0
$\begingroup$

I have got the following equation using the following code after the preprocess. The preprocess is complicated so cannot be displayed here in limited scale, and assuming that the following equations are right and following equations are as this:

a = {a1, a2, a3};
b = {b1, b2, b3};
aAirgap = {a1Airgap, a2Airgap, a3Airgap};
bAirgap = {b1Airgap, b2Airgap, b3Airgap};

equa1 = (Br /. {r -> R2}) == (BrAirgap /. {r -> R2})
equa2 = (H\[Theta] /. {r -> R2}) == (H\[Theta]Airgap /. {r -> R2})
equa3 = ((H\[Theta] /. {r -> R1}) == {0, 0, 0})
equa4 = ((H\[Theta]Airgap /. {r -> R3}) == {0, 0, 0})

Then the concrete equations are as follows, in fact, there are 12 equations with 12 unknown variables:

equa1 = ({{(0.36439934858051215` - 
          0.9312427797057534` I) b2 + (0.36439934858051215` - 
          0.9312427797057534` I) b3 + 
       b1 ((0.` + 0.` I) + (
          0.36439934858051215` - 0.9312427797057534` I)/
          R2^0.15915492717640267`) - (1/R2)
       I ((0.36439934858051215` - 
             0.9312427797057534` I) a2 + (0.36439934858051215` - 
             0.9312427797057534` I) a3 + 
          a1 ((0.` + 
               0.` I) + (0.36439934858051215` - 
                0.9312427797057534` I) R2^0.15915492717640267`)) + 
       R2^2.` ((0.` + 0.` I) + (
          25.201522001588366` - 1.335913512777944`*^-15 I)/(-R1^2 + 
           R2^2)), (0.` + 0.` I) + 
       R2^2.` ((0.` + 0.` I) + (
          25.201522001588366` - 1.335913512777944`*^-15 I)/(-R1^2 + 
           R2^2)), (-0.6401843996644798` + 
          0.768221279597376` I) b1 - (0.6401843996644798` - 
          0.768221279597376` I) b3 + 
       b2 ((0.` + 0.` I) - (
          0.6401843996644798` - 0.768221279597376` I)/
          R2^0.15915492717640264`) - (1/R2)
       I ((-0.6401843996644798` + 
             0.768221279597376` I) a1 - (0.6401843996644798` - 
             0.768221279597376` I) a3 + 
          
          a2 ((0.` + 
               0.` I) - (0.6401843996644798` - 
                0.768221279597376` I) R2^0.15915492717640264`)) + 
       R2^2.` ((0.` + 0.` I) + (
          25.201522001588366` - 1.335913512777944`*^-15 I)/(-R1^2 + 
           R2^2))}, {(0.36439934858051215` - 
          0.9312427797057534` I) b2 + (0.36439934858051215` - 
          0.9312427797057534` I) b3 + 
       b1 ((0.` + 0.` I) + (
          0.36439934858051215` - 0.9312427797057534` I)/
          R2^0.15915492717640267`) - (1/R2)
       I ((0.36439934858051215` - 
             0.9312427797057534` I) a2 + (0.36439934858051215` - 
             0.9312427797057534` I) a3 + 
          a1 ((0.` + 
               0.` I) + (0.36439934858051215` - 
                0.9312427797057534` I) R2^0.15915492717640267`)), 
      0.` + 0.` I, (-0.6401843996644798` + 
          0.768221279597376` I) b1 - (0.6401843996644798` - 
          0.768221279597376` I) b3 + 
       b2 ((0.` + 0.` I) - (
          0.6401843996644798` - 0.768221279597376` I)/
          R2^0.15915492717640264`) - (1/R2)
       I ((-0.6401843996644798` + 
             0.768221279597376` I) a1 - (0.6401843996644798` - 
             0.768221279597376` I) a3 + 
          
