RingMap SimplicialModuleMap -- apply a ring map to a map of simplicial modules

Operator: SPACE
Usage:

phi f
Inputs:
- phi, a ring map, whose source is a ring $R$, and whose target is a ring $S$
- f, a Map of Simplicial Modules, over the ring $R$
Outputs:
- a Map of Simplicial Modules, over the ring $S$

Description

We illustrate the image of a simplicial module map along a ring map.

i1 : R = QQ[a,b,c,d];

i2 : S = QQ[s,t];

i3 : phi = map(S, R, {s, s+t, t, s-t})

o3 = map (S, R, {s, s + t, t, s - t})

o3 : RingMap S <-- R

i4 : I = ideal(a*b, b*c, c*d)

o4 = ideal (a*b, b*c, c*d)

o4 : Ideal of R

i5 : J = I + ideal(a^2, b^2, c^2, d^2)

                            2   2   2   2
o5 = ideal (a*b, b*c, c*d, a , b , c , d )

o5 : Ideal of R

i6 : CI = simplicialModule(freeResolution I, 4, Degeneracy => true)

      1      4      9      16      25
o6 = R  <-- R  <-- R  <-- R   <-- R  <-- ...
                                   
     0      1      2      3       4

o6 : SimplicialModule

i7 : CJ = simplicialModule(freeResolution J, Degeneracy => true)

      1      8      28      71      150
o7 = R  <-- R  <-- R   <-- R   <-- R   <-- ...
                                    
     0      1      2       3       4

o7 : SimplicialModule

i8 : f = simplicialModule(extend(CJ.complex, CI.complex, map(CJ_0, CI_0, 1)), Degeneracy => true)

          1             1
o8 = 0 : R  <--------- R  : 0
               | 1 |

          8                       4
     1 : R  <------------------- R  : 1
               {0} | 1 0 0 0 |
               {2} | 0 0 0 0 |
               {2} | 0 1 0 0 |
               {2} | 0 0 0 0 |
               {2} | 0 0 1 0 |
               {2} | 0 0 0 0 |
               {2} | 0 0 0 1 |
               {2} | 0 0 0 0 |

          28                                 9
     2 : R   <----------------------------- R  : 2
                {0} | 1 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {2} | 0 1 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 1 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 1 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 1 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 1 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 1 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 1 0 |
                {3} | 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 1 |
                {3} | 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 |

          71                                               16
     3 : R   <------------------------------------------- R   : 3
                {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

          150                                                                 25
     4 : R    <------------------------------------------------------------- R   : 4
                 {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

o8 : SimplicialModuleMap

i9 : assert isWellDefined f

i10 : g = phi f

           1             1
o10 = 0 : S  <--------- S  : 0
                | 1 |

           8                       4
      1 : S  <------------------- S  : 1
                {0} | 1 0 0 0 |
                {2} | 0 0 0 0 |
                {2} | 0 1 0 0 |
                {2} | 0 0 0 0 |
                {2} | 0 0 1 0 |
                {2} | 0 0 0 0 |
                {2} | 0 0 0 1 |
                {2} | 0 0 0 0 |

           28                                 9
      2 : S   <----------------------------- S  : 2
                 {0} | 1 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 1 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 1 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 1 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 1 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 1 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 1 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 1 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 1 |
                 {3} | 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 |

           71                                               16
      3 : S   <------------------------------------------- S   : 3
                 {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

           150                                                                 25
      4 : S    <------------------------------------------------------------- S   : 4
                  {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                  {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

o10 : SimplicialModuleMap

i11 : assert isWellDefined g

i12 : dd^(source g)

                1                               4
o12 = (0, 0) : S  <--------------------------- S  : (1, 0)
                     | 1 s2+st st+t2 st-t2 |

                1                   4
      (0, 1) : S  <--------------- S  : (1, 1)
                     | 1 0 0 0 |

                4                                                 9
      (1, 0) : S  <--------------------------------------------- S  : (2, 0)
                     {0} | 1 s2+st st+t2 st-t2 0 0 0 0  0    |
                     {2} | 0 0     0     0     1 0 0 -t 0    |
                     {2} | 0 0     0     0     0 1 0 s  -s+t |
                     {2} | 0 0     0     0     0 0 1 0  s+t  |

                4                                 9
      (1, 1) : S  <----------------------------- S  : (2, 1)
                     {0} | 1 0 0 0 0 0 0 0 0 |
                     {2} | 0 1 0 0 1 0 0 0 0 |
                     {2} | 0 0 1 0 0 1 0 0 0 |
                     {2} | 0 0 0 1 0 0 1 0 0 |

                4                                 9
      (1, 2) : S  <----------------------------- S  : (2, 2)
                     {0} | 1 0 0 0 0 0 0 0 0 |
                     {2} | 0 1 0 0 0 0 0 0 0 |
                     {2} | 0 0 1 0 0 0 0 0 0 |
                     {2} | 0 0 0 1 0 0 0 0 0 |

                9                                                                   16
      (2, 0) : S  <--------------------------------------------------------------- S   : (3, 0)
                     {0} | 1 s2+st st+t2 st-t2 0 0 0 0 0 0 0  0    0  0    0 0 |
                     {2} | 0 0     0     0     1 0 0 0 0 0 -t 0    0  0    0 0 |
                     {2} | 0 0     0     0     0 1 0 0 0 0 s  -s+t 0  0    0 0 |
                     {2} | 0 0     0     0     0 0 1 0 0 0 0  s+t  0  0    0 0 |
                     {2} | 0 0     0     0     0 0 0 1 0 0 0  0    -t 0    0 0 |
                     {2} | 0 0     0     0     0 0 0 0 1 0 0  0    s  -s+t 0 0 |
                     {2} | 0 0     0     0     0 0 0 0 0 1 0  0    0  s+t  0 0 |
                     {3} | 0 0     0     0     0 0 0 0 0 0 0  0    0  0    1 0 |
                     {3} | 0 0     0     0     0 0 0 0 0 0 0  0    0  0    0 1 |

