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## 9.68 RomanNumeral

The Roman numeral package was added to Axiom in MCMLXXXVI for use in denoting higher order derivatives.

For example, let f be a symbolic operator.

f := operator 'f

f

Type: BasicOperator

This is the seventh derivative of f with respect to x.

D(f x,x,7)

f(vii)(x)

Type: Expression Integer

You can have integers printed as Roman numerals by declaring variables to be of type RomanNumeral (abbreviation ROMAN).

a := roman(1978 - 1965)

XIII

Type: RomanNumeral

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.

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..

x : UTS(ROMAN,'x,0) := x

x

Type: UnivariateTaylorSeries(RomanNumeral,x,0)

Was Fibonacci Italian or ROMAN?

recip(1 - x - x**2)

I+x+II x 2+III x 3+V x 4+VIII x 5+XIII x 6+XXI x 7+XXXIV x 8+LV x 9+LXXXIX x 10+O(x 11)

Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...)

You can also construct fractions with Roman numeral numerators and denominators, as this matrix Hilberticus illustrates.

m : MATRIX FRAC ROMAN
Void
m := matrix [ [1/(i + j) for i in 1..3] for j in 1..3]

[I II I III I IV I III I IV I V I IV I V I VI]

Type: Matrix Fraction RomanNumeral

Note that the inverse of the matrix has integral ROMAN entries.

inverse m

[LXXII-CCXL CLXXX-CCXL CM-DCCXX CLXXX-DCCXX DC]

Type: Union(Matrix Fraction RomanNumeral,...)

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.

y := factorial 10

3628800

Type: PositiveInteger

You work it out!

roman y

((((I))))((((I))))((((I))))(((I)))(((I)))(((I)))(((I)))(((I)))(((I)))((I))((I))MMMMMMMMDCCC

Type: RomanNumeral

Issue the system command )show RomanNumeral to display the full list of operations defined by RomanNumeral.

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