Exemple de sortie écran :
 Copy/Past into the octave window.
 Ab=[
+982,+8,+504,-31,-533,+476;
-793,-131,+84,-387,-825,-517;
-393,-17,+350,+56,+994,-705;
+604,-821,+894,+724,+524,+890;
+108,-455,-217,-919,-343,-691]
 rref(Ab.00000000001)
 Press return to continue. 
 Ab :
 +982.0000 +8.0000 +504.0000 -31.0000 -533.0000 +476.0000 
 -793.0000 -131.0000 +84.0000 -387.0000 -825.0000 -517.0000 
 -393.0000 -17.0000 +350.0000 +56.0000 +994.0000 -705.0000 
 +604.0000 -821.0000 +894.0000 +724.0000 +524.0000 +890.0000 
 +108.0000 -455.0000 -217.0000 -919.0000 -343.0000 -691.0000 
 Ab : The work of pivotbest_gj3Ab_mR_mR(Ab,r);
 +982.0000 +8.0000 +504.0000 -31.0000 -533.0000 +476.0000 
 -793.0000 -131.0000 +84.0000 -387.0000 -825.0000 -517.0000 
 -393.0000 -17.0000 +350.0000 +56.0000 +994.0000 -705.0000 
 +604.0000 -821.0000 +894.0000 +724.0000 +524.0000 +890.0000 
 +108.0000 -455.0000 -217.0000 -919.0000 -343.0000 -691.0000 
 Ab : pivot[1][[1]
 The work of zero_under_pivot_gj1Ab_mR();
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 -124.5397 +490.9980 -412.0336 -1255.4165 -132.6130 
 -0.0000 -13.7984 +551.7026 +43.5937 +780.6914 -514.5031 
 +0.0000 -825.9206 +584.0041 +743.0672 +851.8330 +597.2261 
 +0.0000 -455.8798 -272.4297 -915.5906 -284.3809 -743.3503 
 Press return to continue. 
 Ab :
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 -124.5397 +490.9980 -412.0336 -1255.4165 -132.6130 
 -0.0000 -13.7984 +551.7026 +43.5937 +780.6914 -514.5031 
 +0.0000 -825.9206 +584.0041 +743.0672 +851.8330 +597.2261 
 +0.0000 -455.8798 -272.4297 -915.5906 -284.3809 -743.3503 
 Ab : The work of pivotbest_gj3Ab_mR_mR(Ab,r);
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 +0.0000 -825.9206 +584.0041 +743.0672 +851.8330 +597.2261 
 -0.0000 -13.7984 +551.7026 +43.5937 +780.6914 -514.5031 
 -0.0000 -124.5397 +490.9980 -412.0336 -1255.4165 -132.6130 
 +0.0000 -455.8798 -272.4297 -915.5906 -284.3809 -743.3503 
 Ab : pivot[2][[2]
 The work of zero_under_pivot_gj1Ab_mR();
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 -0.0000 +0.0000 +541.9459 +31.1795 +766.4602 -524.4807 
 -0.0000 +0.0000 +402.9366 -524.0799 -1383.8635 -222.6681 
 -0.0000 +0.0000 -594.7800 -1325.7383 -754.5635 -1072.9986 
 Press return to continue. 
 Ab :
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 -0.0000 +0.0000 +541.9459 +31.1795 +766.4602 -524.4807 
 -0.0000 +0.0000 +402.9366 -524.0799 -1383.8635 -222.6681 
 -0.0000 +0.0000 -594.7800 -1325.7383 -754.5635 -1072.9986 
 Ab : The work of pivotbest_gj3Ab_mR_mR(Ab,r);
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 -0.0000 +0.0000 -594.7800 -1325.7383 -754.5635 -1072.9986 
 -0.0000 +0.0000 +402.9366 -524.0799 -1383.8635 -222.6681 
 -0.0000 +0.0000 +541.9459 +31.1795 +766.4602 -524.4807 
 Ab : pivot[3][[3]
 The work of zero_under_pivot_gj1Ab_mR();
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 +0.0000 -0.0000 +1.0000 +2.2290 +1.2686 +1.8040 
 -0.0000 +0.0000 +0.0000 -1422.2078 -1895.0462 -949.5763 
 -0.0000 +0.0000 +0.0000 -1176.7939 +78.9243 -1502.1653 
 Press return to continue. 
