components(SimplicialModuleMap) -- list the components of a direct sum

Function: components
Usage:

components f
Inputs:
- f, a Map of Simplicial Modules,
Outputs:
- a list, the component maps of a direct sum of maps of simplicial modules

Description

A map of simplicial modules stores its component maps.

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

i2 : C = simplicialModule(freeResolution coker vars S, Degeneracy => true)

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

o2 : SimplicialModule

i3 : g1 = id_C

          1             1
o3 = 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 |

o3 : SimplicialModuleMap

i4 : g2 = randomSimplicialMap(C[1], C[2], Boundary => true)

          3                                          3
o4 = 0 : S  <-------------------------------------- S  : 0
               {1} | 24b-36c  -29b+19c -10b-29c |
               {1} | -24a-30c 29a+19c  10a-8c   |
               {1} | 36a+30b  -19a-19b 29a+8b   |

          6                                                       4
     1 : S  <--------------------------------------------------- S  : 1
               {1} | 24b-36c  -29b+19c -10b-29c 0            |
               {1} | -24a-30c 29a+19c  10a-8c   0            |
               {1} | 36a+30b  -19a-19b 29a+8b   0            |
               {2} | 0        0        0        -10a+29b+46c |
               {2} | 0        0        0        -29a-41b-36c |
               {2} | 0        0        0        14a-19b-30c  |

          10                                                                    5
     2 : S   <---------------------------------------------------------------- S  : 2
                {1} | 24b-36c  -29b+19c -10b-29c 0            0            |
                {1} | -24a-30c 29a+19c  10a-8c   0            0            |
                {1} | 36a+30b  -19a-19b 29a+8b   0            0            |
                {2} | 0        0        0        -10a+29b+46c 0            |
                {2} | 0        0        0        -29a-41b-36c 0            |
                {2} | 0        0        0        14a-19b-30c  0            |
                {2} | 0        0        0        0            -10a+29b+46c |
                {2} | 0        0        0        0            -29a-41b-36c |
                {2} | 0        0        0        0            14a-19b-30c  |
                {3} | 0        0        0        0            0            |

          15                                                                                 6
     3 : S   <----------------------------------------------------------------------------- S  : 3
                {1} | 24b-36c  -29b+19c -10b-29c 0            0            0            |
                {1} | -24a-30c 29a+19c  10a-8c   0            0            0            |
                {1} | 36a+30b  -19a-19b 29a+8b   0            0            0            |
                {2} | 0        0        0        -10a+29b+46c 0            0            |
                {2} | 0        0        0        -29a-41b-36c 0            0            |
                {2} | 0        0        0        14a-19b-30c  0            0            |
                {2} | 0        0        0        0            -10a+29b+46c 0            |
                {2} | 0        0        0        0            -29a-41b-36c 0            |
                {2} | 0        0        0        0            14a-19b-30c  0            |
                {2} | 0        0        0        0            0            -10a+29b+46c |
                {2} | 0        0        0        0            0            -29a-41b-36c |
                {2} | 0        0        0        0            0            14a-19b-30c  |
                {3} | 0        0        0        0            0            0            |
                {3} | 0        0        0        0            0            0            |
                {3} | 0        0        0        0            0            0            |

o4 : SimplicialModuleMap

i5 : f = g1 ++ g2

          4                                            4
o5 = 0 : S  <---------------------------------------- S  : 0
               {0} | 1 0        0        0        |
               {1} | 0 24b-36c  -29b+19c -10b-29c |
               {1} | 0 -24a-30c 29a+19c  10a-8c   |
               {1} | 0 36a+30b  -19a-19b 29a+8b   |

          10                                                               8
     1 : S   <----------------------------------------------------------- S  : 1
                {0} | 1 0 0 0 0        0        0        0            |
                {1} | 0 1 0 0 0        0        0        0            |
                {1} | 0 0 1 0 0        0        0        0            |
                {1} | 0 0 0 1 0        0        0        0            |
                {1} | 0 0 0 0 24b-36c  -29b+19c -10b-29c 0            |
                {1} | 0 0 0 0 -24a-30c 29a+19c  10a-8c   0            |
                {1} | 0 0 0 0 36a+30b  -19a-19b 29a+8b   0            |
                {2} | 0 0 0 0 0        0        0        -10a+29b+46c |
                {2} | 0 0 0 0 0        0        0        -29a-41b-36c |
                {2} | 0 0 0 0 0        0        0        14a-19b-30c  |

