gradedModule(ZZdFactorization) -- a new ZZ/d-graded factorization in which the differential is zero

i1 : R = ZZ/101[a,b,c]/(a^3+b^3+c^3);

i2 : C = tailMF ideal vars R

       ZZ       4       ZZ       4       ZZ       4
o2 = (---[a..c])  <-- (---[a..c])  <-- (---[a..c])
      101              101              101
                                        
     0                1                0

o2 : ZZdFactorization

i3 : dd^C

           ZZ       4                             ZZ       4
o3 = 1 : (---[a..c])  <------------------------ (---[a..c])  : 0
          101            {5} | -a -c2 b2 0  |    101
                         {5} | -c a2  0  b2 |
                         {5} | b  0   a2 c2 |
                         {6} | 0  -b  -c a  |

           ZZ       4                               ZZ       4
     0 : (---[a..c])  <-------------------------- (---[a..c])  : 1
          101            {3} | -a2 -c2 b2 0   |    101
                         {4} | -c  a   0  -b2 |
                         {4} | b   0   a  -c2 |
                         {4} | 0   b   c  a2  |

o3 : ZZdFactorizationMap

i4 : G = gradedModule C

       ZZ       4       ZZ       4       ZZ       4
o4 = (---[a..c])  <-- (---[a..c])  <-- (---[a..c])
      101              101              101
                                        
     0                1                0

o4 : ZZdFactorization

i5 : dd^G

o5 = 0

o5 : ZZdFactorizationMap

i6 : dd^G == 0

o6 = true

i7 : assert((isdFactorization G)_0)

i8 : assert(G != C)

i9 : assert(HH G == G)