/*****************************************************************************
*                                                                            *
*   REPROOT.SPL    Copyright (C) 2003 DSP Development Corporation            *
*                               All Rights Reserved                          *
*                                                                            *
*   Author:      Randy Race                                                  *
*                                                                            *
*   Synopsis:    Checks for repeated roots of a polynomial                   *
*                                                                            *
*   Revisions:    3 Oct 2003  RRR  Creation                                  *
*                                                                            *
*****************************************************************************/

#include 

#if @HELP_REPROOT

    REPROOT

    Purpose: Checks for repeated roots of a polynomial.

    Syntax:  REPROOT(p, findroots, tol)

                       p - A series, the coefficients of the polynomial
                           in descending powers (highest order to lowest).
                           If findroots is 0, p represents the roots of
                           the polynomial.

               findroots - Optional. An integer. If 1, p contains the
                           polynomial coefficients and the roots are
                           calculated. If 0, p contains the roots.
                           Defaults to 1.

                     tol - Optional. A real, the tolerance threshold to
                           determine repeated roots. Defaults to 1e-3.

    Returns: An integer. 1 if repeated roots exist else 0.

    Example:

             For p(x) = x^3 + 3x^2 + 3x + 1

             reproot({1, 3, 3, 1})

             returns 1.

    Example:

             For p(x) = (x + 1)(x + 1)(x + 2)

             reproot(poly({1, 1, 2}))

             returns 1.

    Remarks:
             REPROOT is used as a support routine for residue and
             residuez.

    See Also:
             Poly
             Polyroot
             Residue
             Residuez
#endif


/* true if multiple roots exist within a tolerance */
reproot(z, findroots, tol)
{
        local r, d, status;

        if (argc < 3)
        {
                tol = 1e-3;
                
                if (argc < 2)
                {
                        findroots = 1;
                }
        }

        if (findroots)
        {
                /* polynomial coefficients passed in, find roots */
                z = roots(z);
        }

        /* get sorted poles */
        r = sort(z);

        /* find differences */
        d = mag(diff(r));

        /* check if difference less than tolerance */
        status = any(d < tol);

        return(status);
}