-- -*- M2-comint -*- hash: 5064315569775614120

i1 : R = QQ[a..d];

i2 : f0 = matrix {{-b^2+a*c, b*c-a*d, -c^2+b*d}}

o2 = | -b2+ac bc-ad -c2+bd |

             1      3
o2 : Matrix R  <-- R

i3 : f1 = map(source f0,, {{d, c}, {c, b}, {b, a}})

o3 = {2} | d c |
     {2} | c b |
     {2} | b a |

             3      2
o3 : Matrix R  <-- R

i4 : C = complex {f0, f1}

      1      3      2
o4 = R  <-- R  <-- R
                    
     0      1      2

o4 : Complex

i5 : isWellDefined C

o5 = true

i6 : dd^C

          1                               3
o6 = 0 : R  <--------------------------- R  : 1
               | -b2+ac bc-ad -c2+bd |

          3                   2
     1 : R  <--------------- R  : 2
               {2} | d c |
               {2} | c b |
               {2} | b a |

o6 : ComplexMap

i7 : (dd^C)^2

o7 = 0

o7 : ComplexMap

i8 : C = complex R^0

o8 = 0
      
     0

o8 : Complex

i9 : isWellDefined C

o9 = true

i10 : g1 = map(source f0,, {{-d, c}, {c, b}, {b, a}})

o10 = {2} | -d c |
      {2} | c  b |
      {2} | b  a |

              3      2
o10 : Matrix R  <-- R

i11 : C = complex {f0, g1}

       1      3      2
o11 = R  <-- R  <-- R
                     
      0      1      2

o11 : Complex

i12 : isWellDefined C

o12 = false

i13 : debugLevel = 1

o13 = 1

i14 : isWellDefined C
-- expected maps in the differential to compose to zero 
--   differentials at indices (2, 1) fail this condition

o14 = false

i15 : (dd^C)^2

           1                       2
o15 = 0 : R  <------------------- R  : 2
                | 2b2d-2acd 0 |

o15 : ComplexMap

i16 : 
