Safe Haskell | Safe |
---|---|

Language | Haskell98 |

Ronald C. Read. "Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations." /Annals of Discrete Mathematics/ 2:107–20, 1978.

- type Code = Int
- type Array = [Bool]
- array_pp :: Array -> String
- parse_array :: String -> Array
- array_to_code :: Array -> Code
- code_to_array :: Int -> Code -> Array
- array_to_set :: Integral i => [Bool] -> [i]
- set_to_array :: Integral i => i -> [i] -> Array
- set_to_code :: Integral i => i -> [i] -> Code
- array_complement :: Array -> Array
- array_is_prime :: Array -> Bool
- array_augment :: Array -> [Array]
- enumerate_half :: (Array -> Bool) -> Int -> [(Int, [Array])]
- encode :: Integral i => [i] -> Code
- decode :: Integral i => i -> Code -> [i]
- encode_prime :: Integral i => Z i -> [i] -> [i]

# Documentation

parse_array :: String -> Array Source #

Parse PP of `Array`

.

parse_array "01001" == [False,True,False,False,True]

array_to_code :: Array -> Code Source #

code_to_array :: Int -> Code -> Array Source #

Inverse of `array_to_code`

.

code_to_array 13 6428 == map toEnum [1,1,0,0,1,0,0,0,1,1,1,0,0]

array_to_set :: Integral i => [Bool] -> [i] Source #

Array to set.

array_to_set (map toEnum [1,1,0,0,1,0,0,0,1,1,1,0,0]) == [0,1,4,8,9,10] encode [0,1,4,8,9,10] == 1811

set_to_array :: Integral i => i -> [i] -> Array Source #

Inverse of `array_to_set`

, *z* is the degree of the array.

set_to_code :: Integral i => i -> [i] -> Code Source #

`array_to_code`

of `set_to_array`

.

set_to_code 12 [0,2,3,5] == 2880 map (set_to_code 12) (T.z_ti_related (flip mod 12) [0,2,3,5])

array_complement :: Array -> Array Source #

Logical complement.

array_is_prime :: Array -> Bool Source #

The *prime* form is the `maximum`

encoding.

array_is_prime (set_to_array 12 [0,2,3,5]) == False

array_augment :: Array -> [Array] Source #

The augmentation rule adds `1`

in each empty slot at end of array.

map array_pp (array_augment (parse_array "01000")) == ["01100","01010","01001"]

enumerate_half :: (Array -> Bool) -> Int -> [(Int, [Array])] Source #

Enumerate first half of the set-classes under given *prime* function.
The second half can be derived as the complement of the first.

import Music.Theory.Z12.Forte_1973 length scs == 224 map (length . scs_n) [0..12] == [1,1,6,12,29,38,50,38,29,12,6,1,1]

let z12 = map (fmap (map array_to_set)) (enumerate_half array_is_prime 12) map (length . snd) z12 == [1,1,6,12,29,38,50]

This can become slow, edit *z* to find out. It doesn't matter
about *n*. This can be edited so that small *n* would run quickly
even for large *z*.

fmap (map array_to_set) (lookup 5 (enumerate_half array_is_prime 16))

# Alternate (reverse) form.

decode :: Integral i => i -> Code -> [i] Source #

Decoder for `encode_prime`

.

decode 12 843 == [0,1,3,6,8,9]

encode_prime :: Integral i => Z i -> [i] -> [i] Source #

Binary encoding prime form algorithm, equalivalent to Rahn.

encode_prime Z.mod12 [0,1,3,6,8,9] == [0,2,3,6,7,9] Music.Theory.Z12.Rahn_1980.rahn_prime [0,1,3,6,8,9] == [0,2,3,6,7,9]