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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra cden.spad}
+\author{Manuel Bronstein}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package ICDEN InnerCommonDenominator}
+<<package ICDEN InnerCommonDenominator>>=
+)abbrev package ICDEN InnerCommonDenominator
+--% InnerCommonDenominator
+++ Author: Manuel Bronstein
+++ Date Created: 2 May 1988
+++ Date Last Updated: 22 Nov 1989
+++ Description: InnerCommonDenominator provides functions to compute
+++ the common denominator of a finite linear aggregate of elements
+++ of the quotient field of an integral domain.
+++ Keywords: gcd, quotient, common, denominator.
+InnerCommonDenominator(R, Q, A, B): Exports == Implementation where
+  R: IntegralDomain
+  Q: QuotientFieldCategory R
+  A: FiniteLinearAggregate R
+  B: FiniteLinearAggregate Q
+ 
+  Exports ==> with
+    commonDenominator: B -> R 
+      ++ commonDenominator([q1,...,qn]) returns a common denominator
+      ++ d for q1,...,qn.
+    clearDenominator : B -> A 
+      ++ clearDenominator([q1,...,qn]) returns \spad{[p1,...,pn]} such that
+      ++ \spad{qi = pi/d} where d is a common denominator for the qi's.
+    splitDenominator : B -> Record(num: A, den: R)
+      ++ splitDenominator([q1,...,qn]) returns
+      ++ \spad{[[p1,...,pn], d]} such that
+      ++ \spad{qi = pi/d} and d is a common denominator for the qi's.
+ 
+  Implementation ==> add
+    import FiniteLinearAggregateFunctions2(Q, B, R, A)
+ 
+    clearDenominator l ==
+      d := commonDenominator l
+      map(numer(d * #1), l)
+ 
+    splitDenominator l ==
+      d := commonDenominator l
+      [map(numer(d * #1), l), d]
+ 
+    if R has GcdDomain then
+      commonDenominator l == reduce(lcm, map(denom, l),1)
+    else
+      commonDenominator l == reduce("*", map(denom, l), 1)
+
+@
+\section{package CDEN CommonDenominator}
+<<package CDEN CommonDenominator>>=
+)abbrev package CDEN CommonDenominator
+--% CommonDenominator
+++ Author: Manuel Bronstein
+++ Date Created: 2 May 1988
+++ Date Last Updated: 22 Nov 1989
+++ Description: CommonDenominator provides functions to compute the
+++ common denominator of a finite linear aggregate of elements of
+++ the quotient field of an integral domain.
+++ Keywords: gcd, quotient, common, denominator.
+CommonDenominator(R, Q, A): Exports == Implementation where
+  R: IntegralDomain
+  Q: QuotientFieldCategory R
+  A: FiniteLinearAggregate Q
+ 
+  Exports ==> with
+    commonDenominator: A -> R
+      ++ commonDenominator([q1,...,qn]) returns a common denominator
+      ++ d for q1,...,qn.
+    clearDenominator : A -> A
+      ++ clearDenominator([q1,...,qn]) returns \spad{[p1,...,pn]} such that
+      ++ \spad{qi = pi/d} where d is a common denominator for the qi's.
+    splitDenominator : A -> Record(num: A, den: R)
+      ++ splitDenominator([q1,...,qn]) returns
+      ++ \spad{[[p1,...,pn], d]} such that
+      ++ \spad{qi = pi/d} and d is a common denominator for the qi's.
+ 
+  Implementation ==> add
+    clearDenominator l ==
+      d := commonDenominator l
+      map(numer(d * #1)::Q, l)
+ 
+    splitDenominator l ==
+      d := commonDenominator l
+      [map(numer(d * #1)::Q, l), d]
+ 
+    if R has GcdDomain then
+      qlcm: (Q, Q) -> Q
+ 
+      qlcm(a, b)          == lcm(numer a, numer b)::Q
+      commonDenominator l == numer reduce(qlcm, map(denom(#1)::Q, l), 1)
+    else
+      commonDenominator l == numer reduce("*", map(denom(#1)::Q, l), 1)
+
+@
+\section{package UPCDEN UnivariatePolynomialCommonDenominator}
+<<package UPCDEN UnivariatePolynomialCommonDenominator>>=
+)abbrev package UPCDEN UnivariatePolynomialCommonDenominator
+--% UnivariatePolynomialCommonDenominator
+++ Author: Manuel Bronstein
+++ Date Created: 2 May 1988
+++ Date Last Updated: 22 Feb 1990
+++ Description: UnivariatePolynomialCommonDenominator provides
+++ functions to compute the common denominator of the coefficients of
+++ univariate polynomials over the quotient field of a gcd domain.
