SimplicialModule == SimplicialModule -- whether two simplicial modules are equal

Operator: ==
Usage:

C == D

C == 0
Inputs:
- C, a Simplicial Module,
- D, a Simplicial Module,
Outputs:
- a Boolean value, that is true when C and D are equal

Description

Two simplicial modules are equal if the corresponding objects and corresponding maps at each index are equal.

i1 : S = ZZ/101[a..c]

o1 = S

o1 : PolynomialRing

i2 : C = simplicialModule(K = freeResolution coker vars S, 4)

      1      4      10      20      35
o2 = S  <-- S  <-- S   <-- S   <-- S  <-- ...
                                    
     0      1      2       3       4

o2 : SimplicialModule

i3 : D = image id_C;

i4 : C === D

o4 = false

i5 : C == D

o5 = true

Both the maps and the objects must be equal.

i6 : E = simplicialModule(complex for i from 1 to 3 list 0*dd^K_i, 4)

      1      4      10      20      35
o6 = S  <-- S  <-- S   <-- S   <-- S  <-- ...
                                    
     0      1      2       3       4

o6 : SimplicialModule

i7 : dd^E

               1                   4
o7 = (0, 0) : S  <--------------- S  : (1, 0)
                    | 1 0 0 0 |

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

               4                                   10
     (1, 0) : S  <------------------------------- S   : (2, 0)
                    {0} | 1 0 0 0 0 0 0 0 0 0 |
                    {1} | 0 0 0 0 1 0 0 0 0 0 |
                    {1} | 0 0 0 0 0 1 0 0 0 0 |
                    {1} | 0 0 0 0 0 0 1 0 0 0 |

               4                                   10
     (1, 1) : S  <------------------------------- S   : (2, 1)
                    {0} | 1 0 0 0 0 0 0 0 0 0 |
                    {1} | 0 1 0 0 1 0 0 0 0 0 |
                    {1} | 0 0 1 0 0 1 0 0 0 0 |
                    {1} | 0 0 0 1 0 0 1 0 0 0 |

               4                                   10
     (1, 2) : S  <------------------------------- S   : (2, 2)
                    {0} | 1 0 0 0 0 0 0 0 0 0 |
                    {1} | 0 1 0 0 0 0 0 0 0 0 |
                    {1} | 0 0 1 0 0 0 0 0 0 0 |
                    {1} | 0 0 0 1 0 0 0 0 0 0 |

               10                                                       20
     (2, 0) : S   <--------------------------------------------------- S   : (3, 0)
                     {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 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 1 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |

               10                                                       20
     (2, 1) : S   <--------------------------------------------------- S   : (3, 1)
                     {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 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 1 0 0 1 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 |

               10                                                       20
     (2, 2) : S   <--------------------------------------------------- S   : (3, 2)
                     {0} | 1 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 0 0 0 0 0 0 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 0 0 0 0 0 |
                     {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 |

               10                                                       20
     (2, 3) : S   <--------------------------------------------------- S   : (3, 3)
                     {0} | 1 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 0 0 0 0 0 0 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 0 0 0 0 0 |
                     {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 1 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 |
                     {2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |

               20                                                                                     35
     (3, 0) : S   <--------------------------------------------------------------------------------- S   : (4, 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 0 0 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 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 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 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 0 0 0 0 0 0 0 0 0 1 |

               20                                                                                     35
     (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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 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 1 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 1 0 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 0 0 1 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 0 0 0 1 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 0 0 0 0 1 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 0 0 0 0 0 1 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 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 0 0 0 0 0 0 0 0 1 1 |

               20                                                                                     35
     (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 0 0 0 0 0 0 0 0 0 0 |
                     {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 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 0 0 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 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 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 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 0 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 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 0 0 0 0 0 |
                     {2} | 0 0 0 0 0 0 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 0 0 0 0 |
                     {2} | 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 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 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 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 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 1 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 0 0 1 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 0 0 0 0 0 0 0 1 1 0 |

               20                                                                                     35
     (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 0 0 0 0 0 0 0 0 0 0 |
                     {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 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 0 0 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 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 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 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 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 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 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 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 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 0 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 0 |
                     {2} | 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 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 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 1 1 0 0 |

