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# LieDerivation - LieDerivation -- subtraction of Lie derivations

- Operator: -
- Usage:
    `u = d - e`
- Inputs:
  - d, an instance of the type LieDerivation,
  - e, an instance of the type LieDerivation,
- Outputs:
  - u, an instance of the type LieDerivation, the difference of $d$ and $e$

## Description

The symbol - is used as infix notation for the subtraction of Lie derivations $M\ \to\ L$ with the same defining map $f: M\ \to\ L$.

    i1 : M = lieAlgebra{a,b}

    o1 = M

    o1 : LieAlgebra

    i2 : L = lieAlgebra{a1,b1}

    o2 = L

    o2 : LieAlgebra

    i3 : f = map(L,M,{b1,a1})

    o3 = f

    o3 : LieAlgebraMap

    i4 : d = lieDerivation(f,{a1,b1})

    o4 = d

    o4 : LieDerivation

    i5 : e = lieDerivation(f,{2 b1,2 a1})

    o5 = e

    o5 : LieDerivation

    i6 : u = d-e

    o6 = u

    o6 : LieDerivation

    i7 : describe u

    o7 = a => a1 - 2 b1
         b =>  - 2 a1 + b1
         map => f
         sign => 0
         weight => {0, 0}
         source => M
         target => L

    i8 : u a b

    o8 =  - 4 (b1 a1)

    o8 : L

## Ways to use this method:

- LieDerivation - LieDerivation -- subtraction of Lie derivations

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc.m2:2511:0.