/********************************************************
*  Calculate a limited development of a real function   *
*  f(x)/g(x) at x=0 up at order 25, knowing the limited *
*  developments of f(x) and g(x).                       *
* ----------------------------------------------------- *
* SAMPLE RUN:                                           *
*                                                       *
* Limited development of a real function f(x)/g(x):     *
*                                                       *
* Function to develop: exp(x)/1+x                       *
*                                                       *
* Limited development of f(x)=exp(x) is:                *
*   1 + x + x^2/2! + x^3/3! + ... + x^n/n! + ...        *
*                                                       *
* Limited development of g(x)=1+x is:                   *
*   1 + x                                               *
*                                                       *
* Order of development (max=25): 6                      *
*                                                       *
* Input coefficients of limited dev. of f(x):           *
*  a0 = 1                                               * 
*  a1 = 1                                               *
*  a2 = 0.5                                             *
*  a3 = 0.1666667                                       *
*  a4 = 0.0416667                                       *
*  a5 = 0.0083333                                       *
*  a6 = 0.0013889                                       *
*                                                       *
* Input coefficients of limited dev. of g(x):           *
*  b0 = 1                                               * 
*  b1 = 1                                               *
*  b2 = 0                                               *
*  b3 = 0                                               *
*  b4 = 0                                               *
*  b5 = 0                                               *
*  b6 = 0                                               *
*                                                       *
* The coefficients of limited dev. of f(x)/g(x) are:    *
*  c0 =  1.0000000                                      *
*  c1 =  0.0000000                                      *
*  c2 =  0.5000000                                      *
*  c3 = -0.3333333                                      *
*  c4 =  0.3750000                                      *
*  c5 = -0.3666667                                      *
*  c6 =  0.3680556                                      *
*                                                       *
* Function to develop: 1/1+sh(x)                        *
*                                                       *
* Limited development of g(x)=1+sh(x) is:               *
*  1 + x + x^3/3! + x^5/5! + ... + x^2n+1/(2n+1)! + ... *
*                                                       *
* Order of development (max=25): 6                      *
*                                                       *
* Input coefficients of limited dev. of f(x):           *
*  a0 = 1                                               * 
*  a1 = 0                                               *
*  a2 = 0                                               *
*  a3 = 0                                               *
*  a4 = 0                                               *
*  a5 = 0                                               *
*  a6 = 0                                               *
*                                                       *
* Input coefficients of limited dev. of g(x):           *
*  b0 = 1                                               * 
*  b1 = 1                                               *
*  b2 = 0                                               *
*  b3 = 0.1666667                                       *
*  b4 = 0                                               *
*  b5 = 0.0083333                                       *
*  b6 = 0                                               *
*                                                       *
* The coefficients of limited dev. of f(x)/g(x) are:    *
*  c0 =  1.0000000                                      *
*  c1 = -1.0000000                                      *
*  c2 =  1.0000000                                      *
*  c3 = -1.1666667                                      *
*  c4 =  1.3333334                                      *
*  c5 = -1.5083334                                      *
*  c6 =  1.7111112                                      *
*                                                       *
* ----------------------------------------------------- *
* Ref.: "Mathematiques en Turbo Pascal By Alain         *
*        Reverchon and Marc Ducamp, Editions Eyrolles,  *
*        Paris, 1991" [BIBLI 03].                       *
*                                                       *
*                            C++ version by J-P Moreau. *
*                                (www.jpmoreau.fr)      *
********************************************************/
#include <stdio.h>
#include <math.h>

#define  SIZE  25

int i,m;
double T1[SIZE+1],T2[SIZE+1],R[SIZE+1];


void ar_dldiv(int n, double *t1, double *t2, double *res)  {
  int i,j; double x;
  if (n > SIZE) return;
  if (fabs(t2[0]) < 1e-12) return;
  res[0]=t1[0]/t2[0]; 
  for (i=1; i<=n; i++) {
    x=t1[i];
    for (j=1; j<=i; j++)  x -= t2[j]*res[i-j];
    res[i]=x;
  }
}


void main()  {

  printf("\n Limited development of a real function f(x)/g(x):\n\n");
  printf(" Function to develop: exp(x)/1+x\n\n");
  printf(" Limited development of f(x)=exp(x) is:\n");
  printf("  1 + x + x^2/2! + x^3/3! + ... + x^n/n! + ...\n\n");
  printf(" Limited development of g(x)=1+x is:\n");
  printf("  1 + x\n");
  printf("\n Order of development (max=25): "); scanf("%d",&m);
  printf("\n\n Input coefficients of limited dev. of f(x):\n");
  for (i=0; i<=m; i++) {
    printf("  a%d = ",i); scanf("%lf",&T1[i]);
  }
  printf("\n\n Input coefficients of limited dev. of g(x):\n");
  for (i=0; i<=m; i++) {
    printf("  b%d = ",i); scanf("%lf",&T2[i]);
  }
  printf("\n\n");

  ar_dldiv(m,T1,T2,R);

  printf(" The coefficients of limited dev. of f(x)/g(x) are:\n");
  for (i=0; i<=m; i++) 
	printf("  c%d = %10.7f\n", i, R[i]);
  printf("\n\n");

}

// end of file ltddev2.cpp