roman - Maple Help

convert/roman

convert positive integers to Roman numerals

 Calling Sequence convert(n, roman, opts)

Parameters

 n - positive integer opts - (optional) equation(s) of the form option=value where option is one of large, period, or symbol; specify options for the conversion

Description

 • The convert(n, roman) function converts the positive integer n to the Roman numeral represented as a string.
 • The following table gives the Roman letters representing various integers.

 Letter Value I 1 V 5 X 10 L 50 C 100 D 500 M 1000

 • Give a value $N$ where $N$ is a power of 10. To write the value for either $2N$, $3N$, or $4N$, repeat the Roman numeral for $N$ either $2$, $3$, or $4$ times. For example, $2$, $30$, $400$ can be represented by II, XXX and CCCC, respectively.
 • Give a value $N$ where $N$ is a power of 10. To write the value for either $6N$, $7N$, $8N$, or $9N$, write the Roman numeral for $5N$ followed by the Roman numeral for $N$ either $1$, $2$, $3$, or $4$ times. For example, $6$, $70$, $900$ are represented by VI, LXX, and DCCCC, respectively.
 • There is a modification to writing Roman numerals for numbers that are a power of $10$ multiplied by $4$ or $9$. The Roman numeral for $4N$ or $9N$ is written as $N$ followed by the Roman numeral for $5N$ or $10N$, respectively. For example, $4$, $9$, $40$, and $900$ can be represented by IV, IX, XL, and CM, respectively.  This modification was introduced near the end of the Republic.
 • All other numbers are created by taking these multiples and placing them together with the largest value on the left and smallest value on the right.  For example, $1527$ is the sum of $1000$, $500$, $20$, and $7$, which are represented by M, D, XX, and VII, forming MDXXVII.
 Originally, the Roman numerals for $500$ and $1000$ were represented as I9 and CI9 where the $9$ is used in place of a backwards C, or apostrophus.  Further multiples of 10 were denoted by adding an extra apostrophus for multiples of $500$ and surrounding CI9 by another C and 9 pair.  The following table gives these values up to one million:

 Value Historic Roman Number 500 I9 1000 CI9 5000 I99 10 000 CCI99 50 000 I999 100 000 CCCI999

 Values greater than $100000$ have not been observed historically.
 Over time, the I9 was simplified to D and the CI9 was replaced by an M.  With this new format, the logarithmic method of denoting larger numbers was lost. To denote values like $12000$, it was necessary to use MMMMMMMMMMMM.
 To solve this problem, drawing a horizontal line (or vinculum, titulus) over V, X, L, and C indicates a multiple of $1000$ of these numbers. Thus, 97607 would be written as:

 ___ XCVMMDCVII

 There is no historical evidence that a further multiple of $1000$ could be indicated by a second line.
 The values $500000$ and $1000000$ were represented by Q (from quingenta milia) and a box around the letter X (for decies centena milia, or 10 hundred thousand), respectively.  There is no historical evidence that a C surrounded by a box is intended to represent $10000000$.
 Other unsupported formats are:
 1 Using a C instead of an apostrophus, for example, IC and CIC for $500$ and $1000$, respectively.
 2 Using an infinity or a capital Phi symbol for $1000$.
 3 Writing multiples of $1000$ by prefixing an M by the multiple, for example, $7000$ would be VII M.
 4 Using subtractive notation while using apostrophi, but this would require spacing to avoid confusion, for example, C I9 is $400$ but CI9 is $1000$.
 5 Using double subtraction, for example, IIX and CCM instead of VIII and DCCC to represent $8$ and $800$, respectively.
 • You can modify the properties of the conversion by including options opts. The opts argument can contain one or more of the following equations.
 period = early, middle, or late
 In early times, all values were displayed using the additive format.  In the transition, it was still common to use the additive format for values $4$ and $9$ but the subtractive format for larger values. In the late period, almost all numbers were written using the subtractive format exclusively.  Clock faces (using IIII for $4$ is one exception.)
 large = apostrophus or repeated
 By default, large numbers are created by repeating an M sufficiently many times.  If this option is set to apostrophus, the older version using CI9 to represent $1000$ is used.  For ease of reading, values greater than $100$ are separated by spaces.
 symbol = truefalse
 The default output is a string.  If the option symbol is set to true, then the result is a symbol.

Examples

 > $\mathrm{convert}\left(2849,\mathrm{roman}\right)$
 ${"MMDCCCXLIX"}$ (1)
 > $\mathrm{convert}\left(2849,\mathrm{roman},\mathrm{period}=\mathrm{early},\mathrm{symbol}\right)$
 ${\mathrm{MMDCCCXXXXVIIII}}$ (2)
 > $\mathrm{convert}\left(35034,\mathrm{roman},\mathrm{large}=\mathrm{apostrophus}\right)$
 ${"CCI99 CCI99 CCI99 I99 XXXIV"}$ (3)
 > $\mathrm{plots}\left[\mathrm{listplot}\right]\left(\left[\mathrm{seq}\left(\mathrm{length}\left(\mathrm{convert}\left(i,\mathrm{roman},\mathrm{large}=\mathrm{apostrophus}\right)\right),i=1..2400\right)\right]\right)$
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