          a2 ((0.` + 
               0.` I) - (0.6401843996644798` - 
                0.768221279597376` I) R2^0.15915492717640264`))}, \
{(0.36439934858051215` - 
          0.9312427797057534` I) b2 + (0.36439934858051215` - 
          0.9312427797057534` I) b3 + 
       b1 ((0.` + 0.` I) + (
          0.36439934858051215` - 0.9312427797057534` I)/
          R2^0.15915492717640267`) - (1/R2)
       I ((0.36439934858051215` - 
             0.9312427797057534` I) a2 + (0.36439934858051215` - 
             0.9312427797057534` I) a3 + 
          a1 ((0.` + 
               0.` I) + (0.36439934858051215` - 
                0.9312427797057534` I) R2^0.15915492717640267`)) + 
       R2^2.` ((0.` + 0.` I) - (
          25.201522001588366` + 1.335913512777944`*^-15 I)/(-R1^2 + 
           R2^2)), (0.` + 0.` I) + 
       R2^2.` ((0.` + 0.` I) - (
          25.201522001588366` + 1.335913512777944`*^-15 I)/(-R1^2 + 
           R2^2)), (-0.6401843996644798` + 
          0.768221279597376` I) b1 - (0.6401843996644798` - 
          0.768221279597376` I) b3 + 
       b2 ((0.` + 0.` I) - (
          0.6401843996644798` - 0.768221279597376` I)/
          R2^0.15915492717640264`) - (1/R2)
       I ((-0.6401843996644798` + 
             0.768221279597376` I) a1 - (0.6401843996644798` - 
             0.768221279597376` I) a3 + 
          a2 ((0.` + 
               0.` I) - (0.6401843996644798` - 
                0.768221279597376` I) R2^0.15915492717640264`)) + 
       R2^2.` ((0.` + 0.` I) - (
          25.201522001588366` + 1.335913512777944`*^-15 I)/(-R1^2 + 
           R2^2))}} == {{-b1Airgap - b2Airgap - b3Airgap - (
       I (-a1Airgap - a2Airgap - a3Airgap))/R2, 0, 
      b1Airgap + b3Airgap + b2Airgap/R2 - (
       I (a1Airgap + a3Airgap + a2Airgap R2))/R2}, {-b1Airgap - 
       b2Airgap - b3Airgap - (I (-a1Airgap - a2Airgap - a3Airgap))/R2,
       0, b1Airgap + b3Airgap + b2Airgap/R2 - (
       I (a1Airgap + a3Airgap + a2Airgap R2))/R2}, {-b1Airgap - 
       b2Airgap - b3Airgap - (I (-a1Airgap - a2Airgap - a3Airgap))/R2,
       0, b1Airgap + b3Airgap + b2Airgap/R2 - (
       I (a1Airgap + a3Airgap + a2Airgap R2))/R2}});


equa2 = {b2 ((6.10842*10^-17 - 1.56104*10^-16 I)/
        R2^1.15915 - (0.364399 - 0.931243 I)/R2^1.) + 
    b1 (-((0.364399 - 0.931243 I)/R2^1.15915) + (6.10842*10^-17 - 
          1.56104*10^-16 I)/R2^1.) - 
    a1 ((6.10842*10^-17 - 1.56104*10^-16 I)/
        R2^1. - (0.364399 - 0.931243 I)/R2^0.840845) - 
    a2 (-((0.364399 - 0.931243 I)/R2^1.) + (6.10842*10^-17 - 
          1.56104*10^-16 I)/
        R2^0.840845) + ((0.364399 - 0.931243 I) a3)/
     R2^1. - ((0.364399 - 0.931243 I) b3)/R2^1. - 
    2 R2 . {(-9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 - 
           1.82695*10^-47 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 - 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (-5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 + 
           9.74558*10^-48 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (6.28319 - 
           2.06542*10^-48 I) ((0. + 
             
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2))}, 
   b1 ((1.30923*10^-16 - 4.36411*10^-17 I)/
        R2^1.15915 + (1.87122*10^-17 - 1.35743*10^-16 I)/R2^1.) + 
    b2 (-((2.48862*10^-17 + 1.35743*10^-16 I)/
          R2^1.15915) + (1.74522*10^-16 - 4.36411*10^-17 I)/R2^1.) - 
    a2 ((1.74522*10^-16 - 4.36411*10^-17 I)/
        R2^1. - (2.48862*10^-17 + 1.35743*10^-16 I)/R2^0.840845) - 
    a1 ((1.87122*10^-17 - 1.35743*10^-16 I)/
        R2^1. + (1.30923*10^-16 - 4.36411*10^-17 I)/
        R2^0.840845) - ((1.49635*10^-16 - 1.79384*10^-16 I) a3)/
     R2^1. + ((1.49635*10^-16 - 1.79384*10^-16 I) b3)/R2^1. - 
    2 R2 . {(-9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 - 
           1.82695*10^-47 I) ((0. + 
             
