Mathc matrices/c25c2

Application

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	c02.c

/* ------------------------------------ */
/*  Save as :   c02.c                   */
/* ------------------------------------ */
#include "v_a.h"
#include   "d.h"
/* --------------------------------- */
int main(void)
{
double   p[R3*C2] ={ -5, 1,     
                      3,-3,     
                      9, 9 };

double **Ap =  ca_A_mR(p,        i_mR(R3,C2));
double **A  = m_parabola_A_mR(Ap,i_mR(R4,C4));
int r;

  clrscrn();
  printf(" Theorem.\n\n");
  printf(" A homogeneous linear system with as many equations\n");
  printf(" as unknowns has a nontrivial  solution if and only\n");
  printf(" if the determinant  of the  coefficient  matrix is\n");
  printf(" zero.\n\n");
  
  printf(" Equation of a parabola:   \n\n");
  printf(" c1 y  + c2 x^2 + c3 x + c4 = 0\n\n");    
  
  printf(" The same equation with the values of the three points:\n\n");
  for(r=R1;r<Ap[R_SIZE][C0];r++)
      printf(" c1y%d + c2x%d^2 + c3x%d + c4 = 0\n",
                r,r,r);      
  
  printf("\n The four equation:\n\n");
  printf(" c1y   + c2x^2  + c3x  + c4 = 0\n");    
  for(r=R1;r<Ap[R_SIZE][C0];r++)
      printf(" c1y%d  + c2x%d^2 + c3x%d + c4 = 0\n",
                r,r,r);      
  stop();
  
  clrscrn();
  printf(" The three points:\n\n");
  for(r=R1;r<Ap[R_SIZE][C0];r++)
       printf(" P%d(%+.0f,%+.0f)",r,Ap[r][C1],Ap[r][C2]);

  printf(" The determinant :\n\n (cofactor expansion along the first row)\n\n");
  
  printf("     y    x^2    x     1");
  p_Det_mR(A,6,0);
  
  printf(" The equation of the parabola : \n\n");
  
  printf(" %+.0f y %+.0f x^2 %+.0f x %+.0f = 0\n\n",
           cofactor_R(A,R1,C1),
           cofactor_R(A,R1,C2),
           cofactor_R(A,R1,C3),
           cofactor_R(A,R1,C4));
           
  printf(" Verify the result : \n\n");           
  for(r=R1;r<Ap[R_SIZE][C0];r++)
      verify_eq_parabola_mR(A, Ap[r][C1],
                               Ap[r][C2]);
           
 
  stop();
  
  f_mR(Ap);
  f_mR(A);

  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Exemple de sortie écran :

 ------------------------------------ 
 Theorem.

 A homogeneous linear system with as many equations
 as unknowns has a nontrivial  solution if and only
 if the determinant  of the  coefficient  matrix is
 zero.

 Equation of a parabola:   

 c1 y  + c2 x^2 + c3 x + c4 = 0

 The same equation with the values of the three points:

 c1y1 + c2x1^2 + c3x1 + c4 = 0
 c1y2 + c2x2^2 + c3x2 + c4 = 0
 c1y3 + c2x3^2 + c3x3 + c4 = 0

 The four equation:

 c1y   + c2x^2  + c3x  + c4 = 0
 c1y1  + c2x1^2 + c3x1 + c4 = 0
 c1y2  + c2x2^2 + c3x2 + c4 = 0
 c1y3  + c2x3^2 + c3x3 + c4 = 0
 Press return to continue. 


 The three points:

 P1(-5,+1) P2(+3,-3) P3(+9,+9) The determinant :

 (cofactor expansion along the first row)

     y    x^2    x     1
    +1   +25    -5    +1
    -3    +9    +3    +1
    +9   +81    +9    +1

 The equation of the parabola : 

 -672 y +120 x^2 -96 x -2808 = 0

 Verify the result : 

 With x= -5.0 y= +1.0  eq=+0.00000
 With x= +3.0 y= -3.0  eq=+0.00000
 With x= +9.0 y= +9.0  eq=+0.00000
 Press return to continue.