From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Tue, 14 Aug 2007 05:14:52 +0000
Subject: Initial population.

---
 src/input/lode.input.pamphlet | 66 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 66 insertions(+)
 create mode 100644 src/input/lode.input.pamphlet

(limited to 'src/input/lode.input.pamphlet')

diff --git a/src/input/lode.input.pamphlet b/src/input/lode.input.pamphlet
new file mode 100644
index 00000000..364f7202
--- /dev/null
+++ b/src/input/lode.input.pamphlet
@@ -0,0 +1,66 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input lode.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1991.
+@
+<<*>>=
+<<license>>
+-------------------------------- lode.input ---------------------------
+ 
+)cl all
+-- this will be the unknown
+y := operator y
+ 
+-- homogeneous equation with constant coefficients
+deq := differentiate(y x, x, 2) + differentiate(y x, x) + y x
+solve(deq, y, x).basis
+ 
+-- initial value problem: y'' + y = 0, y(0) = y'(0) = 1
+deq := differentiate(y x, x, 2) + y x
+solve(deq, y, x = 0, [1, 1])
+ 
+-- same with a non-constant right-hand side
+solve(deq = sin x, y, x)
+ 
+-- some inhomogenuous equations with rational coefficients
+deq := x**3 * differentiate(y x, x, 3) + x**2 * differentiate(y x, x, 2) - _
+2 * x * differentiate(y x, x) + 2 * y x = 2 * x**4
+solve(deq, y, x)
+-- same with initial conditions
+solve(deq, y, x = 1, [b, 0, a])
+ 
+-- third order equation with nontrivial singularities
+deq := (x**9 + x**3) * differentiate(y x, x, 3) + _
+18 * x**8 * differentiate(y x, x,2) - 90 * x * differentiate(y x, x) - _
+30 * (11*x**6-3) * y x
+solve(deq, y, x).basis
+ 
+-- third order equation on a curve of genus 0
+deq := (2*x+2)* differentiate(y x, x, 3) + 3* differentiate(y x, x, 2) + _
+(2*x**2+2*x)* differentiate(y x,x) - sqrt(x+1) * y x = 2 * x**2 + x - 1
+solve(deq, y, x).particular
+ 
+-- this equation is irreducible over the rational functions
+deq := 2*x**3*differentiate(y x,x,2) + 3*x**2*differentiate(y x,x) - 2*y x
+solve(deq,y,x).basis
+ 
+ 
+ 
+
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
-- 
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