LieDerivation - LieDerivation -- subtraction of Lie derivations

Synopsis

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 $e$

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