/****************************************************
*       ROOT TESTING PROGRAM OF A POLYNOMIAL        *
* ------------------------------------------------- *
*     Ref.: Basic Scientific Subroutines Vol. II    *
*     By F.R. Ruckdeschel. BYTE/McGRAW-HILL, 1981   *
*     [BIBLI 01].                                   *
* ------------------------------------------------- *
*                      C++ version by J-P Moreau    *
*                          (www.jpmoreau.fr)        *
* ------------------------------------------------- *
* SAMPLE RUN:                                       *
* (Example: Where to look for roots of polynomial   *
*           X^5+5*X^4+10*X^3+10*X^2+5*X+1)          *
*                                                   *
*   This program will help you determine            *
*  where to look for roots of a polynomial.         *
*                                                   *
*  What is the degree of the polynomial: 5          *
*                                                   *
*  Input the polynomial coefficients as prompted:   *
*                                                   *
*     A( 0) = 1                                     *
*     A( 1) = 5                                     *
*     A( 2) = 10                                    *
*     A( 3) = 10                                    *
*     A( 4) = 5                                     *
*     A( 5) = 1                                     *
*                                                   *
*  There are 5 roots.                               *
*                                                   *
*  The magnitude of the largest root is <= 2.236068 *
*                                                   *
*  There is at least one negative real root.        *
*                                                   *
*  There are at most 5 negative real roots.         *
*                                                   *
****************************************************/
#include <stdio.h>
#include <math.h>

// LABELS: e100,e200,e300

double aa, A[10];
int    b,c,d,i,n;

void main()  {
  printf("  This program will help you determine   \n");
  printf(" where to look for roots of a polynomial.\n\n");
  printf(" What is the degree of the polynomial: "); scanf("%d",&n);
  printf("\n Input the polynomial coefficients as prompted:\n\n");
  for (i=0; i<n+1; i++) {
    printf("   A(%d) = ",i); scanf("%lf",&A[i]);
  }
  printf("\n\n There are %d roots.\n\n",n);
  // Find the maximum value of root
  aa=A[n-1]*A[n-1]-2.0*A[n-2];
  if (aa>0) goto e100;
  printf(" There are at least two complex roots.\n\n");
  return;
e100: aa=sqrt(aa);
  printf("\n The magnitude of the largest root is <= %f\n\n",aa);
  aa=-1.0;
  if ((n % 2)==0) aa=-aa;
  aa=A[0]/aa;
  // b will flag a negative root
  b=0;
  if (aa>0) goto e200;
  printf(" There is at least one negative real root.\n\n");
  b=1;
e200: // Test for Descartes rule nø 1
  c=0;
  for (i=1; i<n+1; i++)
    if (A[i-1]*A[i]<0) c++;
  if (c==1) printf(" There is at most one positive ");
  if (c>1)  printf(" There are at most %d positive ",c);
  if (c==1) printf("real root.\n\n");
  if (c>1)  printf("real roots.\n\n");
  // Test for Descartes rule nø 2
  d=0;
  for (i=1; i<n+1; i++)
    if (A[i-1]*A[i]>0) d++;
  if (d==1) printf(" There is at most one negative ");
  if (d>1)  printf(" There are at most %d negative ",d);
  if (d==1) printf("real root.\n\n");
  if (d>1)  printf("real roots.\n\n");
  if ((c % 2)==0) goto e300;
  printf(" There is at least one positive real root.\n");
e300: if ((d % 2)==0) return;
  if (b==0)
    printf(" There is at least one negative real root.\n");
  printf("\n\n");
}

// End of file Roottest.cpp