               20                                                                                     35
     (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 0 0 0 0 0 0 0 0 0 0 |
                     {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 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 0 0 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 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 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                     {2} | 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 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 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 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 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 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 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 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 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 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 0 0 0 0 0 0 1 0 0 0 |

o7 : SimplicialModuleMap

i8 : C == E

o8 = false

i9 : E == 0

o9 = false

A simplicial module is equal to zero if all the objects and maps are zero. This could require computation to determine if something that is superficially not zero is in fact zero.

i10 : f = id_C

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

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

           10                                   10
      2 : S   <------------------------------- S   : 2
                 {0} | 1 0 0 0 0 0 0 0 0 0 |
                 {1} | 0 1 0 0 0 0 0 0 0 0 |
                 {1} | 0 0 1 0 0 0 0 0 0 0 |
                 {1} | 0 0 0 1 0 0 0 0 0 0 |
                 {1} | 0 0 0 0 1 0 0 0 0 0 |
                 {1} | 0 0 0 0 0 1 0 0 0 0 |
                 {1} | 0 0 0 0 0 0 1 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 1 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 1 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 1 |

           20                                                       20
      3 : S   <--------------------------------------------------- S   : 3
                 {0} | 1 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 0 0 0 0 0 0 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 0 0 0 0 0 |
                 {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 0 0 0 0 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 1 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 |
                 {2} | 0 0 0 0 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 1 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                 {2} | 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 1 |

           35                                                                                     35
      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 0 0 0 0 0 0 0 0 0 0 |
                 {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 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 0 0 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 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 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 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 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 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 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 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 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 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 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 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 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 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 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 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 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 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 0 0 0 0 0 0 0 0 0 1 |

o10 : SimplicialModuleMap

i11 : D = coker f

o11 = cokernel | 1 | <-- cokernel {0} | 1 0 0 0 | <-- cokernel {0} | 1 0 0 0 0 0 0 0 0 0 | <-- cokernel {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- cokernel {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 0 0 0 0 0 0 0 0 0 0 |<-- ...
                                  {1} | 0 1 0 0 |              {1} | 0 1 0 0 0 0 0 0 0 0 |              {1} | 0 1 0 0 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 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 0 0 |
      0                           {1} | 0 0 1 0 |              {1} | 0 0 1 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                  {1} | 0 0 0 1 |              {1} | 0 0 0 1 0 0 0 0 0 0 |              {1} | 0 0 0 1 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 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 0 0 |
                                                               {1} | 0 0 0 0 1 0 0 0 0 0 |              {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                         1                                     {1} | 0 0 0 0 0 1 0 0 0 0 |              {1} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                                                               {1} | 0 0 0 0 0 0 1 0 0 0 |              {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |              {1} | 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 |              {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                                                               {2} | 0 0 0 0 0 0 0 0 1 0 |              {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |              {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                                                               {2} | 0 0 0 0 0 0 0 0 0 1 |              {1} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |              {1} | 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 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 |              {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                                                      2                                                 {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |              {1} | 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 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 |              {1} | 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 0 0 0 0 0 0 0 0 0 0 |
                                                                                                        {2} | 0 0 0 0 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 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 1 0 0 0 0 0 |              {2} | 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 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 1 0 0 0 0 |              {2} | 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 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 1 0 0 0 |              {2} | 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 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 1 0 0 |              {2} | 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 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 1 0 |              {2} | 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 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 |              {2} | 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                               3                                                                     {2} | 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 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 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 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 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 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 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 0 0 0 0 0 0 0 0 0 1 |
                                                                                                                                                             
                                                                                                                                                            4

o11 : SimplicialModule

i12 : D == 0

o12 = true

i13 : C0 = simplicialModule( S^0, 5, Degeneracy => true)

o13 = 0 <-- 0 <-- 0 <-- 0 <-- 0 <-- 0<-- ...
                                     
      0     1     2     3     4     5

o13 : SimplicialModule

i14 : C1 = simplicialModule(complex(S^0, Base => 2), 5, Degeneracy => true)

o14 = 0 <-- 0 <-- 0 <-- 0 <-- 0 <-- 0<-- ...
                                     
      0     1     2     3     4     5

o14 : SimplicialModule

i15 : topDegree C0 == topDegree C1

o15 = true

i16 : C0 == C1

o16 = true

i17 : C0 == 0

o17 = true

i18 : C1 == 0

o18 = true

Caveat

Testing for equality is not the same as testing for isomorphism.

Ways to use this method:

SimplicialModule == SimplicialModule -- whether two simplicial modules are equal
SimplicialModule == ZZ
ZZ == SimplicialModule

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:735:0.