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 - 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (-5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 + 
           9.74558*10^-48 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (6.28319 - 
           2.06542*10^-48 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2))}, 
   b1 ((1.07314*10^-16 - 1.28777*10^-16 I)/
        R2^1.15915 - (0.640184 - 0.768221 I)/R2^1.) + 
    b2 (-((0.640184 - 0.768221 I)/R2^1.15915) + (1.07314*10^-16 - 
          1.28777*10^-16 I)/R2^1.) - 
    a2 ((1.07314*10^-16 - 1.28777*10^-16 I)/
        R2^1. - (0.640184 - 0.768221 I)/R2^0.840845) - 
    a1 (-((0.640184 - 0.768221 I)/R2^1.) + (1.07314*10^-16 - 
          1.28777*10^-16 I)/
        R2^0.840845) + ((0.640184 - 0.768221 I) a3)/
     R2^1. - ((0.640184 - 0.768221 I) b3)/R2^1. - 
    2 R2 . {(-9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 - 
           1.82695*10^-47 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 - 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (-5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 + 
           9.74558*10^-48 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (6.28319 - 
           2.06542*10^-48 I) ((0. + 
             
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2))}} == {-2 R2 . {0, 0, 
      0}, -((2500000 a1Airgap)/\[Pi]) + (2500000 b1Airgap)/(\[Pi] \
R2^2) - (2500000 a2Airgap)/(\[Pi] R2) - (2500000 a3Airgap)/(\[Pi] R2) \
+ (2500000 b2Airgap)/(\[Pi] R2) + (2500000 b3Airgap)/(\[Pi] R2) - 
    2 R2 . {0, 0, 
       0}, -((2500000 a2Airgap)/\[Pi]) + (2500000 b2Airgap)/(\[Pi] \
R2^2) - (2500000 a1Airgap)/(\[Pi] R2) - (2500000 a3Airgap)/(\[Pi] R2) \
+ (2500000 b1Airgap)/(\[Pi] R2) + (2500000 b3Airgap)/(\[Pi] R2) - 
    2 R2 . {0, 0, 0}}


equa3 = {b2 ((6.10842*10^-17 - 1.56104*10^-16 I)/
        R1^1.15915 - (0.364399 - 0.931243 I)/R1^1.) + 
    b1 (-((0.364399 - 0.931243 I)/R1^1.15915) + (6.10842*10^-17 - 
          1.56104*10^-16 I)/R1^1.) - 
    a1 ((6.10842*10^-17 - 1.56104*10^-16 I)/
        R1^1. - (0.364399 - 0.931243 I)/R1^0.840845) - 
    a2 (-((0.364399 - 0.931243 I)/R1^1.) + (6.10842*10^-17 - 
          1.56104*10^-16 I)/
        R1^0.840845) + ((0.364399 - 0.931243 I) a3)/
     R1^1. - ((0.364399 - 0.931243 I) b3)/R1^1. - 
    2 R1 . {(-9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 - 
           1.82695*10^-47 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 - 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (-5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 + 
           9.74558*10^-48 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (6.28319 - 
           2.06542*10^-48 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2))}, 
   b1 ((1.30923*10^-16 - 4.36411*10^-17 I)/
        R1^1.15915 + (1.87122*10^-17 - 1.35743*10^-16 I)/R1^1.) + 
    b2 (-((2.48862*10^-17 + 1.35743*10^-16 I)/
          R1^1.15915) + (1.74522*10^-16 - 4.36411*10^-17 I)/R1^1.) - 
    a2 ((1.74522*10^-16 - 4.36411*10^-17 I)/
        R1^1. - (2.48862*10^-17 + 1.35743*10^-16 I)/R1^0.840845) - 
    a1 ((1.87122*10^-17 - 1.35743*10^-16 I)/
        R1^1. + (1.30923*10^-16 - 4.36411*10^-17 I)/
        R1^0.840845) - ((1.49635*10^-16 - 1.79384*10^-16 I) a3)/
     R1^1. + ((1.49635*10^-16 - 1.79384*10^-16 I) b3)/R1^1. - 
    2 R1 . {(-9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 - 
           1.82695*10^-47 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 - 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (-5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 + 
           9.74558*10^-48 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (6.28319 - 
           2.06542*10^-48 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2))}, 
   b1 ((1.07314*10^-16 - 1.28777*10^-16 I)/
        R1^1.15915 - (0.640184 - 0.768221 I)/R1^1.) + 
    b2 (-((0.640184 - 0.768221 I)/R1^1.15915) + (1.07314*10^-16 - 
          1.28777*10^-16 I)/R1^1.) - 
    a2 ((1.07314*10^-16 - 1.28777*10^-16 I)/
        R1^1. - (0.640184 - 0.768221 I)/R1^0.840845) - 
    a1 (-((0.640184 - 0.768221 I)/R1^1.) + (1.07314*10^-16 - 
          1.28777*10^-16 I)/
        R1^0.840845) + ((0.640184 - 0.768221 I) a3)/
     R1^1. - ((0.640184 - 0.768221 I) b3)/R1^1. - 
    2 R1 . {(-9.99201*10^-16 + 
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 - 
           1.82695*10^-47 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 - 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (-5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) + (6.28319 + 
           9.74558*10^-48 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2)), (6.28319 - 
           2.06542*10^-48 I) ((0. + 
             0. I) - (25.2015 + 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (9.99201*10^-16 + 
           
           3.33067*10^-16 I) ((0. + 
             0. I) - (25.2015 - 1.33591*10^-15 I)/(-R1^2 + 
              R2^2)) - (5.55112*10^-16 + 
           6.66134*10^-16 I) ((0. + 
             0. I) - (4.45305*10^-15 - 7.88861*10^-31 I)/(-R1^2 + 
              R2^2))}} == {0, 0, 0}


equa4 = {-2 R3 . {0, 0, 
      0}, -((2500000 a1Airgap)/\[Pi]) + (2500000 b1Airgap)/(\[Pi] \
R3^2) - (2500000 a2Airgap)/(\[Pi] R3) - (2500000 a3Airgap)/(\[Pi] R3) \
+ (2500000 b2Airgap)/(\[Pi] R3) + (2500000 b3Airgap)/(\[Pi] R3) - 
    2 R3 . {0, 0, 
       0}, -((2500000 a2Airgap)/\[Pi]) + (2500000 b2Airgap)/(\[Pi] \
R3^2) - (2500000 a1Airgap)/(\[Pi] R3) - (2500000 a3Airgap)/(\[Pi] R3) \
+ (2500000 b1Airgap)/(\[Pi] R3) + (2500000 b3Airgap)/(\[Pi] R3) - 
    2 R3 . {0, 0, 0}} == {0, 0, 0}

and the parameters are

R1 = N[25/1000];
R2 = N[39/1000];
R3 = N[40/1000];

Finally I use

Solve[{equa1, equa2, equa3, equa4}, {a1, a2, a3, b1, b2, b3, a1Airgap,
   a2Airgap, a3Airgap, b1Airgap, b2Airgap, b3Airgap}]

But I cannot get the solution and the result is empty:

{}

So how to judge whether this equation group really doesn't have the solution? And what is the reason?

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$\endgroup$
3
  • $\begingroup$ You have several typos: R3 . {0, 0, 0} should be R3*{0, 0, 0}? But that is just {0, 0, 0}. And there are a few other "dot products" that don't make sense. You have 3 of the 4 equations named incorrectly: euqa1, euqa2, and eqau4. I'm also not seeing why you have several instances of (0. + 0. I). Rather than Solve you should consider Reduce. $\endgroup$
    – JimB
    May 26 at 4:39
  • $\begingroup$ @JimB,Thank you, I have corrected them, and as R3 is one constant, so R3 . {0, 0, 0} is equal to R3*{0, 0, 0}, and (0. + 0. I) is generated by the preprocess via Mathematica, so it should be right. And I have used Reduce, and the answer is False, so I do not know what is the reason. $\endgroup$
    – fhrl
    May 26 at 9:49
  • $\begingroup$ You need to take a closer look at your code. For instance in equa4 I see multiple instances of -2 R3 . {0, 0, 0}. And the dimensions for all 4 equations are wrong. When you combine them together (using Join rather than {equa1, equal2, equa3, equa4}) you should get 12 equations. $\endgroup$
    – JimB
    May 26 at 16:50

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