@@ -1,83 +1,83 @@
-\documentstyle[11pt,reduce]{article}
-\title{A REDUCE Limits Package}
-\date{}
-\author{Stanley L. Kameny \\ Email: stan\%valley.uucp@rand.org}
-\begin{document}
-\maketitle
-
-\index{LIMITS package}
-LIMITS is a fast limit package for REDUCE for functions which are
-continuous except for computable poles and singularities, based on some
-earlier work by Ian Cohen and John P. Fitch.  The Truncated Power Series
-package is used for non-critical points, at which the value of the
-function is the constant term in the expansion around that point.
-\index{l'H\^opital's rule}
-l'H\^opital's rule is used in critical cases, with preprocessing of
-$\infty - \infty$ forms and reformatting of product forms in order
-to apply l'H\^opital's rule.  A limited amount of bounded arithmetic
-is also employed where applicable.
-
-\section{Normal entry points}
-\ttindex{LIMIT}
-\vspace{.1in}
-\noindent {\tt LIMIT}(EXPRN:{\em algebraic}, VAR:{\em kernel},
-LIMPOINT:{\em algebraic}):{\em algebraic}
-\vspace{.1in}
-
-This is the standard way of calling limit, applying all of the methods. The
-result is the limit of EXPRN as VAR approaches LIMPOINT.
-
-
-\section{Direction-dependent limits}
-
-\ttindex{LIMIT+} \ttindex{LIMIT-}
-\vspace{.1in}
-\noindent {\tt LIMIT!+}(EXPRN:{\em algebraic}, VAR:{\em kernel},
-LIMPOINT:{\em algebraic}):{\em algebraic} \\
-\noindent {\tt LIMIT!-}(EXPRN:{\em algebraic}, VAR:{\em kernel},
-LIMPOINT:{\em algebraic}):{\em algebraic}
-\vspace{.1in}
-
-If the limit depends upon the direction of approach to the {\tt LIMPOINT},
-the functions {\tt LIMIT!+} and {\tt LIMIT!-} may be used.  They are
-defined by:
-
-\vspace{.1in}
-\noindent{\tt LIMIT!+ (LIMIT!-)} (EXP,VAR,LIMPOINT) $\rightarrow$ \\
-\hspace*{2em}{\tt LIMIT}(EXP*,$\epsilon$,0)
-EXP*=sub(VAR=VAR+(-)$\epsilon^2$,EXP)
-
-\section{Diagnostic Functions}
-
-\ttindex{LIMIT0}
-\vspace{.1in}
-\noindent {\tt LIMIT0}(EXPRN:{\em algebraic}, VAR:{\em kernel},
-LIMPOINT:{\em algebraic}):{\em algebraic}
-\vspace{.1in}
-
-This function will use all parts of the limits package, but it does not
-combine log terms before taking limits, so it may fail if there is a sum
-of log terms which have a removable singularity in some of the terms.
-
-\ttindex{LIMIT1}
-\vspace{.1in}
-\noindent {\tt LIMIT1}(EXPRN:{\em algebraic}, VAR:{\em kernel},
-LIMPOINT:{\em algebraic}):{\em algebraic}
-\vspace{.1in}
-
-\index{TPS package}
-This function uses the TPS branch only, and will fail if the limit point is
-singular.
-
-\ttindex{LIMIT2}
-\vspace{.1in}
-\begin{tabbing}
-{\tt LIMIT2}(\=TOP:{\em algebraic}, \\
-\>BOT:{\em algebraic}, \\
-\>VAR:{\em kernel}, \\
-\>LIMPOINT:{\em algebraic}):{\em algebraic}
-\end{tabbing}
-\vspace{.1in}
-
-This function applies l'H\^opital's rule to the quotient (TOP/BOT).
-\end{document}
+\documentstyle[11pt,reduce]{article}
+\title{A REDUCE Limits Package}
+\date{}
+\author{Stanley L. Kameny \\ Email: stan\%valley.uucp@rand.org}
+\begin{document}
+\maketitle
+
+\index{LIMITS package}
+LIMITS is a fast limit package for REDUCE for functions which are
+continuous except for computable poles and singularities, based on some
+earlier work by Ian Cohen and John P. Fitch.  The Truncated Power Series
+package is used for non-critical points, at which the value of the
+function is the constant term in the expansion around that point.
+\index{l'H\^opital's rule}
+l'H\^opital's rule is used in critical cases, with preprocessing of
+$\infty - \infty$ forms and reformatting of product forms in order
+to apply l'H\^opital's rule.  A limited amount of bounded arithmetic
+is also employed where applicable.
+
+\section{Normal entry points}
+\ttindex{LIMIT}
+\vspace{.1in}
+\noindent {\tt LIMIT}(EXPRN:{\em algebraic}, VAR:{\em kernel},
+LIMPOINT:{\em algebraic}):{\em algebraic}
+\vspace{.1in}
+
+This is the standard way of calling limit, applying all of the methods. The
+result is the limit of EXPRN as VAR approaches LIMPOINT.
+
+
+\section{Direction-dependent limits}
+
+\ttindex{LIMIT+} \ttindex{LIMIT-}
+\vspace{.1in}
+\noindent {\tt LIMIT!+}(EXPRN:{\em algebraic}, VAR:{\em kernel},
+LIMPOINT:{\em algebraic}):{\em algebraic} \\
+\noindent {\tt LIMIT!-}(EXPRN:{\em algebraic}, VAR:{\em kernel},
+LIMPOINT:{\em algebraic}):{\em algebraic}
+\vspace{.1in}
+
+If the limit depends upon the direction of approach to the {\tt LIMPOINT},
+the functions {\tt LIMIT!+} and {\tt LIMIT!-} may be used.  They are
+defined by:
+
+\vspace{.1in}
+\noindent{\tt LIMIT!+ (LIMIT!-)} (EXP,VAR,LIMPOINT) $\rightarrow$ \\
+\hspace*{2em}{\tt LIMIT}(EXP*,$\epsilon$,0)
+EXP*=sub(VAR=VAR+(-)$\epsilon^2$,EXP)
+
+\section{Diagnostic Functions}
+
+\ttindex{LIMIT0}
+\vspace{.1in}
+\noindent {\tt LIMIT0}(EXPRN:{\em algebraic}, VAR:{\em kernel},
+LIMPOINT:{\em algebraic}):{\em algebraic}
+\vspace{.1in}
+
+This function will use all parts of the limits package, but it does not
+combine log terms before taking limits, so it may fail if there is a sum
+of log terms which have a removable singularity in some of the terms.
+
+\ttindex{LIMIT1}
+\vspace{.1in}
+\noindent {\tt LIMIT1}(EXPRN:{\em algebraic}, VAR:{\em kernel},
+LIMPOINT:{\em algebraic}):{\em algebraic}
+\vspace{.1in}
+
+\index{TPS package}
+This function uses the TPS branch only, and will fail if the limit point is
+singular.
+
+\ttindex{LIMIT2}
+\vspace{.1in}
+\begin{tabbing}
+{\tt LIMIT2}(\=TOP:{\em algebraic}, \\
+\>BOT:{\em algebraic}, \\
+\>VAR:{\em kernel}, \\
+\>LIMPOINT:{\em algebraic}):{\em algebraic}
+\end{tabbing}
+\vspace{.1in}
+
+This function applies l'H\^opital's rule to the quotient (TOP/BOT).
+\end{document}