{ "info": { "author": "Electrostatus", "author_email": "", "bugtrack_url": null, "classifiers": [ "Development Status :: 3 - Alpha", "Natural Language :: English", "Operating System :: OS Independent", "Programming Language :: Python :: 2", "Programming Language :: Python :: 3" ], "description": "numsys\r\n======\r\nnumeral system conversion module; converts values from one number base to another\r\n\r\nAny real or complex number can be converted to/from a base of any real or imaginary value\r\n\r\nStandard\r\n--------\r\nrepresentation in a positional numeral system (base ten, base sixty)\r\n\r\nNumber 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.\r\n\r\nNon-standard\r\n------------\r\nrepresentation in a non-positional numeral system (roman, factorial)\r\n\r\nA 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.\r\n\r\nDigits\r\n------\r\nThe 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).\r\n\r\n\r\nReferences\r\n----------\r\npositive real base conversion: (`Ref. A`_) A. R\u00e9nyi, \"Representations for real numbers and their ergodic properties\", *Acta Mathematica Academic Sci. Hungar.*, **1957**, vol. 8, pp. 433-493\r\n\r\nnegative real base conversion: (`Ref. B`_) S. Ito, T. Sadahiro, \"Beta-expansions with negative bases\", *Integers*, **2009**, vol. 9, pp. 239-259\r\n\r\nbase 2i: (`Ref. C`_) D. Knuth, \"An Imaginary Number System\", *Communications of the ACM*, **1960**, vol. 3, pp. 245-247\r\n\r\nbase -10: (Ref. D) V. Gr\u00fcnwald, \"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\r\n\r\nimaginary base conversion/summary: (`Ref. E`_) P. Herd, \"Imaginary Number Bases\"\r\n\r\n\r\n.. _`Ref. A`: https://doi.org/10.1007/BF02020331\r\n.. _`Ref. B`: https://doi.org/10.1515/INTEG.2009.023\r\n.. _`Ref. C`: https://doi.org/10.1145/367177.367233\r\n.. _`Ref. 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