music.InterestingPermutations¶

class music.InterestingPermutations(nelements=4, method='dimino')[source]¶

Bases: object

Get permutations of n elements in meaningful sequences. Mirrors are ordered by swaps (0,n-1…).

Parameters:

nelementsinteger: How many elements are permuted. Every group generated here – symmetric, alternating, cyclic, dihedral – is the group on this many elements, so it also sets how many permutations there are.
methodstr: The generation method handed to sympy’s group generate(): "dimino" or "coset". It changes the order the permutations come out in, which is the sequence this class exists to make meaningful, and not which permutations they are.

Methods

`get_alternating`()	Generates permutations in the alternating group.
`get_rotations`()	Generates rotations of permutations.
`get_mirrors`()	Generates mirror permutations.
`get_swaps`()	Generates swap permutations.
`even_odd`(sequence)	Determines if a permutation is even or odd.
`get_full_symmetry`()	Generates permutations with full symmetry.

Raises:

ValueError: If nelements is less than two, or method is neither of the two sympy generates by. One element has no swaps, mirrors or second rotation, and failed inside sympy; an unknown method failed there as NotImplementedError.

Examples

>>> structures = InterestingPermutations(nelements=4)
>>> len(structures.rotations), len(structures.dihedral)
(4, 8)
>>> rows = [p(list("abcd")) for p in structures.rotations]
>>> ["".join(row) for row in rows]
['abcd', 'bcda', 'cdab', 'dabc']

__init__(nelements=4, method='dimino')[source]¶

Methods

`__init__`([nelements, method])
`even_odd`(sequence)	Determines if a permutation is even or odd.
`get_alternating`()	Generates permutations in the alternating group.
`get_full_symmetry`()	Generates permutations with full symmetry.
`get_mirrors`()	Generates mirror permutations.
`get_rotations`()	Generates rotations of permutations.
`get_swaps`()	Generates swap permutations.

Attributes

`permutations_by_sizes`
`permutations`
`alternations`
`alternations_complement`
`alternations_by_sizes`
`neighbor_swaps`
`swaps_by_stepsizes`
`swaps_as_comes`
`swaps`
`rotations`
`mirrors`
`dihedral`

permutations_by_sizes: list¶

permutations: list¶

alternations: list¶

alternations_complement: list¶

alternations_by_sizes: list¶

neighbor_swaps: list¶

swaps_by_stepsizes: list¶

swaps_as_comes: list¶

swaps: list¶

rotations: list¶

mirrors: list¶

dihedral: list¶

get_alternating()[source]¶

Generates permutations in the alternating group.

This method generates permutations in the alternating group of the specified size using the provided generation method.

get_rotations()[source]¶

Generates rotations of permutations.

This method generates rotations of permutations of the specified size using the provided generation method.

get_mirrors()[source]¶

Generates mirror permutations.

This method generates mirror permutations of the specified size using the provided generation method.

get_swaps()[source]¶

Generates swap permutations.

This method generates swap permutations of the specified size using the provided generation method.

even_odd(sequence)[source]¶

Determines if a permutation is even or odd.

This method determines if a given permutation is even or odd based on its sequence of elements.

Parameters:

sequencelist: The sequence of elements representing the permutation.

Returns:

str: Either ‘even’ or ‘odd’ indicating the parity of the permutation.

Raises:

ValueError: If sequence is not a permutation of 0 to n - 1. A repeated entry used to be read as a cycle, so [1, 1] was ‘odd’.

get_full_symmetry()[source]¶

Generates permutations with full symmetry.

This method generates permutations with full symmetry of the specified size using the provided generation method.