          20                                                                                        15
     2 : S   <------------------------------------------------------------------------------------ S   : 2
                {0} | 1 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            |
                {1} | 0 0 1 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            |
                {1} | 0 0 0 0 1 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            |
                {1} | 0 0 0 0 0 0 1 0 0 0 0        0        0        0            0            |
                {2} | 0 0 0 0 0 0 0 1 0 0 0        0        0        0            0            |
                {2} | 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 1 0        0        0        0            0            |
                {1} | 0 0 0 0 0 0 0 0 0 0 24b-36c  -29b+19c -10b-29c 0            0            |
                {1} | 0 0 0 0 0 0 0 0 0 0 -24a-30c 29a+19c  10a-8c   0            0            |
                {1} | 0 0 0 0 0 0 0 0 0 0 36a+30b  -19a-19b 29a+8b   0            0            |
                {2} | 0 0 0 0 0 0 0 0 0 0 0        0        0        -10a+29b+46c 0            |
                {2} | 0 0 0 0 0 0 0 0 0 0 0        0        0        -29a-41b-36c 0            |
                {2} | 0 0 0 0 0 0 0 0 0 0 0        0        0        14a-19b-30c  0            |
                {2} | 0 0 0 0 0 0 0 0 0 0 0        0        0        0            -10a+29b+46c |
                {2} | 0 0 0 0 0 0 0 0 0 0 0        0        0        0            -29a-41b-36c |
                {2} | 0 0 0 0 0 0 0 0 0 0 0        0        0        0            14a-19b-30c  |
                {3} | 0 0 0 0 0 0 0 0 0 0 0        0        0        0            0            |

          35                                                                                                                         26
     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 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            |
                {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 1 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            |
                {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            |
                {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            |
                {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            |
                {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            |
                {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            |
                {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            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            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            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            |
                {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            |
                {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            |
                {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            |
                {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            |
                {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            |
                {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            0            |
                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24b-36c  -29b+19c -10b-29c 0            0            0            |
                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -24a-30c 29a+19c  10a-8c   0            0            0            |
                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 36a+30b  -19a-19b 29a+8b   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        -10a+29b+46c 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        -29a-41b-36c 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        14a-19b-30c  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            -10a+29b+46c 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            -29a-41b-36c 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            14a-19b-30c  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            -10a+29b+46c |
                {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            -29a-41b-36c |
                {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            14a-19b-30c  |
                {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            |
                {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            |
                {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            |

o5 : SimplicialModuleMap

i6 : assert isWellDefined f

i7 : L = components f

           1             1                                                   
o7 = {0 : S  <--------- S  : 0                                            , 0
                | 1 |                                                        
                                                                             
           4                       4                                         
      1 : S  <------------------- S  : 1
                {0} | 1 0 0 0 |                                              
                {1} | 0 1 0 0 |                                             1
                {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 |                                2
                 {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 |            3
                 {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 |
     ------------------------------------------------------------------------
        3                                          3
     : S  <-------------------------------------- S  : 0                     
             {1} | 24b-36c  -29b+19c -10b-29c |
             {1} | -24a-30c 29a+19c  10a-8c   |
             {1} | 36a+30b  -19a-19b 29a+8b   |

        6                                                       4
     : S  <--------------------------------------------------- S  : 1
             {1} | 24b-36c  -29b+19c -10b-29c 0            |
             {1} | -24a-30c 29a+19c  10a-8c   0            |
             {1} | 36a+30b  -19a-19b 29a+8b   0            |
             {2} | 0        0        0        -10a+29b+46c |
             {2} | 0        0        0        -29a-41b-36c |
             {2} | 0        0        0        14a-19b-30c  |

