roots

Scilab Function
Last update : 02/11/2005

roots - roots of polynomials

### Calling Sequence

  `[x]=roots(p)`
  `[x]=roots(p,'e')`

### Parameters

- `p` : polynomial with real or complex coefficients or vector of the polynomial coefficients in decreasing degree order (Matlab compatibility).

### Description

`x=roots(p)` returns in the complex vector `x` the roots of the polynomial `p` . For real polynomials of degree <=100 the fast RPOLY algorithm is used. In the other cases the roots are computed as the eigenvalues of the associated companion matrix. Use `x=roots(p,'e')` to force this algorithm in any cases.

### Examples

    p=poly([0,10,1+%i,1-%i],'x');
    roots(p)
    A=rand(3,3);roots(poly(A,'x'))    // Evals by characteristic polynomial
    spec(A)

### See Also

`poly` , `spec` , `companion` ,

### Authors

  Serge Steer (INRIA)

### Bibliography

The RPOLY algorithm is described in ACM TOMS 1 (1975) 178-189

### Used Function

The rpoly.f source codes can be found in the directory routines/control of a Scilab source distribution. The eigenvalue computation is perfomed using DGEEV and ZGEEV LAPACK codes.