9.42 LieExponentials

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)

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LieExponentials(Symbol,FractionInteger,3)

_{Type: Domain}

lpoly := LiePolynomial(Symbol, coef)

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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)}