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# differential -- make the derivation defined by the differential

- Usage:
    `d=differential(L)`
- Inputs:
  - L, an instance of the type LieAlgebra,
- Outputs:
  - d, an instance of the type LieDerivation, the derivation defined by the differential

## Description

If the current Lie algebra has no differential, then 0 is returned.

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

    o1 = L

    o1 : LieAlgebra

    i2 : L=differentialLieAlgebra{0_L,a}

    o2 = L

    o2 : LieAlgebra

    i3 : d=differential(L)

    o3 = d

    o3 : LieDerivation

    i4 : d b b a

    o4 = (3/2)(b a a)

    o4 : L

## See also

- lieAlgebra -- make a free Lie algebra
- lieDerivation -- make a graded derivation

## For the programmer

The object differential is a function closure.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc2.m2:1382:0.