                9                                               16
      (2, 1) : S  <------------------------------------------- S   : (3, 1)
                     {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                     {3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 |
                     {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 |

                9                                               16
      (2, 2) : S  <------------------------------------------- S   : (3, 2)
                     {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 |
                     {3} | 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 |
                     {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 |

                9                                               16
      (2, 3) : S  <------------------------------------------- S   : (3, 3)
                     {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                     {3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                     {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |

                16                                                                                         25
      (3, 0) : S   <------------------------------------------------------------------------------------- S   : (4, 0)
                      {0} | 1 s2+st st+t2 st-t2 0 0 0 0 0 0 0 0 0 0  0    0  0    0  0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     1 0 0 0 0 0 0 0 0 -t 0    0  0    0  0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 1 0 0 0 0 0 0 0 s  -s+t 0  0    0  0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 0 1 0 0 0 0 0 0 0  s+t  0  0    0  0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 0 0 1 0 0 0 0 0 0  0    -t 0    0  0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 0 0 0 1 0 0 0 0 0  0    s  -s+t 0  0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 0 0 0 0 1 0 0 0 0  0    0  s+t  0  0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 0 0 0 0 0 1 0 0 0  0    0  0    -t 0    0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 0 0 0 0 0 0 1 0 0  0    0  0    s  -s+t 0 0 0 0 0 0 |
                      {2} | 0 0     0     0     0 0 0 0 0 0 0 0 1 0  0    0  0    0  s+t  0 0 0 0 0 0 |
                      {3} | 0 0     0     0     0 0 0 0 0 0 0 0 0 0  0    0  0    0  0    1 0 0 0 0 0 |
                      {3} | 0 0     0     0     0 0 0 0 0 0 0 0 0 0  0    0  0    0  0    0 1 0 0 0 0 |
                      {3} | 0 0     0     0     0 0 0 0 0 0 0 0 0 0  0    0  0    0  0    0 0 1 0 0 0 |
                      {3} | 0 0     0     0     0 0 0 0 0 0 0 0 0 0  0    0  0    0  0    0 0 0 1 0 0 |
                      {3} | 0 0     0     0     0 0 0 0 0 0 0 0 0 0  0    0  0    0  0    0 0 0 0 1 0 |
                      {3} | 0 0     0     0     0 0 0 0 0 0 0 0 0 0  0    0  0    0  0    0 0 0 0 0 1 |

                16                                                                 25
      (3, 1) : S   <------------------------------------------------------------- S   : (4, 1)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |

                16                                                                 25
      (3, 2) : S   <------------------------------------------------------------- S   : (4, 2)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 |

                16                                                                 25
      (3, 3) : S   <------------------------------------------------------------- S   : (4, 3)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 |

                16                                                                 25
      (3, 4) : S   <------------------------------------------------------------- S   : (4, 4)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |

o12 : SimplicialModuleMap

i13 : ss^(source g)

                4                 1
o13 = (1, 0) : S  <------------- S  : (0, 0)
                     {0} | 1 |
                     {2} | 0 |
                     {2} | 0 |
                     {2} | 0 |

                9                       4
      (2, 0) : S  <------------------- S  : (1, 0)
                     {0} | 1 0 0 0 |
                     {2} | 0 0 0 0 |
                     {2} | 0 0 0 0 |
                     {2} | 0 0 0 0 |
                     {2} | 0 1 0 0 |
                     {2} | 0 0 1 0 |
                     {2} | 0 0 0 1 |
                     {3} | 0 0 0 0 |
                     {3} | 0 0 0 0 |

                9                       4
      (2, 1) : S  <------------------- S  : (1, 1)
                     {0} | 1 0 0 0 |
                     {2} | 0 1 0 0 |
                     {2} | 0 0 1 0 |
                     {2} | 0 0 0 1 |
                     {2} | 0 0 0 0 |
                     {2} | 0 0 0 0 |
                     {2} | 0 0 0 0 |
                     {3} | 0 0 0 0 |
                     {3} | 0 0 0 0 |

                16                                 9
      (3, 0) : S   <----------------------------- S  : (2, 0)
                      {0} | 1 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 1 |

                16                                 9
      (3, 1) : S   <----------------------------- S  : (2, 1)
                      {0} | 1 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 1 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |

                16                                 9
      (3, 2) : S   <----------------------------- S  : (2, 2)
                      {0} | 1 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 1 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 |

                25                                               16
      (4, 0) : S   <------------------------------------------- S   : (3, 0)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |

                25                                               16
      (4, 1) : S   <------------------------------------------- S   : (3, 1)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |

                25                                               16
      (4, 2) : S   <------------------------------------------- S   : (3, 2)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

                25                                               16
      (4, 3) : S   <------------------------------------------- S   : (3, 3)
                      {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                      {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

o13 : SimplicialModuleMap

i14 : dd^(target g);

i15 : prune HH normalize g

o15 = 0 : cokernel | t2 st s2 | <--------- cokernel | t2 st s2 | : 0
                                   | 1 |

o15 : ComplexMap

Ways to use this method:

RingMap SimplicialModuleMap -- apply a ring map to a map of simplicial modules

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:2403:0.

RingMap SimplicialModuleMap -- apply a ring map to a map of simplicial modules

Description

See also

Ways to use this method: