### 27.6 Miscellaneous Functions

— Function File: poly (a)

> 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. As an example we can use this to find the eigenvalues of a as the roots of `poly (`a`)`.

>               roots(poly(eye(3)))
>               => 1.00000 + 0.00000i
>               => 1.00000 - 0.00000i
>               => 1.00000 + 0.00000i

> In real-life examples you should, however, use the `eig` function for computing eigenvalues.

> If x is a vector, `poly (`x`)` is a vector of coefficients of the polynomial whose roots are the elements of x. That is, of c is a polynomial, then the elements of d`= roots (poly (`c`))` are contained in c. The vectors c and d are, however, not equal due to sorting and numerical errors.

> See also: eig, roots.

— Function File: polyout (c, x)

> 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: polyval, polyvalm, poly, roots, conv, deconv, residue, filter, polyderiv, and polyinteg.

— Function File: polyreduce (c)

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

> See also: poly, roots, conv, deconv, residue, filter, polyval, polyvalm, polyderiv, polyinteg.