 Ab :
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 +0.0000 -0.0000 +1.0000 +2.2290 +1.2686 +1.8040 
 -0.0000 +0.0000 +0.0000 -1422.2078 -1895.0462 -949.5763 
 -0.0000 +0.0000 +0.0000 -1176.7939 +78.9243 -1502.1653 
 Ab : The work of pivotbest_gj3Ab_mR_mR(Ab,r);
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 +0.0000 -0.0000 +1.0000 +2.2290 +1.2686 +1.8040 
 -0.0000 +0.0000 +0.0000 -1422.2078 -1895.0462 -949.5763 
 -0.0000 +0.0000 +0.0000 -1176.7939 +78.9243 -1502.1653 
 Ab : pivot[4][[4]
 The work of zero_under_pivot_gj1Ab_mR();
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 +0.0000 -0.0000 +1.0000 +2.2290 +1.2686 +1.8040 
 +0.0000 -0.0000 -0.0000 +1.0000 +1.3325 +0.6677 
 +0.0000 +0.0000 +0.0000 +0.0000 +1646.9644 -716.4463 
 Press return to continue. 
 Ab :
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 +0.0000 -0.0000 +1.0000 +2.2290 +1.2686 +1.8040 
 +0.0000 -0.0000 -0.0000 +1.0000 +1.3325 +0.6677 
 +0.0000 +0.0000 +0.0000 +0.0000 +1646.9644 -716.4463 
 Ab : The work of pivotbest_gj3Ab_mR_mR(Ab,r);
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 +0.0000 -0.0000 +1.0000 +2.2290 +1.2686 +1.8040 
 +0.0000 -0.0000 -0.0000 +1.0000 +1.3325 +0.6677 
 +0.0000 +0.0000 +0.0000 +0.0000 +1646.9644 -716.4463 
 Ab : pivot[5][[5]
 The work of zero_under_pivot_gj1Ab_mR();
 +1.0000 +0.0081 +0.5132 -0.0316 -0.5428 +0.4847 
 -0.0000 +1.0000 -0.7071 -0.8997 -1.0314 -0.7231 
 +0.0000 -0.0000 +1.0000 +2.2290 +1.2686 +1.8040 
 +0.0000 -0.0000 -0.0000 +1.0000 +1.3325 +0.6677 
 +0.0000 +0.0000 +0.0000 +0.0000 +1.0000 -0.4350 
 Press return to continue. 
 gj_PP_mR(Ab,YES) :
 +1.00000 +0.00000 +0.00000 +0.00000 +0.00000 +0.50861 
 -0.00000 +1.00000 +0.00000 +0.00000 +0.00000 -0.34960 
 -0.00000 +0.00000 +1.00000 +0.00000 +0.00000 -0.42431 
 +0.00000 -0.00000 -0.00000 +1.00000 +0.00000 +1.24731 
 +0.00000 +0.00000 +0.00000 +0.00000 +1.00000 -0.43501 
 Press return to continue
 Press X to stop

Mathc matrices/e1608
Étude du code
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : gj08.c */
/* ------------------------------------ */
void xx_gj3_T_mR(
double **Ab,
int below
int r= R1;
int c= C1;
 while( (r<Ab[R_SIZE][C0]) &&
 (c<Ab[C_SIZE_A][C0]) )
 if(pivotbest_gj3Ab_mR(Ab,r,c)>ERROR_E) 
 zero_under_pivot_gj3Ab_mR(Ab,r,c);
 else r--;
 r++;
 c++;
 r = Ab[R_SIZE][C0];
 if(below)
 while(r>R2)
 r--;
 c=C1;
 while(fabs(Ab[r][c])<ERROR_E && c<(Ab[C_SIZE_A][C0]-C1) ) c++;

if(fabs(Ab[r][c])>ERROR_E)
 printf(" Ab : pivot[%d][[%d] ",r,c); 
 p_mR(Ab,S8,P4,C8); 
 zero_below_pivot_gj3Ab_mR(Ab,r,c);
 printf(" Ab : pivot[%d][[%d]"
 " The work of zero_below_pivot_gj1Ab_mR();",r,c); 
 p_mR(Ab,S8,P4,C8); 
 stop();
 clrscrn(); 
/* ------------------------------------ */
double **XX_gj_PP_mR(
double **Ab,
int below
 xx_gj3_T_mR(Ab,below);
return(Ab);
/* ------------------------------------ */
void fun(int r)
double **A = i_mR(r,r);
double **b = i_mR(r,C1);
double **Ab = i_Abr_Ac_bc_mR(r,r,C1);
/* i_Abr_Ac_bc_mR(R_Ab,C_A,C_b)); */
 do
 r_mR(A,999.);
 printf(".");
 }while(!det_R(A));
 r_mR(b,999.);
 c_A_b_Ab_mR(A,b,Ab);
 clrscrn();
 printf(" Copy/Past into the octave window.\n\n");
 p_Octave_mR(Ab,"Ab",P0);
 printf("\n rref(Ab.00000000001)\n\n");
 stop();
 clrscrn();
 XX_gj_PP_mR(Ab,YES);
 printf(" gj_PP_mR(Ab,YES) :");
 p_mR(Ab,S10,P4,C7);