class Mystic::ForteNumbers

• Mystic::ForteNumbers
• Reference
• Object

Overview

Table of prime forms and Forte numbers, retrieved from https://en.wikipedia.org/wiki/List_of_set_classes

Defined in:

mystic/forte_numbers.cr

Constant Summary

FORTE_TABLE = PRIME_TABLE.to_h.invert

Table of Forte Numbers => Prime Forms

PRIME_TABLE = {[] of Int32 => "0-1", [0] => "1-1", [0, 1] => "2-1", [0, 2] => "2-2", [0, 3] => "2-3", [0, 4] => "2-4", [0, 5] => "2-5", [0, 6] => "2-6", [0, 1, 2] => "3-1", [0, 3, 6] => "3-10", [0, 3, 7] => "3-11A", [0, 4, 7] => "3-11B", [0, 4, 8] => "3-12", [0, 1, 3] => "3-2A", [0, 2, 3] => "3-2B", [0, 1, 4] => "3-3A", [0, 3, 4] => "3-3B", [0, 1, 5] => "3-4A", [0, 4, 5] => "3-4B", [0, 1, 6] => "3-5A", [0, 5, 6] => "3-5B", [0, 2, 4] => "3-6", [0, 2, 5] => "3-7A", [0, 3, 5] => "3-7B", [0, 2, 6] => "3-8A", [0, 4, 6] => "3-8B", [0, 2, 7] => "3-9", [0, 1, 2, 3] => "4-1", [0, 2, 3, 5] => "4-10", [0, 1, 3, 5] => "4-11A", [0, 2, 4, 5] => "4-11B", [0, 2, 3, 6] => "4-12A", [0, 3, 4, 6] => "4-12B", [0, 1, 3, 6] => "4-13A", [0, 3, 5, 6] => "4-13B", [0, 2, 3, 7] => "4-14A", [0, 4, 5, 7] => "4-14B", [0, 1, 5, 7] => "4-16A", [0, 2, 6, 7] => "4-16B", [0, 3, 4, 7] => "4-17", [0, 1, 4, 7] => "4-18A", [0, 3, 6, 7] => "4-18B", [0, 1, 4, 8] => "4-19A", [0, 3, 4, 8] => "4-19B", [0, 1, 5, 8] => "4-20", [0, 2, 4, 6] => "4-21", [0, 2, 4, 7] => "4-22A", [0, 3, 5, 7] => "4-22B", [0, 2, 5, 7] => "4-23", [0, 2, 4, 8] => "4-24", [0, 2, 6, 8] => "4-25", [0, 3, 5, 8] => "4-26", [0, 2, 5, 8] => "4-27A", [0, 3, 6, 8] => "4-27B", [0, 3, 6, 9] => "4-28", [0, 1, 2, 4] => "4-2A", [0, 2, 3, 4] => "4-2B", [0, 1, 3, 4] => "4-3", [0, 1, 2, 5] => "4-4A", [0, 3, 4, 5] => "4-4B", [0, 1, 2, 6] => "4-5A", [0, 4, 5, 6] => "4-5B", [0, 1, 2, 7] => "4-6", [0, 1, 4, 5] => "4-7", [0, 1, 5, 6] => "4-8", [0, 1, 6, 7] => "4-9", [0, 1, 4, 6] => "4-z15A", [0, 2, 5, 6] => "4-z15B", [0, 1, 3, 7] => "4-z29A", [0, 4, 6, 7] => "4-z29B", [0, 1, 2, 3, 4] => "5-1", [0, 1, 3, 4, 6] => "5-10A", [0, 2, 3, 5, 6] => "5-10B", [0, 2, 3, 4, 7] => "5-11A", [0, 3, 4, 5, 7] => "5-11B", [0, 1, 2, 4, 8] => "5-13A", [0, 2, 3, 4, 8] => "5-13B", [0, 1, 2, 5, 7] => "5-14A", [0, 2, 5, 6, 7] => "5-14B", [0, 1, 2, 6, 8] => "5-15", [0, 1, 3, 4, 7] => "5-16A", [0, 3, 4, 6, 7] => "5-16B", [0, 1, 3, 