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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input newton.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1994.
@
<<*>>=
<<license>>
-- Newton's Iteration function
-- newtonStep(f) returns a newton's iteration function for the
-- expression f.
newtonStep(f) ==
fun := complexNumericFunction f
deriv := complexDerivativeFunction(f,1)
(b:Complex DoubleFloat):Complex DoubleFloat +->
b - fun(b)/deriv(b)
-- create complex numeric functions from an expression
complexFunPack := MakeUnaryCompiledFunction(EXPR INT, Complex DoubleFloat, Complex DoubleFloat)
-- create a complex numeric function from an expression
complexNumericFunction x ==
v := theVariable x
compiledFunction(x, v)$complexFunPack
-- create a complex numeric derivatiave function from an expression
complexDerivativeFunction(x,n) ==
v := theVariable x
df := differentiate(x,v,n)
compiledFunction(df, v)$complexFunPack
-- return the unique variable in x, or an error if it is multivariate
theVariable x ==
vl := variables x
nv := # vl
nv > 1 => error "Expression is not univariate."
nv = 0 => 'x
first vl
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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