Mathc matrices/c26c2
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c02.c */
int main(void)
double xy[6] ={
 1, -1,
 2, -9,
 3, -8 };
double **XY = ca_A_mR(xy,i_mR(R3,C2));
double **A = i_mR(R5,C5);
double **b = i_mR(R5,C1);
double **Ab = i_Abr_Ac_bc_mR(R5,C5,C1);
 clrscrn();
 printf("\n");
 printf(" Find the coefficients a, b, c, d, of a circle \n\n");
 printf(" ax**2 + ay**2 + bx + cy + d = 0 \n\n");
 printf(" that passes through these three XY. \n\n");
 printf(" x y");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Using the given XY, we obtain this matrix.\n");
 printf(" (a = 1. This is my choice)\n\n");
 printf(" x**2 y**2 x y ");
 i_A_b_with_XY_mR(XY,A,b);
 c_A_b_Ab_mR(A,b,Ab);
 p_mR(Ab,S7,P2,C6);
 stop();
 clrscrn();
 printf(" The Gauss Jordan process will reduce this matrix to : \n");
 gj_TP_mR(Ab);
 p_mR(Ab,S7,P2,C6);
 printf(" The coefficients a, b, c, d, e, of the curve are : \n\n");
 p_eq_circle_mR(Ab);
 stop();
 clrscrn();
 printf(" x y \n");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Verify the result : \n\n");
 verify_XY_mR(Ab,XY[R1][C1],XY[R1][C2]);
 verify_XY_mR(Ab,XY[R2][C1],XY[R2][C2]);
 verify_XY_mR(Ab,XY[R3][C1],XY[R3][C2]);
 printf("\n\n\n");
 stop();
 f_mR(XY);
 f_mR(A);
 f_mR(b);
 f_mR(Ab);
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 Find the coefficients a, b, c, d, of a circle 
 ax**2 + ay**2 + bx + cy + d = 0 
 that passes through these three points. 
 x y
 +1 -1 
 +2 -9 
 +3 -8 
 Using the given points, we obtain this matrix.
 (a = 1. This is my choice)
 x**2 y**2 x y 
 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 
 +1.00 +1.00 +1.00 -1.00 +1.00 +0.00 
 +4.00 +81.00 +2.00 -9.00 +1.00 +0.00 
 +9.00 +64.00 +3.00 -8.00 +1.00 +0.00 
 Press return to continue. 
 The Gauss Jordan process will reduce this matrix to : 
 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +0.00 +1.00 +0.00 +0.00 +1.44 
 +0.00 +0.00 -0.00 +1.00 +0.00 +10.56 
 +0.00 +0.00 +0.00 +0.00 +1.00 +7.11 
 The coefficients a, b, c, d, e, of the curve are : 
 +1.00x**2 +1.00y**2 +1.44x +10.56y +7.11 = 0
 Press return to continue. 
 x y 
 +1 -1 
 +2 -9 
 +3 -8 
 Verify the result : 
 With x = +1.0 and y = -1.0 ax**2 + ay**2 + cx+ dy + e = -0.00000 
 With x = +2.0 and y = -9.0 ax**2 + ay**2 + cx+ dy + e = -0.00000 
 With x = +3.0 and y = -8.0 ax**2 + ay**2 + cx+ dy + e = +0.00000 
 Press return to continue.

Mathc matrices/c26c3
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c03.c */
int main(void)
double xy[6] ={
 1, 10,
 2, 1,
 3, -10 };
double **XY = ca_A_mR(xy,i_mR(R3,C2));
double **A = i_mR(R5,C5);
double **b = i_mR(R5,C1);
double **Ab = i_Abr_Ac_bc_mR(R5,C5,C1);
 clrscrn();
 printf("\n");
 printf(" Find the coefficients a, b, c, d, of a circle \n\n");
 printf(" ax**2 + ay**2 + bx + cy + d = 0 \n\n");
 printf(" that passes through these three XY. \n\n");
 printf(" x y");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Using the given XY, we obtain this matrix.\n");
 printf(" (a = 1. This is my choice)\n\n");
 printf(" x**2 y**2 x y ");
 i_A_b_with_XY_mR(XY,A,b);
 c_A_b_Ab_mR(A,b,Ab);
 p_mR(Ab,S7,P2,C6);
 stop();
 clrscrn();
 printf(" The Gauss Jordan process will reduce this matrix to : \n");
 gj_TP_mR(Ab);
 p_mR(Ab,S7,P2,C6);
 printf(" The coefficients a, b, c, d, e, of the curve are : \n\n");
 p_eq_circle_mR(Ab);
 stop();
 clrscrn();
 printf(" x y \n");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Verify the result : \n\n");
 verify_XY_mR(Ab,XY[R1][C1],XY[R1][C2]);
 verify_XY_mR(Ab,XY[R2][C1],XY[R2][C2]);
 verify_XY_mR(Ab,XY[R3][C1],XY[R3][C2]);
 printf("\n\n\n");
 stop();
 f_mR(XY);
 f_mR(A);
 f_mR(b);
 f_mR(Ab);
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 Find the coefficients a, b, c, d, of a circle 
 ax**2 + ay**2 + bx + cy + d = 0 
 that passes through these three points. 
 x y
 +1 +10 
 +2 +1 
 +3 -10 
 Using the given points, we obtain this matrix.
