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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input ode.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1996.
@
<<*>>=
<<license>>
--A bug when one one uses a diff.eq. with a free variable other than x.
)set break resume
y:=operator 'y
deqx:= differentiate(y x,x,2)+differentiate(y x,x) +y x
solve(deqx,y,x) --OK
solve(deqx,y,x=0,[1]) --OK
deqt:= differentiate(y t,t,2)+differentiate(y t,t) +y t
solve(deqt,y,t) --OK
solve(deqt,y,t=0,[1]) -- BUG!
deqz:= differentiate(y z,z,2)+differentiate(y z,z) +y z
solve(deqz,y,z) --OK
solve(deqz,y,z=0,[1]) -- BUG!
--I think the bug is in
-- file odeef.spad
-- constructor ODEEF
-- function solve(diffeq:F,y:OP,center:EQ,y0:List F)
--the second line of the body was
-- kx:K:=kernel x
--which uses uninitialised x. I think it should be
-- kx:K:=kernel(retract(lhs(center))@SY)
--as the line immediately below it. That change certainly fixes THIS bug!
--Also, maybe a check should be made that this kx is indeed to be found
--in the diffeq -- my system reports segmenttion violation if I do
solve(deqt,y,x=0,[1])
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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