/*
    Pieter Suurmond, 2006.
    C++ API for Laguerre's root finding method.
    Allows both the input (polynome coefficients) and the output (the roots) to
    be complex.

     IN: The degree of the input polynome.
         An array of complex coefficients.
     
    OUT: The actual degree of the polynome (high-degree-null-coeffs removed).
         An array of complex roots (with size 1 less than input array).
    
    Memory for the output array must be allocated by the caller?
*/

/*
    Returns zero in case of success. Returns a non-zero error number in case of
    failure. Coefficients must be supplied in ASCENDING order of degree!
*/

int find_roots(int                    num_coeffs,   // Degree + 1.
               const complex<double>* coeffs,       // Input array, size=num_coeffs.
               int*                   num_roots,    // Actual degree of the polynome.
               complex<double>*       roots);       // Found roots are written here.