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# cycles -- make the subalgebra of cycles

- Usage:
    `C=cycles(L)`
- Inputs:
  - L, an instance of the type LieAlgebra,
- Outputs:
  - C, an instance of the type LieSubAlgebra, the kernel of the differential

## Description

    i1 : L=lieAlgebra({a,b},Signs=>{1,0},Weights=>{{2,0},{2,1}},
            Field=>ZZ/3,LastWeightHomological=>true)

    o1 = L

    o1 : LieAlgebra

    i2 : D=differentialLieAlgebra({0_L,a})

    o2 = D

    o2 : LieAlgebra

    i3 : C=cycles D

    o3 = C

    o3 : LieSubAlgebra

    i4 : dims(10,C)

    o4 = | 0 1 0 1 0 0 0 0 0 0 |
         | 0 0 0 0 0 1 0 1 0 1 |
         | 0 0 0 0 0 1 0 1 0 1 |
         | 0 0 0 0 0 0 0 0 0 1 |
         | 0 0 0 0 0 0 0 0 0 0 |
         | 0 0 0 0 0 0 0 0 0 0 |
         | 0 0 0 0 0 0 0 0 0 0 |
         | 0 0 0 0 0 0 0 0 0 0 |
         | 0 0 0 0 0 0 0 0 0 0 |
         | 0 0 0 0 0 0 0 0 0 0 |

                  10       10
    o4 : Matrix ZZ   <-- ZZ

## See also

- boundaries -- make the subalgebra of boundaries
- lieHomology -- make the homology as a vector space

## Ways to use cycles:

- `cycles(LieAlgebra)`

## For the programmer

The object cycles is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc2.m2:1203:0.