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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/input/intg0.input.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input intg0.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1994.
+@
+<<*>>=
+<<license>>
+
+)cl all
+-- some genus 0 integrations
+y := sqrt(a * x + b)
+integrate(%,x)
+x * y
+integrate(%,x)
+z := sqrt(a**2 - x**2)
+1 / z
+integrate(%,x)
+x**2 * z
+integrate(%,x)
+x**3 / (a+b*x)**(1/3)
+integrate(%,x)
+1 / (x**3 * (a+b*x)**(1/3))
+integrate(%,x)
+-- examples of transcendentals over a curve of genus 0
+x / (y + y**2) + log(y + 1)
+integrate(%,x)
+(2 + 1/sqrt(x)) * cos(x + sqrt x)
+integrate(%,x)
+-- one which does not have an elementary integral
+log(1 + y) / x
+integrate(%,x)
+-- integrals of hyperbolic trigs are returned in terms of hyperb. trigs.
+(sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b))))
+integrate(%,x)
+-- examples of genus 0 functions presented as transcendentals
+tan(atan(x)/2)
+integrate(%,x)
+tan(atan(x)/3)
+integrate(%,x)
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}