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ChainComplex ^ Array -- projection onto summand

Description

The chain complex M should be a direct sum, and the result is the map obtained by projection onto the sum of the components numbered or named i, j, ..., k. Free modules are regarded as direct sums of modules.

i1 : M = ZZ^2 ++ ZZ^3

       5
o1 = ZZ

o1 : ZZ-module, free
i2 : M^[0]

o2 = | 1 0 0 0 0 |
     | 0 1 0 0 0 |

              2       5
o2 : Matrix ZZ  <-- ZZ
i3 : M^[1]

o3 = | 0 0 1 0 0 |
     | 0 0 0 1 0 |
     | 0 0 0 0 1 |

              3       5
o3 : Matrix ZZ  <-- ZZ
i4 : M^[1,0]

o4 = | 0 0 1 0 0 |
     | 0 0 0 1 0 |
     | 0 0 0 0 1 |
     | 1 0 0 0 0 |
     | 0 1 0 0 0 |

              5       5
o4 : Matrix ZZ  <-- ZZ

If the components have been given names (see directSum), use those instead.
i5 : R = QQ[x,y,z];
i6 : C = res coker vars R

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

o6 : ChainComplex
i7 : D = (a=>C) ++ (b=>C)

      2      6      6      2
o7 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o7 : ChainComplex
i8 : D^[a]

          1               2
o8 = 0 : R  <----------- R  : 0
               | 1 0 |

          3                           6
     1 : R  <----------------------- R  : 1
               {1} | 1 0 0 0 0 0 |
               {1} | 0 1 0 0 0 0 |
               {1} | 0 0 1 0 0 0 |

          3                           6
     2 : R  <----------------------- R  : 2
               {2} | 1 0 0 0 0 0 |
               {2} | 0 1 0 0 0 0 |
               {2} | 0 0 1 0 0 0 |

          1                   2
     3 : R  <--------------- R  : 3
               {3} | 1 0 |

     4 : 0 <----- 0 : 4
              0

o8 : ChainComplexMap

See also

Ways to use this method:


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/OldChainComplexes/docs/caret-doc.m2:72:0.