id _ ZZdFactorization -- the identity map of a ZZ/d-graded factorization

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

o1 = S

o1 : PolynomialRing

i2 : R = S/(a^2+b^2+c^2);

i3 : m = ideal vars R

o3 = ideal (a, b, c)

o3 : Ideal of R

i4 : C = tailMF m

      4      4      4
o4 = S  <-- S  <-- S
                    
     0      1      0

o4 : ZZdFactorization

i5 : D = tailMF (m^2)

      8      8      8
o5 = S  <-- S  <-- S
                    
     0      1      0

o5 : ZZdFactorization

i6 : f = id_C

          4                       4
o6 = 0 : S  <------------------- S  : 0
               {3} | 1 0 0 0 |
               {3} | 0 1 0 0 |
               {3} | 0 0 1 0 |
               {3} | 0 0 0 1 |

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

o6 : ZZdFactorizationMap

i7 : assert isWellDefined f

i8 : assert isFactorizationMorphism f

i9 : g = id_D

          8                               8
o9 = 0 : S  <--------------------------- S  : 0
               {4} | 1 0 0 0 0 0 0 0 |
               {4} | 0 1 0 0 0 0 0 0 |
               {4} | 0 0 1 0 0 0 0 0 |
               {4} | 0 0 0 1 0 0 0 0 |
               {4} | 0 0 0 0 1 0 0 0 |
               {4} | 0 0 0 0 0 1 0 0 |
               {4} | 0 0 0 0 0 0 1 0 |
               {4} | 0 0 0 0 0 0 0 1 |

          8                               8
     1 : S  <--------------------------- S  : 1
               {5} | 1 0 0 0 0 0 0 0 |
               {5} | 0 1 0 0 0 0 0 0 |
               {5} | 0 0 1 0 0 0 0 0 |
               {5} | 0 0 0 1 0 0 0 0 |
               {5} | 0 0 0 0 1 0 0 0 |
               {5} | 0 0 0 0 0 1 0 0 |
               {5} | 0 0 0 0 0 0 1 0 |
               {5} | 0 0 0 0 0 0 0 1 |

o9 : ZZdFactorizationMap

i10 : assert isWellDefined g

i11 : assert isFactorizationMorphism g