Mathc matrices/c26b3
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c03.c */
int main(void)
double xy[8] ={
 1, 4,
 2, 5,
 3, -7,
 4, 5 };
double **XY = ca_A_mR(xy,i_mR(R4,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, e, of the curve \n\n");
 printf(" ax**2 + by**2 + cx + dy + e = 0 \n\n");
 printf(" that passes through these four points. \n\n");
 printf(" x y");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Using the given points, 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_conica_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]);
 verify_XY_mR(Ab,XY[R4][C1],XY[R4][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, e, of the curve 
 ax**2 + by**2 + cx + dy + e = 0 
 that passes through these four points. 
 x y
 +1 +4 
 +2 +5 
 +3 -7 
 +4 +5 
 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 
 +1.00 +16.00 +1.00 +4.00 +1.00 +0.00 
 +4.00 +25.00 +2.00 +5.00 +1.00 +0.00 
 +9.00 +49.00 +3.00 -7.00 +1.00 +0.00 
 +16.00 +25.00 +4.00 +5.00 +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 +0.28 
 -0.00 -0.00 +1.00 -0.00 -0.00 -6.00 
 +0.00 +0.00 +0.00 +1.00 +0.00 +0.48 
 +0.00 -0.00 +0.00 +0.00 +1.00 -1.39 
 The coefficients a, b, c, d, e, of the curve are : 
 +1.00x**2 +0.28y**2 -6.00x +0.48y -1.39 = 0
 Press return to continue. 
 x y 
 +1 +4 
 +2 +5 
 +3 -7 
 +4 +5 
 Verify the result : 
 With x = +1.0 and y = +4.0 ax**2 + by**2 + cx+ dy + e = -0.00000 
 With x = +2.0 and y = +5.0 ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x = +3.0 and y = -7.0 ax**2 + by**2 + cx+ dy + e = -0.00000 
 With x = +4.0 and y = +5.0 ax**2 + by**2 + cx+ dy + e = +0.00000 
 Press return to continue.

Mathc matrices/c26b4
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c04.c */
int main(void)
double xy[8] ={
 1, 2,
 2, -8,
 3, -8,
 4, -3 };
double **XY = ca_A_mR(xy,i_mR(R4,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, e, of the curve \n\n");
 printf(" ax**2 + by**2 + cx + dy + e = 0 \n\n");
 printf(" that passes through these four points. \n\n");
 printf(" x y");
 p_mR(XY,S5,P0,C6);
 printf("\n");
 printf(" Using the given points, 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_conica_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]);
 verify_XY_mR(Ab,XY[R4][C1],XY[R4][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, e, of the curve 
 ax**2 + by**2 + cx + dy + e = 0 
 that passes through these four points. 
 x y
 +1 +2 
 +2 -8 
 +3 -8 
 +4 -3 
 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 
 +1.00 +4.00 +1.00 +2.00 +1.00 +0.00 
 +4.00 +64.00 +2.00 -8.00 +1.00 +0.00 
 +9.00 +64.00 +3.00 -8.00 +1.00 +0.00 
 +16.00 +9.00 +4.00 -3.00 +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 +0.04 
 -0.00 -0.00 +1.00 -0.00 -0.00 -5.00 
 +0.00 +0.00 +0.00 +1.00 +0.00 +0.04 
 +0.00 +0.00 +0.00 +0.00 +1.00 +3.76 
 The coefficients a, b, c, d, e, of the curve are : 
 +1.00x**2 +0.04y**2 -5.00x +0.04y +3.76 = 0
 Press return to continue. 
 x y 
 +1 +2 
 +2 -8 
 +3 -8 
 +4 -3 
 Verify the result : 
 With x = +1.0 and y = +2.0 ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x = +2.0 and y = -8.0 ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x = +3.0 and y = -8.0 ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x = +4.0 and y = -3.0 ax**2 + by**2 + cx+ dy + e = -0.00000 
 Press return to continue.