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# dual(ChainComplexMap) -- dual of a chain complex

- Function: dual
- Usage:
    `dual C`
- Inputs:
  - C, a chain complex map
- Outputs:
  - a chain complex map, the dual of the chain complex C

## Description

    i1 : R = QQ[a..f]

    o1 = R

    o1 : PolynomialRing

    i2 : M = coker genericMatrix(R,a,2,3)

    o2 = cokernel | a c e |
                  | b d f |

                                2
    o2 : R-module, quotient of R

    i3 : res M

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

         0      1      2      3

    o3 : ChainComplex

    i4 : dual oo

                 1      3      2
    o4 = 0  <-- R  <-- R  <-- R

         -3     -2     -1     0

    o4 : ChainComplex

## Ways to use this method:

- dual(ChainComplexMap) -- dual of a chain complex

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldChainComplexes/docs/doc9.m2:515:0.