\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input elfuts.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1994.
@
<<*>>=
<<license>>

)cl all
--demo of Jacobian elliptic functions expanded as power series
)set streams calculate 10
)expose ELFUTS
macro RN == FRAC INT
macro QF == FRAC
xx : UTS(RN, 'x, 0) := x
jacobiSn(xx, 1::RN)
jacobiCn(xx, 1::RN)
jacobiDn(xx, 1::RN)
yy : UTS(FRAC UP(m, RN),'y, 0) := y
snn := jacobiSn(yy, m::QF UP(m, RN))
cnn := jacobiCn(yy, m::QF UP(m, RN))
dnn := jacobiDn(yy, m::QF UP(m, RN))
snn^2 + cnn^2
mm := (m::UP(m, RN))
dnn^2 + mm*snn^2
(differentiate snn)^2
(1 - snn^2)*(1 - mm*snn^2)
(differentiate cnn)^2
(1 - cnn^2)*(1 - mm + mm*cnn^2)
(differentiate dnn)^2
(1 - dnn^2)*(dnn^2 - 1 + mm)

kkk := integrate(1/((1 - yy^2)*(1 - mm*yy^2))^(1/2))
snn - revert kkk

-- Theta-functions expanded as power series

--q0=*/[1-q^2*n for n in 1..]
--q1=*/[1+q^2*n for n in 1..]
--q2=*/[1+q^(2*n-1) for n in 1..]
--q3=*/[1-q^(2*n-1) for n in 1..]
eprod x==exp evenlambert log x
qq:UTS(RN,'q,0):=q
q0:=eprod(1-qq)
q1:=eprod(1+qq)
oprod x == exp oddlambert log x
q2:=oprod(1+qq)
q3:=oprod(1-qq)
q1*q2*q3
q2^8-q3^8
16*qq*q1^8
--(q1^2/q2^2)^2
--(q3^2/q2^2)^2
q0^3
q1^2*q0
q2^2*q0
q3^2*q0
qqq:UTS(FRAC UP(a,RN),'q,0):=q
a:=a::FRAC UP(a,RN)

--Jacobi's triple product
eprod(1-qqq)*oprod(1-a*qqq)*oprod(1-qqq/a)
sq:=mm*snn^2
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
