src/input/is.input.pamphlet


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

--  This is the 3n + 1 function:   f(n) = n/2    if n is even,
--                                        3n + 1 otherwise
--
-- It can obviously be coded as
--  f n ==
--    even? n => n quo 2
--    3 * n + 1

-- but we code using the pattern matching syntax:
-- f n ==
--    n is 2*m% => m%
--    3 * n + 1

-- The 'integer' is to return an integer instead of a polynomial
f n ==
   not empty?(u := Is(n, 2*m%)) => integer eval(m%, u)
   3 * n + 1

)set stream showall on

-- The function g generates the stream of the repeated applications of f
g(n:INT):STREAM(INT) == generate(f, n)

-- There is a conjecture that g(n) gets into the cycle (1 4 2)
-- for every n
s := g 27
extend(s, 150)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}