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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input allfact.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1991.
+@
+<<*>>=
+<<license>>
+
+)cl all
+
+--  Examples of all the factor functions in the system.
+
+-- factorization of integer numbers
+n:=45234258258293
+factor n
+
+-- factorization of gaussian integers
+m:(Complex Integer) := 1324567+%i*53523582
+factor m
+
+-- factorization of polynomials over finite fields
+u:UP(x,PF(19)) :=3*x**4+2*x**2+15*x+18
+factor u
+
+-- factorization of polynomials over the integers
+v:UP(x,INT):= (4*x**3+2*x**2+1)*(12*x**5-x**3+12)
+factor v
+
+-- factorization of multivariate polynomial over the integers
+w:MPOLY([x,y,z],INT) :=(x**2-y**2-z**2)*(x**2+y**2+z**2)*(z*y+3*z)
+factor w
+
+-- factorization of univariate and multivariate over the rational numbers
+f:MPOLY([x,y,z],FRAC INT) :=(4/9*x**2-1/16)*(x**3/27+125)
+factor f
+
+-- factorization over rational functions
+g:DMP([x,y],FRAC POLY INT):=a**2*x**2/b**2 -c**2*y**2/d**2
+factor g
+
+-- decomposition of a rational function
+r:FRAC POLY INT:= (a**3/b**3-c**3/(b+1)**3)*(a*d+a/c)
+factorFraction r
+
+-- factorization over simple algebraic extensions
+aa|aa**2+aa+1
+p:UP(x,SAEaa) :=(x**3+aa**2*x+1)*(aa*x**2+aa*x+aa)**2
+factor(p)$SAEFACT(UP('aa,FRAC INT),SAEaa,UP(x,SAEaa))
+
+-- factorization over algebraic numbers
+a:=rootOf(a**2+3)$AN
+factor(x**2+x+1,[a])
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}