music.PlainChanges¶

class music.PlainChanges(nelements=4, nhunts=None, hunts=None)[source]¶

Bases: object

Presents plain changes as swaps and acts in domains to make peals.

__init__(nelements=4, nhunts=None, hunts=None)[source]¶

Initializes a PlainChanges object.

Parameters:

nelementsint, optional: The number of elements. Defaults to 4.
nhuntsint, optional: The number of hunts. Defaults to None.
huntsdict, optional: The hunts dictionary. Defaults to None.

Raises:

ValueError: If the number of hunts is invalid.

Methods

`__init__`([nelements, nhunts, hunts])	Initializes a PlainChanges object.
`act`([domain, peal])	Acts in a domain using a peal.
`act_all`([domain])	Acts in all peals using a domain.
`initialize_hunts`([nelements, nhunts])	Initializes the hunts dictionary.
`perform_change`(nelements, hunts[, hunt])	Performs a change procedure.
`perform_peal`(nelements[, hunts])	Performs a peal.
`saturating_hunts`(nelements)	Number of hunts that yields a peal over the whole symmetric group.

static saturating_hunts(nelements)[source]¶

Number of hunts that yields a peal over the whole symmetric group.

For nelements bells this is nelements - 3, floored at one. Below it the peal is a proper subset of the permutations: with the old default of two hunts, PlainChanges(6) produced 120 of the 720 rows and PlainChanges(8) produced 224 of 40320. Above it nothing is gained, which is what the warning in initialize_hunts reports.

Parameters:

nelementsint: The number of elements.

Returns:

int: The saturating number of hunts.

initialize_hunts(nelements=4, nhunts=None)[source]¶

Initializes the hunts dictionary.

Parameters:

nelementsint, optional: The number of elements. Defaults to 4.
nhuntsint, optional: The number of hunts. Defaults to the value of saturating_hunts(nelements), which is the number that makes the peal traverse every permutation exactly once. Pass a smaller value deliberately for a shorter peal.

Returns:

dict: The hunts dictionary.

Raises:

ValueError: If the number of hunts is invalid.

perform_peal(nelements, hunts=None)[source]¶

Performs a peal.

Parameters:

nelementsint: The number of elements.
huntsdict, optional: The hunts dictionary. Defaults to None.

Returns:

dict: The updated hunts dictionary.

perform_change(nelements, hunts, hunt=None)[source]¶

Performs a change procedure.

Parameters:

nelementsint: The number of elements.
huntsdict: The hunts dictionary.
huntstr, optional: The current hunt. Defaults to None.

Returns:

Permutation: The permutation of the change.
dict: The updated hunts dictionary.

act(domain=None, peal=None)[source]¶

Acts in a domain using a peal.

Parameters:

domainlist, optional: The domain. Defaults to None.
peallist, optional: The peal. Defaults to None.

Returns:

list: The acted domain.

act_all(domain=None)[source]¶

Acts in all peals using a domain.

Parameters:

domainlist, optional: The domain. Defaults to None.