numerical_semigroup

class pocketpartition.core.numerical_semigroup.NumericalSemigroup(gaps=None, generators=None)

Bases: NumericalSet

property genus

apery_set(n)

Compute the Apéry set of the numerical set with respect to n.

Parameters: n (int): The modulus for the Apéry set computation.

Returns: set of int: The Apéry set with respect to n.

minimal_generating_set()

Compute the minimal generating set of the numerical semigroup.

Returns: list of int: The minimal generating set of the numerical semigroup.

The algorithm used here is based on the method described by Rosales and Vasco in their works on numerical semigroups.

void()

Compute the void of the numerical semigroup.

Returns: set: The void of the numerical semigroup.

gap_poset()

Compute the poset of the gaps of the numerical semigroup.

Returns: set of tuple: The poset of the gaps of the numerical semigroup.

void_poset()

Compute the poset of the void of the numerical semigroup.

Returns: set of tuple: The poset of the void of the numerical semigroup.

effective_weight()

Calculates the effective weight of the numerical partition.

The effective weight is the sum of the number of boxes above each minimal generating set element.

Returns:

int: The effective weight of the numerical partition.

apery_weight()

Calculates the Apery weight of the numerical partition.

The effective weight is the sum of the number of boxes above each Apery set element. We look use m instead of 0 for the weight about 0 residue class.

Returns:

int: The apery weight of the numerical partition.

pseudofrobenius_numbers()

Calculate the pseudo-Frobenius numbers of the semigroup.

Returns:

list of int – The unique pseudo-Frobenius numbers.

type()

depth()

remove_minimal_generator(n)

Remove a minimal generator from a numerical semigroup.

Parameters: n (int): The minimal generator to remove.

Returns: NumericalSemigroup: The resulting numerical semigroup after removal.

effective_generators()

get_children()

get_parent()

special_gaps()

Compute the gaps that can be added to S and still yield a numerical semigroup.

Returns:

list of int – The special gaps of S.

add_specialgap(p)

Add a special gap to the numerical semigroup.

get_frobchildren()