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# freeExteriorSummand -- find the free summands of a module over an exterior algebra

- Usage:
    `F = freeExteriorSummand M`
- Inputs:
  - M, a module, over an exterior algebra
- Outputs:
  - F, a matrix, Map from a free module to M. Image is the largest free summand

## Description

    i1 : kk= ZZ/101

    o1 = kk

    o1 : QuotientRing

    i2 : E = kk[e,f,g, SkewCommutative => true]

    o2 = E

    o2 : PolynomialRing, 3 skew commutative variable(s)

    i3 : M = E^1++module ideal vars E++E^{-1}

    o3 = image {0} | 1 0 0 0 0 |
               {0} | 0 e f g 0 |
               {1} | 0 0 0 0 1 |

                                 3
    o3 : E-module, submodule of E

    i4 : freeExteriorSummand M

    o4 = {0} | 1 0 |
         {1} | 0 0 |
         {1} | 0 0 |
         {1} | 0 0 |
         {1} | 0 1 |

                       2
    o4 : Matrix M <-- E

## Ways to use freeExteriorSummand:

- `freeExteriorSummand(Module)`

## For the programmer

The object freeExteriorSummand is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CompleteIntersectionResolutions.m2:4285:0.