Initial population.

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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}