Mathc initiation/Fichiers h : x 18c03b

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c03b.c

/* ---------------------------------- */
/* save as c03b.c                     */
/* ---------------------------------- */
#include "x_a.h"
/* ---------------------------------- */
# define   DEGREE     3
# define   COEFF_NB   DEGREE + 1
/* ---------------------------------- */
int main(void)
{
double x = 8.;

double *Pa  = I_Px( COEFF_NB);
double *Pt  = I_Px( COEFF_NB);
double *Pqr = I_Px( COEFF_NB);
double *Pq  = I_Px((COEFF_NB-1));

double a[COEFF_NB]={2,1,0,-3600};

 clrscrn();
 
 x = 3.;
 c_a_Px(a,Pa);
 printf("\n If P(x) is : \n\n");
 p_Px(Pa);
 
 printf(" Find an upper bound for the zeros of P(x).\n\n");
 printf(" If we divide P(x) by : x - (%+.2f)\n\n",x);
 compute_horner(x,Pa,Pt,Pqr,Pq);
 p_horner(Pa,Pt,Pqr);
 
 printf(" The third row have some negative numbers\n\n");
 printf(" So %+.3f is not an upper bound for the zeros of P(x)\n\n",x);
 stop();

 clrscrn();
 
 x = 13.;
 printf(" If we divide P(x) by : x - (%+.2f)\n\n",x);
 compute_horner(x,Pa,Pt,Pqr,Pq);
 p_horner(Pa,Pt,Pqr);
 
 printf(" The third row are nonnegative numbers.\n\n");
 printf(" So %+.2f is an upper bound for the zeros of P(x).\n\n",x);
 
 stop();
 
 free(Pa);
 free(Pt);
 free(Pqr);
 free(Pq);

 return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */

Vérifier les calculs à la main. (Voir le premier exemple pour apprendre la méthode de Horner)

Exemple de sortie écran :

  If p_A is : 

   +2.00*x**3  + x**2  -3600.00  


 Find an upper bound for the zeros of p_A.

 If we divide p_A by : x - (+3.00)


     +2.00     +1.00     +0.00   -3600.00   
     +0.00     +6.00    +21.00    +63.00   
   ----------------------------------------
     +2.00     +7.00    +21.00   -3537.00   


 The third row have some negative numbers

 So +3.000 is not an upper bound for the zeros of p_A

 Press return to continue.

Fichier de commande gnuplot :

# ---------------------
# Copy and past this file into the screen of gnuplot
#
#
set zeroaxis lt 3 lw 1
plot [-10.:15.] [-4500.:1000.]\
      +2.00*x**3  + x**2  -3600.00
reset
# ---------------------