### 28.6 Miscellaneous Functions

Function File: poly (A)
Function File: 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: roots, eig.

Function File: polyout (c)
Function File: polyout (c, x)
Function File: str = polyout (…)

  Write formatted polynomial

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

  and return it as a string or write it to the screen (if nargout is zero). x defaults to the string `"s"`.

  See also: polyreduce.

Function File: polyreduce (c)

  Reduce a polynomial coefficient vector to a minimum number of terms by stripping off any leading zeros.

  See also: polyout.