Proposal: Extended Roman Numerals

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This is a proposal for how to express Roman numerals in Lojban.

Introduction

Modern Roman numerals rely on a multi-pivot positionally-balanced additive system. Strings are read from left to right. There is an alphabet of symbols which represent the various elements of A = {1, 5, 10, 50, 100, 500, 1000} (in decimal notation) and, in a minor extension, 1000*A. "I" represents 1; "V" represents 5; "X" represents 10 (ten); "L" represents 50 (fifty); "C" represents 100 (one hundred); "D" represents 500 (five hundred); "M" represents 1000 (one thousand); underlined versions of these symbols represent the product of the value represented by the corresponding non-underlined symbol as multiplied by one thousand (and "I" (for one thousand) is not used). A string of symbols is broken into a concatenation of the maximal/longest substrings (here called "canonical substrings") such that the value of each symbol is not greater than the one previous (to its left) in the canonical substring. Id est: the symbols in a canonical substring are weakly monotonically decreasing. The value represented by a canonical substring is the sum of the values represented by each symbol composing it; canonical substrings expressed prior to/left of others have their value subtracted from the value represented by the later-expressed/right canonical substring. Typically in conventional modern notation, no symbol is repeated more than thrice consecutively; preference is given to reducing the number of canonical substrings in a given representation of a number, then reducing the length of each canonical substring, and then using symbols of smaller value (so, for example, three hundred is represented by "CCC", not "CCD"). Consequently, any symbol representing a value of , for some , may not be used consecutively (in a nontrivial manner: more than once).

Goal

  • Preserve the feel and system of modern Roman numerals.
  • Be unambiguous.
  • Extend the system so that it can express any integer.
  • Allow for multiple ways to express the same number

Activation of Various Modes

Macrodigits

Representing the Numeric Alphabet in Lojban

Use of "pi'e"

Zero

Negatives