From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Tue, 14 Aug 2007 05:14:52 +0000
Subject: Initial population.

---
 src/input/realclos.input.pamphlet | 67 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 67 insertions(+)
 create mode 100644 src/input/realclos.input.pamphlet

(limited to 'src/input/realclos.input.pamphlet')

diff --git a/src/input/realclos.input.pamphlet b/src/input/realclos.input.pamphlet
new file mode 100644
index 00000000..e56da691
--- /dev/null
+++ b/src/input/realclos.input.pamphlet
@@ -0,0 +1,67 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input realclos.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+<<*>>=
+)clear all
+
+-- computing without a table manipulation when creating objects
+Ran := RECLOS(FRAC INT)
+-- Some simple signs for square roots, these correspond to an extension
+-- of degree 16 of the rational numbers.
+
+fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran ==
+           sqrt(a)+sqrt(b) - sqrt(c)-sqrt(d)
+
+
+
+squareDiff := fourSquares(73,548,60,586)
+recip(squareDiff)
+sign(squareDiff)
+squareDiff := fourSquares(165,778,86,990)
+recip(squareDiff)
+sign(squareDiff)
+squareDiff := fourSquares(217,708,226,692)
+recip(squareDiff)
+sign(squareDiff)
+squareDiff := fourSquares(155,836,162,820) 
+recip(squareDiff)
+sign(squareDiff)
+squareDiff := fourSquares(591,772,552,818)
+recip(squareDiff)
+sign(squareDiff)
+squareDiff := fourSquares(434,1053,412,1088)
+recip(squareDiff)
+sign(squareDiff)
+squareDiff := fourSquares(514,1049,446,1152)
+recip(squareDiff)
+sign(squareDiff)
+
+squareDiff := fourSquares(190,1751,208,1698)
+recip(squareDiff)
+sign(squareDiff)
+)cl prop s2 s5 s10 l
+
+-- a more complicated test that involve an extension of degree 256
+(s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran);
+sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)
+%::Boolean
+
+-- the sum of these 4 numbers is 0
+l := allRootsOf((x^2-2)^2-2)$Ran
+l.1+l.2+l.3+l.4
+
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
-- 
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