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# transpose(ChainComplexMap) -- transpose a map of chain complexes

- Function: transpose
- Usage:
    `transpose f`
- Inputs:
  - f, a chain complex map
- Outputs:
  - a chain complex map, the transpose of f

## Description

The output of transpose is a map from the duals of the original source and target free modules. See the degree of the target module in the following example

    i1 : S = ZZ/10007[x,y,z];

    i2 : F = res ideal vars S;

    i3 : F.dd

              1                 3
    o3 = 0 : S  <------------- S  : 1
                   | x y z |

              3                        3
         1 : S  <-------------------- S  : 2
                   {1} | -y -z 0  |
                   {1} | x  0  -z |
                   {1} | 0  x  y  |

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

              1
         3 : S  <----- 0 : 4
                   0

    o3 : ChainComplexMap

    i4 : transpose F.dd

                        1
    o4 = -4 : 0 <----- S  : -3
                   0

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

               3                        3
         -2 : S  <-------------------- S  : -1
                    {-2} | y -x 0  |
                    {-2} | z 0  -x |
                    {-2} | 0 z  -y |

               3                  1
         -1 : S  <-------------- S  : 0
                    {-1} | x |
                    {-1} | y |
                    {-1} | z |

    o4 : ChainComplexMap

Note that M2 treats the differentials of a chain complex map as map of degree -1.

## Ways to use this method:

- transpose(ChainComplexMap) -- transpose a map of chain complexes

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldChainComplexes/docs/docs.m2:253:0.