\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input allfact.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
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\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}
