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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input genups.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1991.
@
<<*>>=
<<license>>
)cl all
taylor(n +-> 1/factorial(n),x = 0) -- expansion of exp(x) at x = 0
taylor(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1
taylor(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x)
laurent(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion
laurent(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0
puiseux(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0
-- puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
puiseux(j +-> j,x = 8,-4/3..,1/2)
puiseux(j +-> j,x = 8,-4/3..1/6,1/2)
-- same computations using expressions instead of functions
taylor(1/factorial(n),n,x = 0) -- expansion of exp(x) at x = 0
taylor((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1
taylor((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x)
laurent(m**2,m,x = 7,-2..) -- infinite Laurent expansion
laurent(m**2,m,x = 7,-2..5) -- finite Laurent expansion
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0
puiseux((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0
-- puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
puiseux(j,j,x = 8,-4/3..,1/2)
puiseux(j,j,x = 8,-4/3..1/6,1/2)
-- all of the above commands should still work when the functions 'taylor',
-- 'laurent', and 'puiseux' are replaced by 'series':
series(n +-> 1/factorial(n),x = 0) -- expansion of exp(x) at x = 0
series(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1
series(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x)
series(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion
series(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0
series(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0
-- series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
series(j +-> j,x = 8,-4/3..,1/2)
series(j +-> j,x = 8,-4/3..1/6,1/2)
-- same computations using expressions instead of functions
series(1/factorial(n),n,x = 0) -- expansion of exp(x) at x = 0
series((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1
series((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x)
series(m**2,m,x = 7,-2..) -- infinite Laurent expansion
series(m**2,m,x = 7,-2..5) -- finite Laurent expansion
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0
series((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0
-- series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
series(j,j,x = 8,-4/3..,1/2)
series(j,j,x = 8,-4/3..1/6,1/2)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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