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/hyper/pages/HEXADEC.ht | 59 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 src/hyper/pages/HEXADEC.ht

(limited to 'src/hyper/pages/HEXADEC.ht')

diff --git a/src/hyper/pages/HEXADEC.ht b/src/hyper/pages/HEXADEC.ht
new file mode 100644
index 00000000..e807f91f
--- /dev/null
+++ b/src/hyper/pages/HEXADEC.ht
@@ -0,0 +1,59 @@
+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\HexadecimalExpansionXmpTitle}{HexadecimalExpansion}
+\newcommand{\HexadecimalExpansionXmpNumber}{9.33}
+%
+% =====================================================================
+\begin{page}{HexadecimalExpansionXmpPage}{9.33 HexadecimalExpansion}
+% =====================================================================
+\beginscroll
+
+All rationals have repeating hexadecimal expansions.
+The operation \spadfunFrom{hex}{HexadecimalExpansion} returns these
+expansions of type \spadtype{HexadecimalExpansion}.
+Operations to access the individual numerals of a hexadecimal expansion can
+be obtained by converting the value to \spadtype{RadixExpansion(16)}.
+More examples of expansions are available in the
+\downlink{`DecimalExpansion'}{DecimalExpansionXmpPage}\ignore{DecimalExpansion},
+\downlink{`BinaryExpansion'}{BinaryExpansionXmpPage}\ignore{BinaryExpansion}, and
+\downlink{`RadixExpansion'}{RadixExpansionXmpPage}\ignore{RadixExpansion}.
+
+\showBlurb{HexadecimalExpansion}
+
+\xtc{
+This is a hexadecimal expansion of a rational number.
+}{
+\spadpaste{r := hex(22/7) \bound{r}}
+}
+\xtc{
+Arithmetic is exact.
+}{
+\spadpaste{r + hex(6/7) \free{r}}
+}
+\xtc{
+The period of the expansion can be short or long \ldots
+}{
+\spadpaste{[hex(1/i) for i in 350..354] }
+}
+\xtc{
+or very long!
+}{
+\spadpaste{hex(1/1007) }
+}
+\xtc{
+These numbers are bona fide algebraic objects.
+}{
+\spadpaste{p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)  \bound{p}}
+}
+\xtc{
+}{
+\spadpaste{q := D(p, x) \free{p}\bound{q}}
+}
+\xtc{
+}{
+\spadpaste{g := gcd(p, q)            \free{p}\free{q}}
+}
+\endscroll
+\autobuttons
+\end{page}
+%
-- 
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