isQuasiIsomorphism(ZZdFactorizationMap) -- whether a map of ZZ/d-graded factorizations is a quasi-isomorphism

i1 : S = ZZ/101[a,b];

i2 : R = S/(a^3+b^3);

i3 : m = ideal vars R

o3 = ideal (a, b)

o3 : Ideal of R

i4 : C = tailMF m

      2      2      2
o4 = S  <-- S  <-- S
                    
     0      1      0

o4 : ZZdFactorization

i5 : D = tailMF (m^2)

      3      3      3
o5 = S  <-- S  <-- S
                    
     0      1      0

o5 : ZZdFactorization

i6 : f = randomFactorizationMap(C, C, Cycle => true) --only scalar mults of the identity

          2                     2
o6 = 0 : S  <----------------- S  : 0
               {2} | 24 0  |
               {3} | 0  24 |

          2                     2
     1 : S  <----------------- S  : 1
               {4} | 24 0  |
               {4} | 0  24 |

o6 : ZZdFactorizationMap

i7 : isQuasiIsomorphism(Hom(f,C))

o7 = true

i8 : g = randomFactorizationMap(D, D, Cycle => true, Degree => 1, InternalDegree => 2)

          3                           3
o8 = 1 : S  <----------------------- S  : 0
               {5} | -26 19  -30 |
               {5} | -1  -36 19  |
               {5} | -38 -29 -10 |

          3                                        3
     0 : S  <------------------------------------ S  : 1
               {3} | 26a+19b 19a+b    30a+36b |
               {3} | -a-10b  36a+38b  19a+29b |
               {3} | 38a+30b -29a-26b 10a+19b |

o8 : ZZdFactorizationMap

i9 : assert isCommutative g

i10 : isQuasiIsomorphism Hom(C,g)

o10 = false

i11 : h = randomFactorizationMap(D, D, Boundary => true)

           3                                                         3
o11 = 0 : S  <----------------------------------------------------- S  : 0
                {3} | -29a2b-8ab2-16b3  16ab2+34b3  -38ab2+8b3  |
                {3} | -22a2b-29ab2+39b3 -39ab2+19b3 41ab2+29b3  |
                {3} | -24a2b-38ab2+21b3 -21ab2-47b3 -23ab2+38b3 |

           3                                                         3
      1 : S  <----------------------------------------------------- S  : 1
                {5} | -29a2b+16ab2+38b3 -16ab2-21b3 34ab2+47b3  |
                {5} | 22a2b-8b3         -39ab2-16b3 -19ab2+34b3 |
                {5} | -24a2b+41ab2-29b3 21ab2+39b3  -47ab2+19b3 |

o11 : ZZdFactorizationMap

i12 : assert( HH Hom(D,h) == 0 )