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# ChainComplexMap ^ ZZ -- iterated composition

- Operator: ^
- Usage:
    `f^n`
- Inputs:
  - f, a chain complex map, or a a graded module map
  - n, an integer
- Outputs:
  - a chain complex map, the composite f o f o ... o f (n times)

## Description

If f is a GradedModuleMap, then so is the result.

One use of this function is to determine if a chain complex is well-defined. The chain complex will be well-defined if the square of the differential is zero.

    i1 : R = QQ[x,y,z];

    i2 : C = res coker vars R

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

         0      1      2      3      4

    o2 : ChainComplex

    i3 : C.dd^2 == 0

    o3 = true

## See also

- ChainComplex -- the class of all chain complexes

## Ways to use this method:

- ChainComplexMap ^ ZZ -- iterated composition
- `GradedModuleMap ^ ZZ`

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldChainComplexes/docs/caret-doc.m2:40:0.