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## 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.

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, 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.

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