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Diffstat (limited to 'src/hyper/pages/ROMAN.ht')
| -rw-r--r-- | src/hyper/pages/ROMAN.ht | 84 |
1 files changed, 84 insertions, 0 deletions
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} +% |