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## 27.6 Miscellaneous Functions

__Function File:__**poly***(*`a`)If

`a`is a square*N*-by-*N*matrix,`poly (`

is the row vector of the coefficients of`a`)`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 (`

is a vector of coefficients of the polynomial whose roots are the elements of`x`)`x`. That is, of`c`is a polynomial, then the elements of

are contained in`d`= roots (poly (`c`))`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.