\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input LPOLY.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
)cl all

RN    := Fraction Integer
Lpoly := LiePolynomial(Symbol,RN)
Dpoly := XDPOLY(Symbol,RN)
Lword := LyndonWord Symbol
a:Symbol := 'a
b:Symbol := 'b
c:Symbol := 'c
aa: Lpoly := a
bb: Lpoly := b
cc: Lpoly := c
p : Lpoly := [aa,bb]
q : Lpoly := [p,bb]
liste : List Lword := LyndonWordsList([a,b], 4)
r: Lpoly := p + q + 3*LiePoly(liste.4)$Lpoly
s:Lpoly := [p,r]
t:Lpoly  := s  + 2*LiePoly(liste.3) - 5*LiePoly(liste.5)
degree t
mirror t
Jacobi(p: Lpoly, q: Lpoly, r: Lpoly): Lpoly == [[p,q]$Lpoly, r] + [[q,r]$Lpoly, p] + [[r,p]$Lpoly, q]
test: Lpoly := Jacobi(a,b,b)
test: Lpoly := Jacobi(p,q,r)
test: Lpoly := Jacobi(r,s,t)
eval(p, a, p)$Lpoly
eval(p, [a,b], [2*bb, 3*aa])$Lpoly
r: Lpoly := [p,c]
r1: Lpoly := eval(r, [a,b,c], [bb, cc, aa])$Lpoly
r2: Lpoly := eval(r, [a,b,c], [cc, aa, bb])$Lpoly
r + r1 + r2
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}