Macaulay2 » Documentation
Packages » OldChainComplexes » ChainComplexMap » ChainComplexMap _ ZZ = Thing
next | previous | forward | backward | up | index | toc

# ChainComplexMap _ ZZ = Thing -- install component of chain complex map

- Operator: _
- Usage:
    `f_i = g`
- Inputs:
  - f, a chain complex map
  - i, an integer
  - g, a thing
- Outputs:
  - install g as the i-th module of the chain complex map f

## Description

    i1 : R = ZZ[x..z]

    o1 = R

    o1 : PolynomialRing

    i2 : C = chainComplex R

    o2 = 0

    o2 : ChainComplex

    i3 : C.dd

    o3 = 0

    o3 : ChainComplexMap

    i4 : C.dd_1 = vars R

    o4 = | x y z |

                 1      3
    o4 : Matrix R  <-- R

    i5 : C.dd_3 = transpose vars R

    o5 = {-1} | x |
         {-1} | y |
         {-1} | z |

                 3      1
    o5 : Matrix R  <-- R

    i6 : C.dd

              1                 3
    o6 = 0 : R  <------------- R  : 1
                   | x y z |

              3         3
         1 : R  <----- R  : 2
                   0

              3                  1
         2 : R  <-------------- R  : 3
                   {-1} | x |
                   {-1} | y |
                   {-1} | z |

    o6 : ChainComplexMap

    i7 : C

          1      3      3      1
    o7 = R  <-- R  <-- R  <-- R

         0      1      2      3

    o7 : ChainComplex

    i8 : HH C

    o8 = 0 : cokernel | x y z |

         1 : image {1} | -y 0  -z |
                   {1} | x  -z 0  |
                   {1} | 0  y  x  |

         2 : cokernel {-1} | x |
                      {-1} | y |
                      {-1} | z |

         3 : image 0

    o8 : GradedModule

    i9 : prune HH C

    o9 = 0 : cokernel | z y x |

         1 : cokernel {2} | z  |
                      {2} | x  |
                      {2} | -y |

         2 : cokernel {-1} | x |
                      {-1} | y |
                      {-1} | z |

         3 : 0

    o9 : GradedModule

## See also

- ChainComplex _ ZZ = Thing -- install component of chain complex

## Ways to use this method:

- ChainComplexMap _ ZZ = Thing -- install component of chain complex map

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldChainComplexes/docs/underscore-doc.m2:89:0.