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ChainComplex _ Array -- inclusion from summand

Description

The chain complex C should be a direct sum, and the result is the map corresponding to inclusion from the sum of the components numbered or named i, j, ..., k.

i1 : R = QQ[a,b];
i2 : C = res coker vars R

      1      2      1
o2 = R  <-- R  <-- R  <-- 0
                           
     0      1      2      3

o2 : ChainComplex
i3 : D = C ++ C

      2      4      2
o3 = R  <-- R  <-- R  <-- 0
                           
     0      1      2      3

o3 : ChainComplex
i4 : D_[0]

          2             1
o4 = 0 : R  <--------- R  : 0
               | 1 |
               | 0 |

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

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

     3 : 0 <----- 0 : 3
              0

o4 : ChainComplexMap
i5 : D_[1,0]

          2               2
o5 = 0 : R  <----------- R  : 0
               | 0 1 |
               | 1 0 |

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

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

     3 : 0 <----- 0 : 3
              0

o5 : ChainComplexMap

If the components have been given names (see directSum), use those instead.
i6 : D = (a=>C) ++ (b=>C)

      2      4      2
o6 = R  <-- R  <-- R  <-- 0
                           
     0      1      2      3

o6 : ChainComplex
i7 : D_[a]

          2             1
o7 = 0 : R  <--------- R  : 0
               | 1 |
               | 0 |

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

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

     3 : 0 <----- 0 : 3
              0

o7 : ChainComplexMap

See also

Ways to use this method:


The source of this document is in OldChainComplexes/docs/underscore-doc.m2:119:0.