
     Display a formatted version of the polynomial C.

     The formatted polynomial

          c(x) = c(1) * x^n + ... + c(n) x + c(n+1)

     is returned as a string or written to the screen if ‘nargout’ is
     zero.

     The second argument X specifies the variable name to use for each
     term and defaults to the string "s".

     See also: Note: polyreduce.

 -- : polyreduce (C)
     Reduce a polynomial coefficient vector to a minimum number of terms
     by stripping off any leading zeros.

     See also: Note: polyout.