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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra ratfact.spad}
+\author{Patrizia Gianni}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package RATFACT RationalFactorize}
+<<package RATFACT RationalFactorize>>=
+)abbrev package RATFACT RationalFactorize
+++ Author: P. Gianni
+++ Date created: ??
+++ Date last updated: December 1993
+++ Factorization of extended polynomials with rational coefficients.
+++ This package implements factorization of extended polynomials
+++ whose coefficients are rational numbers. It does this by taking the
+++ lcm of the coefficients of the polynomial and creating a polynomial
+++ with integer coefficients. The algorithm in \spadtype{GaloisGroupFactorizer} is then
+++ used to factor the integer polynomial. The result is normalized
+++ with respect to the original lcm of the denominators.
+++ Keywords: factorization, hensel, rational number
+I  ==> Integer
+RN ==> Fraction Integer
+ 
+RationalFactorize(RP) : public == private where
+  BP ==> SparseUnivariatePolynomial(I)
+  RP : UnivariatePolynomialCategory RN
+ 
+  public   ==> with
+ 
+     factor           : RP ->  Factored RP
+      ++ factor(p) factors an extended polynomial p over the rational numbers.
+     factorSquareFree : RP -> Factored RP
+      ++ factorSquareFree(p) factors an extended squareFree 
+      ++ polynomial p over the rational numbers.
+
+  private  ==> add
+     import GaloisGroupFactorizer (BP)
+     ParFact   ==> Record(irr:BP,pow:I)
+     FinalFact ==> Record(contp:I,factors:List(ParFact))
+     URNI      ==> UnivariatePolynomialCategoryFunctions2(RN,RP,I,BP)
+     UIRN      ==> UnivariatePolynomialCategoryFunctions2(I,BP,RN,RP)
+     fUnion    ==> Union("nil", "sqfr", "irred", "prime")
+     FFE       ==> Record(flg:fUnion, fctr:RP, xpnt:I)
+ 
+     factor(p:RP) : Factored(RP) ==
+       p = 0 => 0
+       pden: I := lcm([denom c for c in coefficients p])
+       pol : RP := pden*p
+       ipol: BP := map(numer,pol)$URNI
+       ffact: FinalFact := henselFact(ipol,false)
+       makeFR(((ffact.contp)/pden)::RP,
+         [["prime",map(coerce,u.irr)$UIRN,u.pow]$FFE
+                             for u in ffact.factors])
+ 
+     factorSquareFree(p:RP) : Factored(RP) ==
+       p = 0 => 0
+       pden: I := lcm([denom c for c in coefficients p])
+       pol : RP := pden*p
+       ipol: BP := map(numer,pol)$URNI
+       ffact: FinalFact := henselFact(ipol,true)
+       makeFR(((ffact.contp)/pden)::RP,
+         [["prime",map(coerce,u.irr)$UIRN,u.pow]$FFE
+                             for u in ffact.factors])
+
+@
+\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 RATFACT RationalFactorize>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}