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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/input/algfacob.input.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input algfacob.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1991.
+@
+<<*>>=
+<<license>>
+
+-- Examples used in Algebra document: ALGFACOB SCRIPT
+)set history on
+)clear all
+
+-- The Algebra of Factored Integers
+
+(w,x,y,z): FR INT
+x := 2**8 * 78**7 * 111**3 * 74534
+y := nilFactor(2,10) * nilFactor(3,20) * nilFactor(5,30)
+x*y
+w := x+y
+expand w
+f := x/y
+g := (x**9)/y
+f*g
+h := (f*g)/(g*nilFactor(2,200))
+)clear all
+
+-- The Algebra of Factored Polynomials
+
+(u,v,w) : FR POLY INT
+u := factor (x**4 - y**4)
+v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x**2 + y**2,1)
+w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * nilFactor(x-y,2)
+nthFactor(u,1)
+nthFactor(u,2)
+nthFactor(u,3)
+nthFactor(u,4)
+gcd(u,v)
+u + v
+lcm(u,v)
+u * v * w
+expand %
+u/w
+w/(u*v)
+%%(-1) * %%(-2)
+%%(-1) + %%(-2)
+)clear all
+
+-- Some Notes on Using Factored Objects
+
+f : FR INT := 144000
+nthFactor(f,1)
+nthExponent(f,1)
+nthFlag(f,1)
+nthFlag(nilFactor(20,4),1)
+nthFlag(primeFactor(7,9),1)
+factors f
+numberOfFactors f
+f
+reduce(*,[nthFactor(f,i) :: (FR INT) for i in 1..numberOfFactors(f)])
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}