Proposal: Extended Roman Numerals: Difference between revisions

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== Introduction ==
== 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 "<u>I</u>" (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 <math> 5*(10^n) </math>, for some <math> n \in \mathbb{N} </math>, may not be used consecutively (in a nontrivial manner: more than once).
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 <math>A = \{1, 5, 10, 50, 100, 500, 1000\} </math> (in decimal notation) and, in a minor extension, <math>1000*A </math>. "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 "<u>I</u>" (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 <math> 5*(10^n) </math>, for some <math> n \in \mathbb{N} </math>, may not be used consecutively (in a nontrivial manner: more than once).
 
We will call <math>A</math> the set of basic Roman numbers (or "Basics" for short); it will be notated as such throughout this article. The set of symbols (digits) which represent the elements of <math>A</math> bijectively is called the set of basic digits and will be notated, perhaps somewhat ironically, <math>\Lambda</math>. The set of digits which represent the elements of <math>1000*A</math> will be called the set of millials (short: millials); it will be notated as <math>\underline{\Lambda}</math>.


== Goal ==
== Goal ==

Revision as of 09:46, 16 September 2016

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 (in decimal notation) and, in a minor extension, . "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).

We will call the set of basic Roman numbers (or "Basics" for short); it will be notated as such throughout this article. The set of symbols (digits) which represent the elements of bijectively is called the set of basic digits and will be notated, perhaps somewhat ironically, . The set of digits which represent the elements of will be called the set of millials (short: millials); it will be notated as .

Goal

  • Preserve the feel and system of modern Roman numerals.
  • Be unambiguous.
  • Extend the system so that it can express any integer.
  • Possibly: Allow for multiple ways to express the same number
  • Possibly: Be able to represent fractions in a 'Roman' way.

Activation of Various Modes

Macrodigits

Representing the Numeric Alphabet in Lojban

Use of "pi'e"

Zero

Negatives