6, 7] => "5-19A", [0, 1, 4, 6, 7] => "5-19B", [0, 1, 5, 6, 8] => "5-20A", [0, 2, 3, 7, 8] => "5-20B", [0, 1, 4, 5, 8] => "5-21A", [0, 3, 4, 7, 8] => "5-21B", [0, 1, 4, 7, 8] => "5-22", [0, 2, 3, 5, 7] => "5-23A", [0, 2, 4, 5, 7] => "5-23B", [0, 1, 3, 5, 7] => "5-24A", [0, 2, 4, 6, 7] => "5-24B", [0, 2, 3, 5, 8] => "5-25A", [0, 3, 5, 6, 8] => "5-25B", [0, 2, 4, 5, 8] => "5-26A", [0, 3, 4, 6, 8] => "5-26B", [0, 1, 3, 5, 8] => "5-27A", [0, 3, 5, 7, 8] => "5-27B", [0, 2, 3, 6, 8] => "5-28A", [0, 2, 5, 6, 8] => "5-28B", [0, 1, 3, 6, 8] => "5-29A", [0, 2, 5, 7, 8] => "5-29B", [0, 1, 2, 3, 5] => "5-2A", [0, 2, 3, 4, 5] => "5-2B", [0, 1, 4, 6, 8] => "5-30A", [0, 2, 4, 7, 8] => "5-30B", [0, 1, 3, 6, 9] => "5-31A", [0, 2, 3, 6, 9] => "5-31B", [0, 1, 4, 6, 9] => "5-32A", [0, 2, 5, 6, 9] => "5-32B", [0, 2, 4, 6, 8] => "5-33", [0, 2, 4, 6, 9] => "5-34", [0, 2, 4, 7, 9] => "5-35", [0, 1, 2, 4, 5] => "5-3A", [0, 1, 3, 4, 5] => "5-3B", [0, 1, 2, 3, 6] => "5-4A", [0, 3, 4, 5, 6] => "5-4B", [0, 1, 2, 3, 7] => "5-5A", [0, 4, 5, 6, 7] => "5-5B", [0, 1, 2, 5, 6] => "5-6A", [0, 1, 4, 5, 6] => "5-6B", [0, 1, 2, 6, 7] => "5-7A", [0, 1, 5, 6, 7] => "5-7B", [0, 2, 3, 4, 6] => "5-8", [0, 1, 2, 4, 6] => "5-9A", [0, 2, 4, 5, 6] => "5-9B", [0, 1, 3, 5, 6] => "5-z12", [0, 1, 3, 4, 8] => "5-z17", [0, 1, 4, 5, 7] => "5-z18A", [0, 2, 3, 6, 7] => "5-z18B", [0, 1, 2, 4, 7] => "5-z36A", [0, 3, 5, 6, 7] => "5-z36B", [0, 3, 4, 5, 8] => "5-z37", [0, 1, 2, 5, 8] => "5-z38A", [0, 3, 6, 7, 8] => "5-z38B", [0, 1, 2, 3, 4, 5] => "6-1", [0, 1, 3, 4, 5, 8] => "6-14A", [0, 3, 4, 5, 7, 8] => "6-14B", [0, 1, 2, 4, 5, 8] => "6-15A", [0, 3, 4, 6, 7, 8] => "6-15B", [0, 1, 4, 5, 6, 8] => "6-16A", [0, 2, 3, 4, 7, 8] => "6-16B", [0, 1, 2, 5, 7, 8] => "6-18A", [0, 1, 3, 6, 7, 8] => "6-18B", [0, 1, 4, 5, 8, 9] => "6-20", [0, 2, 3, 4, 6, 8] => "6-21A", [0, 2, 4, 5, 6, 8] => "6-21B", [0, 1, 2, 4, 6, 8] => "6-22A", [0, 2, 4, 6, 7, 8] => "6-22B", [0, 1, 3, 4, 6, 9] => "6-27A", [0, 2, 3, 5, 6, 9] => "6-27B", [0, 1, 2, 3, 4, 6] => "6-2A", [0, 2, 3, 4, 5, 6] => "6-2B", [0, 1, 3, 6, 7, 9] => "6-30A", [0, 2, 3, 6, 8, 9] => "6-30B", [0, 1, 4, 5, 7, 9] => "6-31A", [0, 2, 4, 5, 8, 9] => "6-31B", [0, 2, 4, 5, 7, 9] => "6-32", [0, 2, 3, 5, 7, 9] => "6-33A", [0, 2, 4, 6, 7, 9] => "6-33B", [0, 1, 3, 5, 