Mathc matrices/a199
Application 
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00a.c */
int main(void)
double ab[RA*(CA+C1)]={
// x1 x2 x3 x4 b
 1, 0, -1, -0, 0, //N
 3, 0, -0, -2, 0, //H
 0, 2, -1, -1, 0, //O 
double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(RA,CA,Cb));
double **Ab_free = i_Abr_Ac_bc_mR(csize_A_R(Ab),csize_A_R(Ab),Cb+C1);
double **b_free = i_mR(rsize_R(Ab_free),csize_b_R(Ab_free)); 
int r;
 clrscrn();
 printf(" Ab :");
 p_mR(Ab,S10,P4,C10);
 printf(" Ab : gj_PP_mR(Ab,NO) :");
 gj_PP_mR(Ab,NO);
 p_mR(Ab,S10,P4,C10);
 put_var_mR(Ab,Ab_free); 
 printf(" Ab_free : put_var_mR(Ab,Ab_free);"); 
 p_mR(Ab_free,S10,P4,C10); 
 put_freeV_mR(Ab_free);
 printf(" Ab_free : put_freeV_mR(Ab_free);"); 
 p_mR(Ab_free,S10,P4,C10); 
 stop();
 clrscrn();
 r = rsize_R(Ab_free);
 while(r>R1) 
 zero_below_pivot_gj1Ab_mR(Ab_free,r--);
 printf(" Ab_free : zero_below_pivot_gj1Ab_mR(Ab_free,r--);"); 
 p_mR(Ab_free,S10,P4,C10); 
 c_Ab_b_mR(Ab_free,b_free);
 printf(" b_free : free variables");
 p_freeV(b_free,S8,P8);
 printf("Copy/Past These code in the next *.c file.\n\n");
 p_coefxn(b_free);
 stop();
 f_mR(Ab);
 f_mR(Ab_free);
 f_mR(b_free);
 return 0;
/* ------------------------------------ */
 Exemple de sortie écran :
 Ab :
 +1.0000 +0.0000 -1.0000 +0.0000 +0.0000 
 +3.0000 +0.0000 +0.0000 -2.0000 +0.0000 
 +0.0000 +2.0000 -1.0000 -1.0000 +0.0000 
 Ab : gj_PP_mR(Ab,NO) :
 +1.0000 +0.0000 +0.0000 -0.6667 +0.0000 
 +0.0000 +1.0000 -0.5000 -0.5000 +0.0000 
 -0.0000 -0.0000 +1.0000 -0.6667 -0.0000 
 Ab_free : put_var_mR(Ab,Ab_free);
 +1.0000 +0.0000 +0.0000 -0.6667 +0.0000 +0.0000 
 +0.0000 +1.0000 -0.5000 -0.5000 +0.0000 +0.0000 
 -0.0000 -0.0000 +1.0000 -0.6667 -0.0000 +0.0000 
 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 
 Ab_free : put_freeV_mR(Ab_free);
 +1.0000 +0.0000 +0.0000 -0.6667 +0.0000 +0.0000 
 +0.0000 +1.0000 -0.5000 -0.5000 +0.0000 +0.0000 
 -0.0000 -0.0000 +1.0000 -0.6667 -0.0000 +0.0000 
 +0.0000 +0.0000 +0.0000 +1.0000 +0.0000 +1.0000 
 Press return to continue. 
 ---------------------
 Ab_free : zero_below_pivot_gj1Ab_mR(Ab_free,r--);
 +1.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.6667 
 +0.0000 +1.0000 +0.0000 +0.0000 +0.0000 +0.8333 
 +0.0000 +0.0000 +1.0000 +0.0000 +0.0000 +0.6667 
 +0.0000 +0.0000 +0.0000 +1.0000 +0.0000 +1.0000 
 b_free : free variables
 x1 = +0.00000000 +0.66666667*u
 x2 = +0.00000000 +0.83333333*u
 x3 = +0.00000000 +0.66666667*u
 x4 = +0.00000000 +1.00000000*u
Copy/Past These code in the next *.c file.
double x1 = +0.66666667;
double x2 = +0.83333333;
double x3 = +0.66666667;
double x4 = +1.00000000;
 Press return to continue.

Mathc matrices/a197
Application 
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00a.c */
int main(void)
int n = 1;
double x1 = +0.25000000;
double x2 = +1.25000000;
double x3 = +0.75000000;
double x4 = +1.00000000;
 do{ 
 clrscrn();
 printf(" Continue until integers appear : \n\n\n");
 printf(" n = %d -> n*x1 = %0.4f \n",n, n*x1); 
 printf(" n = %d -> n*x2 = %0.4f \n",n, n*x2); 
 printf(" n = %d -> n*x3 = %0.4f \n",n, n*x3); 
 printf(" n = %d -> n*x4 = %0.4f \n",n, n*x4); 
 n++;
 }while(stop_w());
 return 0;
/* ------------------------------------ */
 n = 4 -> n*x1 = 1.0000 
 n = 4 -> n*x2 = 5.0000 
 n = 4 -> n*x3 = 3.0000 
 n = 4 -> n*x4 = 4.0000 
Cela nous donne les coefficients de l'équation :
formula_1
Il suffit de remplacer les x1, x2... par leurs valeurs numériques :
formula_2

