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/ROMAN.ht | 84 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 84 insertions(+)
 create mode 100644 src/hyper/pages/ROMAN.ht

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

diff --git a/src/hyper/pages/ROMAN.ht b/src/hyper/pages/ROMAN.ht
new file mode 100644
index 00000000..44c58a64
--- /dev/null
+++ b/src/hyper/pages/ROMAN.ht
@@ -0,0 +1,84 @@
+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\RomanNumeralXmpTitle}{RomanNumeral}
+\newcommand{\RomanNumeralXmpNumber}{9.68}
+%
+% =====================================================================
+\begin{page}{RomanNumeralXmpPage}{9.68 RomanNumeral}
+% =====================================================================
+\beginscroll
+
+The Roman numeral package was added to \Language{} in MCMLXXXVI
+%-% \HDindex{Roman numerals}{RomanNumeralXmpPage}{9.68}{RomanNumeral}
+for use in denoting higher order derivatives.
+
+\xtc{
+For example, let \spad{f} be a symbolic operator.
+}{
+\spadpaste{f := operator 'f \bound{f}}
+}
+\xtc{
+This is the seventh derivative of \spad{f} with respect to \spad{x}.
+}{
+\spadpaste{D(f x,x,7) \free{f}}
+}
+\xtc{
+You can have integers printed as Roman numerals by declaring variables to
+be of type \spadtype{RomanNumeral} (abbreviation \spadtype{ROMAN}).
+}{
+\spadpaste{a := roman(1978 - 1965) \bound{a}}
+}
+
+This package now has a small but devoted group of followers that claim
+this domain has shown its efficacy in many other contexts.
+They claim that Roman numerals are every bit as useful as ordinary
+integers.
+\xtc{
+In a sense, they are correct, because Roman numerals form a ring and you
+can therefore construct polynomials with Roman numeral coefficients,
+matrices over Roman numerals, etc..
+}{
+\spadpaste{x : UTS(ROMAN,'x,0) := x \bound{x}}
+}
+\xtc{
+Was Fibonacci Italian or ROMAN?
+%-% \HDindex{Fibonacci numbers}{RomanNumeralXmpPage}{9.68}{RomanNumeral}
+}{
+\spadpaste{recip(1 - x - x**2) \free{x}}
+}
+\xtc{
+You can also construct fractions with Roman numeral numerators and
+denominators, as this matrix Hilberticus illustrates.
+}{
+\spadpaste{m : MATRIX FRAC ROMAN \bound{m}}
+}
+\xtc{
+}{
+\spadpaste{m := matrix [[1/(i + j) for i in 1..3] for j in 1..3] \free{m} \bound{m1}}
+}
+\xtc{
+Note that the inverse of the matrix has integral \spadtype{ROMAN} entries.
+}{
+\spadpaste{inverse m \free{m1}}
+}
+\xtc{
+Unfortunately, the spoil-sports say that the fun stops when
+the numbers get big---mostly
+because the Romans didn't establish conventions about representing
+very large numbers.
+}{
+\spadpaste{y := factorial 10 \bound{y}}
+}
+\xtc{
+You work it out!
+}{
+\spadpaste{roman y \free{y}}
+}
+Issue the system command
+\spadcmd{)show RomanNumeral}
+to display the full list of operations defined by
+\spadtype{RomanNumeral}.
+\endscroll
+\autobuttons
+\end{page}
+%
-- 
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