# LieDerivation - LieDerivation -- subtraction of Lie derivations

## Synopsis

• Operator: -
• Usage:
u = d - e
• Inputs:
• 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