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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra real0q.spad}
+\author{Andy Neff, Barry Trager}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package REAL0Q RealZeroPackageQ}
+<<package REAL0Q RealZeroPackageQ>>=
+)abbrev package REAL0Q RealZeroPackageQ
+++ Author: Andy Neff, Barry Trager
+++ Date Created:
+++ Date Last Updated: 7 April 1991
+++ Basic Functions:
+++ Related Constructors: UnivariatePolynomial, RealZeroPackageQ
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++   This package provides functions for finding the real zeros
+++ of univariate polynomials over the rational numbers to arbitrary user-specified 
+++ precision. The results are returned as a list of
+++ isolating intervals, expressed as records with "left" and "right" rational number components.
+ 
+RealZeroPackageQ(Pol): T == C where
+   RN  ==> Fraction Integer
+   I   ==> Integer
+   SUP ==> SparseUnivariatePolynomial
+   Pol: UnivariatePolynomialCategory RN
+   Interval ==> Record(left : RN, right : RN)
+   isoList ==> List(Interval)
+   ApproxInfo ==> Record(approx : RN, exFlag : Boolean)
+   T == with
+    -- next two functions find isolating intervals
+      realZeros: (Pol) -> isoList
+        ++ realZeros(pol) returns a list of isolating intervals for
+        ++ all the real zeros of the univariate polynomial pol.
+      realZeros: (Pol, Interval) -> isoList
+        ++ realZeros(pol, range) returns a list of isolating intervals
+        ++ for all the real zeros of the univariate polynomial pol which
+        ++ lie in the interval expressed by the record range.
+    -- next two functions return intervals smaller then tolerence
+      realZeros: (Pol, RN) -> isoList
+        ++ realZeros(pol, eps) returns a list of intervals of length less
+        ++ than the rational number eps for all the real roots of the
+        ++ polynomial pol.
+      realZeros: (Pol, Interval, RN) -> isoList
+        ++ realZeros(pol, int, eps) returns a list of intervals of length
+        ++ less than the rational number eps for all the real roots of the
+        ++ polynomial pol which lie in the interval expressed by the
+        ++ record int.
+      refine: (Pol, Interval, RN) -> Interval
+        ++ refine(pol, int, eps) refines the interval int containing
+        ++ exactly one root of the univariate polynomial pol to size less
+        ++ than the rational number eps.
+      refine: (Pol, Interval, Interval) -> Union(Interval,"failed")
+        ++ refine(pol, int, range) takes a univariate polynomial pol and
+        ++ and isolating interval int which must contain exactly one real
+        ++ root of pol, and returns an isolating interval which
+        ++ is contained within range, or "failed" if no such isolating interval exists.
+   C == add
+      import RealZeroPackage SparseUnivariatePolynomial Integer
+ 
+      convert2PolInt: Pol -> SparseUnivariatePolynomial Integer
+ 
+      convert2PolInt(f : Pol) ==
+         pden:I :=lcm([denom c for c in coefficients f])
+         map(numer,pden * f)$UnivariatePolynomialCategoryFunctions2(RN,Pol,I,SUP I)
+ 
+      realZeros(f : Pol) == realZeros(convert2PolInt f)
+      realZeros(f : Pol, rn : RN) == realZeros(convert2PolInt f, rn)
+      realZeros(f : Pol, bounds : Interval) ==
+               realZeros(convert2PolInt f, bounds)
+      realZeros(f : Pol, bounds : Interval, rn : RN) ==
+               realZeros(convert2PolInt f, bounds, rn)
+      refine(f : Pol, int : Interval, eps : RN) ==
+               refine(convert2PolInt f, int, eps)
+      refine(f : Pol, int : Interval, bounds : Interval) ==
+               refine(convert2PolInt f, int, bounds)
+
+@
+\section{License}
+<<license>>=
+--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
+--All rights reserved.
+--
+--Redistribution and use in source and binary forms, with or without
+--modification, are permitted provided that the following conditions are
+--met:
+--
+--    - Redistributions of source code must retain the above copyright
+--      notice, this list of conditions and the following disclaimer.
+--
+--    - Redistributions in binary form must reproduce the above copyright
+--      notice, this list of conditions and the following disclaimer in
+--      the documentation and/or other materials provided with the
+--      distribution.
+--
+--    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
+--      names of its contributors may be used to endorse or promote products
+--      derived from this software without specific prior written permission.
+--
+--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
+--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+@
+<<*>>=
+<<license>>
+ 
+<<package REAL0Q RealZeroPackageQ>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}