Mathc initiation/Fichiers h : x 18c03a
Installer et compiler ces fichiers dans votre répertoire de travail.
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c03a.c |
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/* ---------------------------------- */
/* save as c03a.c */
/* ---------------------------------- */
#include "x_a.h"
/* ---------------------------------- */
# define DEGREE 4
# define COEFF_NB DEGREE + 1
/* ---------------------------------- */
int main(void)
{
double x = 3.;
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]={1.,3.,-30.,-6.,56.};
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 = 5.;
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 1 :
If p_A is :
+ x**4 +3.00*x**3 -30.00*x**2 -6.00*x +56.00
Find an upper bound for the zeros of p_A.
If we divide p_A by : x - (+3.00)
+1.00 +3.00 -30.00 -6.00 +56.00
+0.00 +3.00 +18.00 -36.00 -126.00
--------------------------------------------------
+1.00 +6.00 -12.00 -42.00 -70.00
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.
Exemple de sortie écran 2 :
If we divide p_A by : x - (+5.00)
+1.00 +3.00 -30.00 -6.00 +56.00
+0.00 +5.00 +40.00 +50.00 +220.00
--------------------------------------------------
+1.00 +8.00 +10.00 +44.00 +276.00
The third row are nonnegative numbers.
So +5.00 is 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 [-8.:5.] [-450.:100.]\
+ x**4 +3.00*x**3 -30.00*x**2 -6.00*x +56.00
reset
# ---------------------