 (a = 1. This is my choice)
 x**2 y**2 x y 
 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 
 +1.00 +100.00 +1.00 +10.00 +1.00 +0.00 
 +4.00 +1.00 +2.00 +1.00 +1.00 +0.00 
 +9.00 +100.00 +3.00 -10.00 +1.00 +0.00 
 Press return to continue. 
 The Gauss Jordan process will reduce this matrix to : 
 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +0.00 +1.00 +0.00 +0.00 +996.00 
 +0.00 +0.00 +0.00 +1.00 +0.00 +100.00 
 -0.00 -0.00 -0.00 -0.00 +1.00 -2097.00 
 The coefficients a, b, c, d, e, of the curve are : 
 +1.00x**2 +1.00y**2 +996.00x +100.00y -2097.00 = 0
 Press return to continue. 
 x y 
 +1 +10 
 +2 +1 
 +3 -10 
 Verify the result : 
 With x = +1.0 and y = +10.0 ax**2 + ay**2 + cx+ dy + e = -0.00000 
 With x = +2.0 and y = +1.0 ax**2 + ay**2 + cx+ dy + e = -0.00000 
 With x = +3.0 and y = -10.0 ax**2 + ay**2 + cx+ dy + e = -0.00000 
 Press return to continue.

Mathc matrices/c26c4
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c04.c */
int main(void)
double xy[6] ={
 10, 10,
 -5, 1,
 7, -10 };
double **XY = ca_A_mR(xy,i_mR(R3,C2));
double **A = i_mR(R5,C5);
double **b = i_mR(R5,C1);
double **Ab = i_Abr_Ac_bc_mR(R5,C5,C1);
 clrscrn();
 printf("\n");
 printf(" Find the coefficients a, b, c, d, of a circle \n\n");
 printf(" ax**2 + ay**2 + bx + cy + d = 0 \n\n");
 printf(" that passes through these three XY. \n\n");
 printf(" x y");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Using the given XY, we obtain this matrix.\n");
 printf(" (a = 1. This is my choice)\n\n");
 printf(" x**2 y**2 x y ");
 i_A_b_with_XY_mR(XY,A,b);
 c_A_b_Ab_mR(A,b,Ab);
 p_mR(Ab,S7,P2,C6);
 stop();
 clrscrn();
 printf(" The Gauss Jordan process will reduce this matrix to : \n");
 gj_TP_mR(Ab);
 p_mR(Ab,S7,P2,C6);
 printf(" The coefficients a, b, c, d, e, of the curve are : \n\n");
 p_eq_circle_mR(Ab);
 stop();
 clrscrn();
 printf(" x y \n");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Verify the result : \n\n");
 verify_XY_mR(Ab,XY[R1][C1],XY[R1][C2]);
 verify_XY_mR(Ab,XY[R2][C1],XY[R2][C2]);
 verify_XY_mR(Ab,XY[R3][C1],XY[R3][C2]);
 printf("\n\n\n");
 stop();
 f_mR(XY);
 f_mR(A);
 f_mR(b);
 f_mR(Ab);
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 Find the coefficients a, b, c, d, of a circle 
 ax**2 + ay**2 + bx + cy + d = 0 
 that passes through these three points. 
 x y
 +10 +10 
 -5 +1 
 +7 -10 
 Using the given points, we obtain this matrix.
 (a = 1. This is my choice)
 x**2 y**2 x y 
 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 
+100.00 +100.00 +10.00 +10.00 +1.00 +0.00 
 +25.00 +1.00 -5.00 +1.00 +1.00 +0.00 
 +49.00 +100.00 +7.00 -10.00 +1.00 +0.00 
 Press return to continue. 
 The Gauss Jordan process will reduce this matrix to : 
 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 
 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 
 -0.00 -0.00 +1.00 -0.00 +0.00 -11.07 
 +0.00 +0.00 +0.00 +1.00 +0.00 -0.89 
 -0.00 -0.00 -0.00 -0.00 +1.00 -80.44 
 The coefficients a, b, c, d, e, of the curve are : 
 +1.00x**2 +1.00y**2 -11.07x -0.89y -80.44 = 0
 Press return to continue. 
 x y 
 +10 +10 
 -5 +1 
 +7 -10 
 Verify the result : 
 With x = +10.0 and y = +10.0 ax**2 + ay**2 + cx+ dy + e = -0.00000 
 With x = -5.0 and y = +1.0 ax**2 + ay**2 + cx+ dy + e = +0.00000 
 With x = +7.0 and y = -10.0 ax**2 + ay**2 + cx+ dy + e = -0.00000 
 Press return to continue.