numeral systems - number base conversion module

## Project description

numeral system conversion module; converts values from one number base to another

Any real or complex number can be converted to/from a base of any real or imaginary value

## Standard

representation in a positional numeral system (base ten, base sixty)

Number bases here are integers (2, 3, 10, …), negatives, (-2, -10, -25, …), reals (1.5, 3.14159, -2.71828, …) or imaginary (2i, -4.5i, 6i, …). Additionally, inverted values (0.5, -0.36788, 0.001, …) are allowed in use as a base. Invalid values as a base are 0, 1 and any value whose absolute value is 1.

## Non-standard

representation in a non-positional numeral system (roman, factorial)

A non-positional numeral system is one where values do not conform to the positional system. These can be alphabetic, like Roman numerals, or a mixed base system, like factorial. Also included are positional-like bases that have limited representation; not all values can be shown. Examples of these are base one and minus one.

## Digits

The first one hundred digits used (in order) are 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz!"#\$%&'()*+,-./:;<=>?@[\]^_`{|}~ \t\n\r\x0b\x0c. After this, which digits are used will be dependent on your system encoding. However, general order will be from the lowest Unicode plane to the highest (skipping already seen digits).

## References

positive real base conversion: (Ref. A) A. Rényi, “Representations for real numbers and their ergodic properties”, Acta Mathematica Academic Sci. Hungar., 1957, vol. 8, pp. 433-493

negative real base conversion: (Ref. B) S. Ito, T. Sadahiro, “Beta-expansions with negative bases”, Integers, 2009, vol. 9, pp. 239-259

base 2i: (Ref. C) D. Knuth, “An Imaginary Number System”, Communications of the ACM, 1960, vol. 3, pp. 245-247

base -10: (Ref. D) V. Grünwald, “Intorno all’aritmetica dei sistemi numerici a base negativa con particolare riguardo al sistema numerico a base negativo-decimale per lo studio delle sue analogie coll’aritmetica ordinaria (decimale)”, Giornale di matematiche di Battaglini, 1885, vol. 23, pp. 203-221

imaginary base conversion/summary: (Ref. E) P. Herd, “Imaginary Number Bases”