next | previous | forward | backward | up | index | toc

# standardForm(RingElement,LieAlgebra) -- get a Lie element in standard form

## Description

The set of linear polynomials in L#cache.mbRing gives a representation of Lie elements. The function standardForm gives back the standard output and indexForm goes in the other direction.

## Synopsis

• Usage:
standardForm(r,L)
• Inputs:
• r, , an element in L#cache.mbRing
• L, an instance of the type LieAlgebra
• Outputs:
• an instance of the type LieElement, the corresponding Lie element

## Synopsis

• Usage:
standardForm(x,L)
• Inputs:
• x, a list, a list of elements in L#cache.mbRing
• L, an instance of the type LieAlgebra
• Outputs:
• a list, the list of the corresponding Lie elements
 i1 : L = lieAlgebra{a,b} o1 = L o1 : LieAlgebra i2 : b3 = basis(3,L) o2 = {(a b a), (b b a)} o2 : List i3 : Q = L#cache.mbRing o3 = Q o3 : PolynomialRing i4 : gens Q o4 = {mb , mb , mb , mb , mb } {1, 0} {1, 1} {2, 0} {3, 0} {3, 1} o4 : List i5 : c3 = {indexForm a a b,indexForm b a b} o5 = {-mb , -mb } {3, 0} {3, 1} o5 : List i6 : standardForm(c3,L) o6 = { - (a b a), - (b b a)} o6 : List i7 : standardForm(mb_{3,0}+2*mb_{3,1},L) o7 = (a b a) + 2 (b b a) o7 : L i8 : indexForm oo o8 = mb + 2mb {3, 0} {3, 1} o8 : Q