# 9.42 LieExponentialsΒΆ

a: Symbol := 'a

 a

Type: Symbol

b: Symbol := 'b

 b

Type: Symbol

Declarations of domains

coef := Fraction(Integer)

 FractionInteger

Type: Domain

group := LieExponentials(Symbol, coef, 3)

 LieExponentials(Symbol,FractionInteger,3)

Type: Domain

lpoly := LiePolynomial(Symbol, coef)

 LiePolynomial(Symbol,FractionInteger)

Type: Domain

poly := XPBWPolynomial(Symbol, coef)

 XPBWPolynomial(Symbol,FractionInteger)

Type: Domain

Calculations

ea := exp(a::lpoly)$group   e[a] Type: LieExponentials(Symbol,Fraction Integer,3) eb := exp(b::lpoly)$group

 e[b]

Type: LieExponentials(Symbol,Fraction Integer,3)

g: group := ea*eb

 e[b]e(12[ab2])e[ab]e(12[a2b])e[a]

Type: LieExponentials(Symbol,Fraction Integer,3)

g :: poly

 1+[a]+[b]+12[a][a]+[ab]+[b][a]+12[b][b]+16[a][a][a]+12[a2b]+[ab][a]+12[ab2]+12[b][a][a]+[b][ab]+12[b][b][a]+16[b][b][b]

Type: XPBWPolynomial(Symbol,Fraction Integer)

log(g)\$group

 [a]+[b]+12[ab]+112[a2b]+112[ab2]

Type: LiePolynomial(Symbol,Fraction Integer)

g1: group := inv(g)

 e(-[b])e(-[a])

Type: LieExponentials(Symbol,Fraction Integer,3)

g*g1

 1

Type: LieExponentials(Symbol,Fraction Integer,3)