7, 9] => "6-34A", [0, 2, 4, 6, 8, 9] => "6-34B", [0, 2, 4, 6, 8, 10] => "6-35", [0, 1, 2, 3, 6, 7] => "6-5A", [0, 1, 4, 5, 6, 7] => "6-5B", [0, 1, 2, 6, 7, 8] => "6-7", [0, 2, 3, 4, 5, 7] => "6-8", [0, 1, 2, 3, 5, 7] => "6-9A", [0, 2, 4, 5, 6, 7] => "6-9B", [0, 1, 3, 4, 5, 7] => "6-z10A", [0, 2, 3, 4, 6, 7] => "6-z10B", [0, 1, 2, 4, 5, 7] => "6-z11A", [0, 2, 3, 5, 6, 7] => "6-z11B", [0, 1, 2, 4, 6, 7] => "6-z12A", [0, 1, 3, 5, 6, 7] => "6-z12B", [0, 1, 3, 4, 6, 7] => "6-z13", [0, 1, 2, 4, 7, 8] => "6-z17A", [0, 1, 4, 6, 7, 8] => "6-z17B", [0, 1, 3, 4, 7, 8] => "6-z19A", [0, 1, 4, 5, 7, 8] => "6-z19B", [0, 2, 3, 5, 6, 8] => "6-z23", [0, 1, 3, 4, 6, 8] => "6-z24A", [0, 2, 4, 5, 7, 8] => "6-z24B", [0, 1, 3, 5, 6, 8] => "6-z25A", [0, 2, 3, 5, 7, 8] => "6-z25B", [0, 1, 3, 5, 7, 8] => "6-z26", [0, 1, 3, 5, 6, 9] => "6-z28", [0, 2, 3, 6, 7, 9] => "6-z29", [0, 1, 2, 3, 4, 7] => "6-z36A", [0, 3, 4, 5, 6, 7] => "6-z36B", [0, 1, 2, 3, 4, 8] => "6-z37", [0, 1, 2, 3, 7, 8] => "6-z38", [0, 2, 3, 4, 5, 8] => "6-z39A", [0, 3, 4, 5, 6, 8] => "6-z39B", [0, 1, 2, 3, 5, 6] => "6-z3A", [0, 1, 3, 4, 5, 6] => "6-z3B", [0, 1, 2, 4, 5, 6] => "6-z4", [0, 1, 2, 3, 5, 8] => "6-z40A", [0, 3, 5, 6, 7, 8] => "6-z40B", [0, 1, 2, 3, 6, 8] => "6-z41A", [0, 2, 5, 6, 7, 8] => "6-z41B", [0, 1, 2, 3, 6, 9] => "6-z42", [0, 1, 2, 5, 6, 8] => "6-z43A", [0, 2, 3, 6, 7, 8] => "6-z43B", [0, 1, 2, 5, 6, 9] => "6-z44A", [0, 1, 4, 5, 6, 9] => "6-z44B", [0, 2, 3, 4, 6, 9] => "6-z45", [0, 1, 2, 4, 6, 9] => "6-z46A", [0, 2, 4, 5, 6, 9] => "6-z46B", [0, 1, 2, 4, 7, 9] => "6-z47A", [0, 2, 3, 4, 7, 9] => "6-z47B", [0, 1, 2, 5, 7, 9] => "6-z48", [0, 1, 3, 4, 7, 9] => "6-z49", [0, 1, 4, 6, 7, 9] => "6-z50", [0, 1, 2, 5, 6, 7] => "6-z6", [0, 1, 2, 3, 4, 5, 6] => "7-1", [0, 1, 2, 3, 4, 6, 9] => "7-10A", [0, 2, 3, 4, 5, 6, 9] => "7-10B", [0, 1, 3, 4, 5, 6, 8] => "7-11A", [0, 2, 3, 4, 5, 7, 8] => "7-11B", [0, 1, 2, 4, 5, 6, 8] => "7-13A", [0, 2, 3, 4, 6, 7, 8] => "7-13B", [0, 1, 2, 3, 5, 7, 8] => "7-14A", [0, 1, 3, 5, 6, 7, 8] => "7-14B", [0, 1, 2, 4, 6, 7, 8] => "7-15", [0, 1, 2, 3, 5, 6, 9] => "7-16A", [0, 1, 3, 4, 5, 6, 9] => "7-16B", [0, 1, 2, 3, 6, 7, 9] => "7-19A", [0, 1, 2, 3, 6, 8, 9] => "7-19B", [0, 1, 2, 5, 6, 7, 9] => "7-20A", [0, 2, 3, 4, 7, 8, 9] => "7-20B", [0, 1, 2, 4, 5, 