\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input elemfun.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1991.
@
<<*>>=
<<license>>

-- Manipulations of ElementaryFunction Integer
 
)clear all
 
-- some values of trig functions will simplify on application
cos 0
sin 0
exp 0
log 1
sin(%pi/2)
simplify %
 
-- same goes with the usual relations
sin(3)**2 + cos(3)**2
simplify %
 
a := atan 1
t := cos(a)*sin(a)*tan(a)*sec(a)*csc(a)*cot(a)
simplify t
 
-- we can remove selected operations
cot2tan t
cot2trig t
tan2cot t
tan2trig t
cos2sec t
 
-- given such a trig expression not involving any variables,
-- we can get a numeric approximation
 
t := sin(7)**2 - sec(7)/(1 - cot(7) + csc(7)**3)
simplify t
numeric %
 
-- we really didn't need to have simplified
numeric t
 
-- we can get more digits by giving a precision
numeric(t, 100)
 
-- if we do have an expression involving variables, we can use eval
-- to give them values
 
u := exp(sin(x-1)**2 - cos(x-1)/sec(x-1))
eval(u,x=1)
 
-- here is another technique using rewrite rules
v(x) == exp(sin(x-1)**2 - cos(x-1)/sec(x-1))
v x
v 1
v(%pi/3)
numeric %
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}