Mathc initiation/Fichiers h : x 18c03b
Installer et compiler ces fichiers dans votre répertoire de travail.
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c03b.c |
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/* ---------------------------------- */
/* 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
# ---------------------