8, 9] => "7-21A", [0, 1, 3, 4, 5, 8, 9] => "7-21B", [0, 1, 2, 5, 6, 8, 9] => "7-22", [0, 2, 3, 4, 5, 7, 9] => "7-23A", [0, 2, 4, 5, 6, 7, 9] => "7-23B", [0, 1, 2, 3, 5, 7, 9] => "7-24A", [0, 2, 4, 6, 7, 8, 9] => "7-24B", [0, 2, 3, 4, 6, 7, 9] => "7-25A", [0, 2, 3, 5, 6, 7, 9] => "7-25B", [0, 1, 3, 4, 5, 7, 9] => "7-26A", [0, 2, 4, 5, 6, 8, 9] => "7-26B", [0, 1, 2, 4, 5, 7, 9] => "7-27A", [0, 2, 4, 5, 7, 8, 9] => "7-27B", [0, 1, 3, 5, 6, 7, 9] => "7-28A", [0, 2, 3, 4, 6, 8, 9] => "7-28B", [0, 1, 2, 4, 6, 7, 9] => "7-29A", [0, 2, 3, 5, 7, 8, 9] => "7-29B", [0, 1, 2, 3, 4, 5, 7] => "7-2A", [0, 2, 3, 4, 5, 6, 7] => "7-2B", [0, 1, 2, 4, 6, 8, 9] => "7-30A", [0, 1, 3, 5, 7, 8, 9] => "7-30B", [0, 1, 3, 4, 6, 7, 9] => "7-31A", [0, 2, 3, 5, 6, 8, 9] => "7-31B", [0, 1, 3, 4, 6, 8, 9] => "7-32A", [0, 1, 3, 5, 6, 8, 9] => "7-32B", [0, 1, 2, 4, 6, 8, 10] => "7-33", [0, 1, 3, 4, 6, 8, 10] => "7-34", [0, 1, 3, 5, 6, 8, 10] => "7-35", [0, 1, 2, 3, 4, 5, 8] => "7-3A", [0, 3, 4, 5, 6, 7, 8] => "7-3B", [0, 1, 2, 3, 4, 6, 7] => "7-4A", [0, 1, 3, 4, 5, 6, 7] => "7-4B", [0, 1, 2, 3, 5, 6, 7] => "7-5A", [0, 1, 2, 4, 5, 6, 7] => "7-5B", [0, 1, 2, 3, 4, 7, 8] => "7-6A", [0, 1, 4, 5, 6, 7, 8] => "7-6B", [0, 1, 2, 3, 6, 7, 8] => "7-7A", [0, 1, 2, 5, 6, 7, 8] => "7-7B", [0, 2, 3, 4, 5, 6, 8] => "7-8", [0, 1, 2, 3, 4, 6, 8] => "7-9A", [0, 2, 4, 5, 6, 7, 8] => "7-9B", [0, 1, 2, 3, 4, 7, 9] => "7-z12", [0, 1, 2, 4, 5, 6, 9] => "7-z17", [0, 1, 4, 5, 6, 7, 9] => "7-z18A", [0, 2, 3, 4, 5, 8, 9] => "7-z18B", [0, 1, 2, 3, 5, 6, 8] => "7-z36A", [0, 2, 3, 5, 6, 7, 8] => "7-z36B", [0, 1, 3, 4, 5, 7, 8] => "7-z37", [0, 1, 2, 4, 5, 7, 8] => "7-z38A", [0, 1, 3, 4, 6, 7, 8] => "7-z38B", [0, 1, 2, 3, 4, 5, 6, 7] => "8-1", [0, 2, 3, 4, 5, 6, 7, 9] => "8-10", [0, 1, 2, 3, 4, 5, 7, 9] => "8-11A", [0, 2, 4, 5, 6, 7, 8, 9] => "8-11B", [0, 1, 3, 4, 5, 6, 7, 9] => "8-12A", [0, 2, 3, 4, 5, 6, 8, 9] => "8-12B", [0, 1, 2, 3, 4, 6, 7, 9] => "8-13A", [0, 2, 3, 5, 6, 7, 8, 9] => "8-13B", [0, 1, 2, 4, 5, 6, 7, 9] => "8-14A", [0, 2, 3, 4, 5, 7, 8, 9] => "8-14B", [0, 1, 2, 3, 5, 7, 8, 9] => "8-16A", [0, 1, 2, 4, 6, 7, 8, 9] => "8-16B", [0, 1, 3, 4, 5, 6, 8, 9] => "8-17", [0, 1, 2, 3, 5, 6, 8, 9] => "8-18A", [0, 1, 3, 4, 6, 7, 8, 9] => "8-18B", [0, 1, 2, 4, 5, 6, 8, 9] => "8-19A", [0, 1, 3, 