Mathc initiation/Fichiers h : x 18c04b

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c04b.c

/* ---------------------------------- */
/* save as c04b.c                     */
/* ---------------------------------- */
#include "x_a.h"
/* ---------------------------------- */
# define   DEGREE     6
# define   COEFF_NB   DEGREE + 1
/* ---------------------------------- */
int main(void)
{
double x = -1;

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]={5,3,-2,6,5,-2,-9};

 clrscrn();
 x = -1;
 c_a_Px(a,Pa);
 printf(" If P(x) is : \n\n");
 p_Px(Pa);
 printf(" Find an lower bound for the zeros of P(x).\n\n");
 printf(" If we divide P(x) by : x - (%+.2f)\n\n\n",x);
 compute_horner(x,Pa,Pt,Pqr,Pq);
 p_horner(Pa,Pt,Pqr);
 printf(" The third row does not alternate in sign\n\n");
 printf(" So %+.3f is not a lower bound for the zeros of P(x)\n\n",x);
 stop();

 clrscrn();
 x = -2.;
 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 alternates in sign.\n\n");
 printf(" So %+.2f is a lower 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 : 

   +5.00*x**6  +3.00*x**5  -2.00*x**4  +6.00*x**3  +5.00*x**2  -2.00*x  -9.00  


 Find an lower bound for the zeros of p_A.

 If we divide p_A by : x - (-1.00)


     +5.00     +3.00     -2.00     +6.00     +5.00     -2.00     -9.00   
     +0.00     -5.00     +2.00     -0.00     -6.00     +1.00     +1.00   
   ----------------------------------------------------------------------
     +5.00     -2.00     +0.00     +6.00     -1.00     -1.00     -8.00   


 The third row does not alternate in sign

 So -1.000 is not a lower 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 [-2.:1.5] [-10.:20.]\
      +5.00*x**6  +3.00*x**5  -2.00*x**4  +6.00*x**3  +5.00*x**2  -2.00*x  -9.00
reset
# ---------------------