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### 28.6 Miscellaneous Functions

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: roots, 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: polyreduce.

polyreduce (c)

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

See also: polyout.

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