4, 5, 7, 8, 9] => "8-19B", [0, 1, 2, 4, 5, 7, 8, 9] => "8-20", [0, 1, 2, 3, 4, 6, 8, 10] => "8-21", [0, 1, 2, 3, 5, 6, 8, 10] => "8-22A", [0, 1, 3, 4, 5, 6, 8, 10] => "8-22B", [0, 1, 2, 3, 5, 7, 8, 10] => "8-23", [0, 1, 2, 4, 5, 6, 8, 10] => "8-24", [0, 1, 2, 4, 6, 7, 8, 10] => "8-25", [0, 1, 3, 4, 5, 7, 8, 10] => "8-26", [0, 1, 2, 4, 5, 7, 8, 10] => "8-27A", [0, 1, 3, 4, 6, 7, 8, 10] => "8-27B", [0, 1, 3, 4, 6, 7, 9, 10] => "8-28", [0, 1, 2, 3, 4, 5, 6, 8] => "8-2A", [0, 2, 3, 4, 5, 6, 7, 8] => "8-2B", [0, 1, 2, 3, 4, 5, 6, 9] => "8-3", [0, 1, 2, 3, 4, 5, 7, 8] => "8-4A", [0, 1, 3, 4, 5, 6, 7, 8] => "8-4B", [0, 1, 2, 3, 4, 6, 7, 8] => "8-5A", [0, 1, 2, 4, 5, 6, 7, 8] => "8-5B", [0, 1, 2, 3, 5, 6, 7, 8] => "8-6", [0, 1, 2, 3, 4, 5, 8, 9] => "8-7", [0, 1, 2, 3, 4, 7, 8, 9] => "8-8", [0, 1, 2, 3, 6, 7, 8, 9] => "8-9", [0, 1, 2, 3, 4, 6, 8, 9] => "8-z15A", [0, 1, 3, 5, 6, 7, 8, 9] => "8-z15B", [0, 1, 2, 3, 5, 6, 7, 9] => "8-z29A", [0, 2, 3, 4, 6, 7, 8, 9] => "8-z29B", [0, 1, 2, 3, 4, 5, 6, 7, 8] => "9-1", [0, 1, 2, 3, 4, 6, 7, 9, 10] => "9-10", [0, 1, 2, 3, 5, 6, 7, 9, 10] => "9-11A", [0, 1, 2, 4, 5, 6, 7, 9, 10] => "9-11B", [0, 1, 2, 4, 5, 6, 8, 9, 10] => "9-12", [0, 1, 2, 3, 4, 5, 6, 7, 9] => "9-2A", [0, 2, 3, 4, 5, 6, 7, 8, 9] => "9-2B", [0, 1, 2, 3, 4, 5, 6, 8, 9] => "9-3A", [0, 1, 3, 4, 5, 6, 7, 8, 9] => "9-3B", [0, 1, 2, 3, 4, 5, 7, 8, 9] => "9-4A", [0, 1, 2, 4, 5, 6, 7, 8, 9] => "9-4B", [0, 1, 2, 3, 4, 6, 7, 8, 9] => "9-5A", [0, 1, 2, 3, 5, 6, 7, 8, 9] => "9-5B", [0, 1, 2, 3, 4, 5, 6, 8, 10] => "9-6", [0, 1, 2, 3, 4, 5, 7, 8, 10] => "9-7A", [0, 1, 3, 4, 5, 6, 7, 8, 10] => "9-7B", [0, 1, 2, 3, 4, 6, 7, 8, 10] => "9-8A", [0, 1, 2, 4, 5, 6, 7, 8, 10] => "9-8B", [0, 1, 2, 3, 5, 6, 7, 8, 10] => "9-9", [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] => "10-1", [0, 1, 2, 3, 4, 5, 6, 7, 8, 10] => "10-2", [0, 1, 2, 3, 4, 5, 6, 7, 9, 10] => "10-3", [0, 1, 2, 3, 4, 5, 6, 8, 9, 10] => "10-4", [0, 1, 2, 3, 4, 5, 7, 8, 9, 10] => "10-5", [0, 1, 2, 3, 4, 6, 7, 8, 9, 10] => "10-6", [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] => "11-1", [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] => "12-1"}

Table of Prime Forms => Forte Numbers (Technically, this table splits prime forms into the non-inverted and inverted forms)