Exemple de sortie écran :
 Continue until integers appear : 
 n = 1 -> n*x1 = 0.2500 
 n = 1 -> n*x2 = 1.2500 
 n = 1 -> n*x3 = 0.7500 
 n = 1 -> n*x4 = 1.0000 
 Press return to continue
 Press X return to stop 
 ---------------------
 Continue until integers appear : 
 n = 2 -> n*x1 = 0.5000 
 n = 2 -> n*x2 = 2.5000 
 n = 2 -> n*x3 = 1.5000 
 n = 2 -> n*x4 = 2.0000 
 Press return to continue
 Press X return to stop 
 ---------------------
 Continue until integers appear : 
 n = 3 -> n*x1 = 0.7500 
 n = 3 -> n*x2 = 3.7500 
 n = 3 -> n*x3 = 2.2500 
 n = 3 -> n*x4 = 3.0000 
 Press return to continue
 Press X return to stop 
 ---------------------
 Continue until integers appear : 
 n = 4 -> n*x1 = 1.0000 
 n = 4 -> n*x2 = 5.0000 
 n = 4 -> n*x3 = 3.0000 
 n = 4 -> n*x4 = 4.0000 
 Press return to continue
 Press X return to stop

Mathc matrices/a200
Application 
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00a.c */
int main(void)
int n = 1;
double x1 = +0.66666667;
double x2 = +0.83333333;
double x3 = +0.66666667;
double x4 = +1.00000000;
 do{ 
 clrscrn();
 printf(" Continue until integers appear : \n\n\n");
 printf(" n = %d -> n*x1 = %0.4f \n",n, n*x1); 
 printf(" n = %d -> n*x2 = %0.4f \n",n, n*x2); 
 printf(" n = %d -> n*x3 = %0.4f \n",n, n*x3); 
 printf(" n = %d -> n*x4 = %0.4f \n",n, n*x4); 
 n++;
 }while(stop_w());
 return 0;
/* ------------------------------------ */
 n = 6 -> n*x1 = 4.0000 
 n = 6 -> n*x2 = 5.0000 
 n = 6 -> n*x3 = 4.0000 
 n = 6 -> n*x4 = 6.0000 
Cela nous donne les coefficients de l'équation :
formula_1
Il suffit de remplacer les x1, x2... par leurs valeurs numériques :
formula_2

Exemple de sortie écran :
 Continue until integers appear : 
 n = 1 -> n*x1 = 0.6667 
 n = 1 -> n*x2 = 0.8333 
 n = 1 -> n*x3 = 0.6667 
 n = 1 -> n*x4 = 1.0000 
 Press return to continue
 Press X return to stop 
 Continue until integers appear : 
 n = 2 -> n*x1 = 1.3333 
 n = 2 -> n*x2 = 1.6667 
 n = 2 -> n*x3 = 1.3333 
 n = 2 -> n*x4 = 2.0000 
 Press return to continue
 Press X return to stop 
 ---------------------
 Continue until integers appear : 
 n = 3 -> n*x1 = 2.0000 
 n = 3 -> n*x2 = 2.5000 
 n = 3 -> n*x3 = 2.0000 
 n = 3 -> n*x4 = 3.0000 
 Press return to continue
 Press X return to stop 
 ---------------------
 Continue until integers appear : 
 n = 4 -> n*x1 = 2.6667 
 n = 4 -> n*x2 = 3.3333 
 n = 4 -> n*x3 = 2.6667 
 n = 4 -> n*x4 = 4.0000 
 Press return to continue
 Press X return to stop 
 ---------------------
 Continue until integers appear : 
 n = 5 -> n*x1 = 3.3333 
 n = 5 -> n*x2 = 4.1667 
 n = 5 -> n*x3 = 3.3333 
 n = 5 -> n*x4 = 5.0000 
 Press return to continue
 Press X return to stop 
 Continue until integers appear : 
 n = 6 -> n*x1 = 4.0000 
 n = 6 -> n*x2 = 5.0000 
 n = 6 -> n*x3 = 4.0000 
 n = 6 -> n*x4 = 6.0000 
 Press return to continue
 Press X return to stop

Mathc matrices/a203
Application 
Ce système ne fonctionnerait pas avec le Total Pivoting : (Pivot décalé sur la droite)
Matrice singulière, système compatible :
Matrice singulière, système incompatible : (Je change les valeurs de b)

Mathc matrices/a204
Application 
Exemples d'applications : 
Une variable libre :
Deux variables libres :
Trois variables libres :

Mathc matrices/a192
Application 
formula_1
a) Préparation du système :
double ab[RA*(CA+C1)]={
// x1 x2 x3 x4 b
 +0, +0, -0, -0, 0, //C
 +0, +0, -0, -0, 0, //H
 +0, +0, -0, -0, 0, //O 
b) On commence par la première colonne :
formula_2
double ab[RA*(CA+C1)]={
// x1 x2 x3 x4 b
 +1, +0, -0, -0, 0, //C
 +4, +0, -0, -0, 0, //H
 +0, +0, -0, -0, 0, //O 
c) On continu avec la deuxième colonne :
formula_3
double ab[RA*(CA+C1)]={
// x1 x2 x3 x4 b
 +1, +0, -0, -0, 0, //C
 +4, +0, -0, -0, 0, //H
 +0, +2, -0, -0, 0, //O 
d) Le final nous donnera :
formula_1

double ab[RA*(CA+C1)]={
// x1 x2 x3 x4 b
 1, 0, -1, -0, 0, //C
 4, 0, -0, -2, 0, //H
 0, 2, -2, -1, 0, //O 
Il faut maintenant introduire ce système dans le fichier c00a.c.