+++ Keywords: gcd, quotient, common, denominator, polynomial.
+ 
+UnivariatePolynomialCommonDenominator(R, Q, UP): Exports == Impl where
+  R : IntegralDomain
+  Q : QuotientFieldCategory R
+  UP: UnivariatePolynomialCategory Q
+ 
+  Exports ==> with
+    commonDenominator: UP -> R
+      ++ commonDenominator(q) returns a common denominator d for
+      ++ the coefficients of q.
+    clearDenominator : UP -> UP
+      ++ clearDenominator(q) returns p such that \spad{q = p/d} where d is
+      ++ a common denominator for the coefficients of q.
+    splitDenominator : UP -> Record(num: UP, den: R)
+      ++ splitDenominator(q) returns \spad{[p, d]} such that \spad{q = p/d} and d
+      ++ is a common denominator for the coefficients of q.
+ 
+  Impl ==> add
+    import CommonDenominator(R, Q, List Q)
+ 
+    commonDenominator p == commonDenominator coefficients p
+ 
+    clearDenominator p ==
+      d := commonDenominator p
+      map(numer(d * #1)::Q, p)
+ 
+    splitDenominator p ==
+      d := commonDenominator p
+      [map(numer(d * #1)::Q, p), d]
+
+@
+\section{package MCDEN MatrixCommonDenominator}
+<<package MCDEN MatrixCommonDenominator>>=
+)abbrev package MCDEN MatrixCommonDenominator
+--% MatrixCommonDenominator
+++ Author: Manuel Bronstein
+++ Date Created: 2 May 1988
+++ Date Last Updated: 20 Jul 1990
+++ Description: MatrixCommonDenominator provides functions to
+++ compute the common denominator of a matrix of elements of the
+++ quotient field of an integral domain.
+++ Keywords: gcd, quotient, matrix, common, denominator.
+MatrixCommonDenominator(R, Q): Exports == Implementation where
+  R: IntegralDomain
+  Q: QuotientFieldCategory R
+ 
+  VR ==> Vector R
+  VQ ==> Vector Q
+ 
+  Exports ==> with
+    commonDenominator: Matrix Q -> R
+      ++ commonDenominator(q) returns a common denominator d for
+      ++ the elements of q.
+    clearDenominator : Matrix Q -> Matrix R
+      ++ clearDenominator(q) returns p such that \spad{q = p/d} where d is
+      ++ a common denominator for the elements of q.
+    splitDenominator : Matrix Q -> Record(num: Matrix R, den: R)
+      ++ splitDenominator(q) returns \spad{[p, d]} such that \spad{q = p/d} and d
+      ++ is a common denominator for the elements of q.
+ 
+  Implementation ==> add
+    import ListFunctions2(Q, R)
+    import MatrixCategoryFunctions2(Q,VQ,VQ,Matrix Q,R,VR,VR,Matrix R)
+ 
+    clearDenominator m ==
+      d := commonDenominator m
+      map(numer(d * #1), m)
+ 
+    splitDenominator m ==
+      d := commonDenominator m
+      [map(numer(d * #1), m), d]
+ 
+    if R has GcdDomain then
+      commonDenominator m == lcm map(denom, parts m)
+    else
+      commonDenominator m == reduce("*",map(denom, parts m),1)$List(R)
+
+@
+\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 ICDEN InnerCommonDenominator>>
+<<package CDEN CommonDenominator>>
+<<package UPCDEN UnivariatePolynomialCommonDenominator>>
+<<package MCDEN MatrixCommonDenominator>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}