        10                                                                   
     : S   <---------------------------------------------------------------- 
              {1} | 24b-36c  -29b+19c -10b-29c 0            0            |
              {1} | -24a-30c 29a+19c  10a-8c   0            0            |
              {1} | 36a+30b  -19a-19b 29a+8b   0            0            |
              {2} | 0        0        0        -10a+29b+46c 0            |
              {2} | 0        0        0        -29a-41b-36c 0            |
              {2} | 0        0        0        14a-19b-30c  0            |
              {2} | 0        0        0        0            -10a+29b+46c |
              {2} | 0        0        0        0            -29a-41b-36c |
              {2} | 0        0        0        0            14a-19b-30c  |
              {3} | 0        0        0        0            0            |

        15                                                                   
     : S   <-----------------------------------------------------------------
              {1} | 24b-36c  -29b+19c -10b-29c 0            0            0   
              {1} | -24a-30c 29a+19c  10a-8c   0            0            0   
              {1} | 36a+30b  -19a-19b 29a+8b   0            0            0   
              {2} | 0        0        0        -10a+29b+46c 0            0   
              {2} | 0        0        0        -29a-41b-36c 0            0   
              {2} | 0        0        0        14a-19b-30c  0            0   
              {2} | 0        0        0        0            -10a+29b+46c 0   
              {2} | 0        0        0        0            -29a-41b-36c 0   
              {2} | 0        0        0        0            14a-19b-30c  0   
              {2} | 0        0        0        0            0            -10a
              {2} | 0        0        0        0            0            -29a
              {2} | 0        0        0        0            0            14a-
              {3} | 0        0        0        0            0            0   
              {3} | 0        0        0        0            0            0   
              {3} | 0        0        0        0            0            0   
     ------------------------------------------------------------------------
                        }













      5
     S  : 2











                   6
     ------------ S  : 3
              |
              |
              |
              |
              |
              |
              |
              |
              |
     +29b+46c |
     -41b-36c |
     19b-30c  |
              |
              |
              |

o7 : List

i8 : L_0 === g1

o8 = true

i9 : L_1 === g2

o9 = true

i10 : indices f

o10 = {0, 1}

o10 : List

The names of the components are called indices, and are used to access the relevant inclusion and projection maps.

i11 : f^[0]

           1                   4
o11 = 0 : S  <--------------- S  : 0
                | 1 0 0 0 |

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

           10                                             15
      2 : S   <----------------------------------------- S   : 2
                 {0} | 1 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 |
                 {1} | 0 0 1 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 |
                 {1} | 0 0 0 0 1 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 |
                 {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                 {2} | 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 1 0 0 0 0 0 |

           20                                                                   26
      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 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 |
                 {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 1 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 |
                 {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 |
                 {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 |
                 {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 |
                 {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 |
                 {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 |
                 {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 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 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 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 |
                 {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 |
                 {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 |
                 {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 |
                 {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 |
                 {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 |
                 {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 0 |

o11 : SimplicialModuleMap

i12 : f_[0]

           4                 1
o12 = 0 : S  <------------- S  : 0
                {0} | 1 |
                {1} | 0 |
                {1} | 0 |
                {1} | 0 |

           10                       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 |
                 {1} | 0 0 0 0 |
                 {1} | 0 0 0 0 |
                 {1} | 0 0 0 0 |
                 {2} | 0 0 0 0 |
                 {2} | 0 0 0 0 |
                 {2} | 0 0 0 0 |

           20                                   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 |
                 {1} | 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 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0 0 0 0 0 0 0 0 0 0 |

           35                                                       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 |
                 {1} | 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 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 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 |
                 {2} | 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 |
                 {2} | 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 |
                 {2} | 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 |
                 {2} | 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 |
                 {3} | 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 |

o12 : SimplicialModuleMap

Ways to use this method:

components(SimplicialModuleMap) -- list the components of a direct sum

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:1941:0.

components(SimplicialModuleMap) -- list the components of a direct sum

Description

See also

Ways to use this method: