# LieDerivation \\ List -- formal application of a derivation to every element in a list

## Synopsis

• Operator: \\
• Usage:
y = d\\x
• Inputs:
• d, an instance of the type LieDerivation,
• x, a list, the elements in $x$ belong to the source of $d$
• Outputs:
• y, a list, the elements in $y$ are the formal application of $d$ to the elements in $x$

## Description

 i1 : L = lieAlgebra{a,b}/{a a a b,b b b a} o1 = L o1 : LieAlgebra i2 : d = euler L o2 = d o2 : LieDerivation i3 : d\\basis(5,L) o3 = {(a b a b a) + (a b a b a) + (a b a b a) + (a b a b a) + (a b a b a), (b ------------------------------------------------------------------------ b a b a) + (b b a b a) + (b b a b a) + (b b a b a) + (b b a b a)} o3 : List i4 : d\basis(5,L) o4 = {5 (a b a b a), 5 (b b a b a)} o4 : List