The Konieczny.DClass class

This page contains documentation for the nested class Konieczny.DClass.

Contents

DClass	Class representing a \(\mathscr{D}\)-class.
Konieczny.DClass.contains(…)	Test membership of an element.
Konieczny.DClass.is_regular_D_class(…)	Test regularity of a \(\mathscr{D}\)-class.
Konieczny.DClass.number_of_L_classes(…)	Returns the number of \(\mathscr{L}\)-classes.
Konieczny.DClass.number_of_R_classes(…)	Returns the number of \(\mathscr{R}\)-classes.
Konieczny.DClass.number_of_idempotents(…)	Returns the number of idempotents.
Konieczny.DClass.rep(…)	Returns a representative of the \(\mathscr{D}\)-class.
Konieczny.DClass.size(…)	Returns the size of a \(\mathscr{D}\)-class.
Konieczny.DClass.size_H_class(…)	Returns the size of the \(\mathscr{H}\)-classes.

Full API

class Konieczny.DClass

Class representing a \(\mathscr{D}\)-class.

The class Konieczny.DClass represents a \(\mathscr{D}\)-class via a frame as computed in Konieczny’s algorithm; see [Kon94] for more details. Konieczny.DClass objects cannot be directly constructed; instead you should obtain a \(\mathscr{D}\)-class by calling Konieczny.D_class_of_element.

See also

Konieczny.

contains(self: Konieczny.DClass, x: Element) → bool

Test membership of an element.

Given an element x, this function returns whether x is an element of the \(\mathscr{D}\)-class represented by self . This function triggers the computation of most of the frame for self, if it is not already known.

Parameters:

x (Element) – the element.

Returns:

Whether or not x belongs to the \(\mathscr{D}\)-class.

Return type:

bool

is_regular_D_class(self: Konieczny.DClass) → bool

Test regularity of a \(\mathscr{D}\)-class.

Returns:

Whether or not the \(\mathscr{D}\)-class is regular.

Return type:

bool

number_of_L_classes(self: Konieczny.DClass) → int

Returns the number of \(\mathscr{L}\)-classes. This function triggers the computation of most of the frame for self, if it is not already known.

Returns:

The number of \(\mathscr{L}\)-classes.

Return type:

int

number_of_R_classes(self: Konieczny.DClass) → int

Returns the number of \(\mathscr{R}\)-classes. This function triggers the computation of most of the frame for self, if it is not already known.

Returns:

The number of \(\mathscr{R}\)-classes.

Return type:

int

number_of_idempotents(self: Konieczny.DClass) → int

Returns the number of idempotents. This function triggers the computation of most of the frame for self, if it is not already known.

Returns:

The number of idempotents in a \(\mathscr{D}\)-class.

Return type:

int

rep(self: Konieczny.DClass) → Element

Returns a representative of the \(\mathscr{D}\)-class. The frame used to represent \(\mathscr{D}\)-classes depends on the choice of representative. This function returns the representative used by a Konieczny.DClass instance. This may not be the same representative as used to construct the instance, but is guaranteed to not change.

Returns:

A representative of the \(\mathscr{D}\)-class.

Return type:

Element

size(self: Konieczny.DClass) → int

Returns the size of a \(\mathscr{D}\)-class. This function triggers the computation of most of the frame for self, if it is not already known.

Returns:

The size of the \(\mathscr{D}\)-class.

Return type:

int

size_H_class(self: Konieczny.DClass) → int

Returns the size of the \(\mathscr{H}\)-classes. This function triggers the computation of most of the frame for self, if it is not already known.

Returns:

The size of any (and all) \(\mathscr{H}\)-classes in the \(\mathscr{D}\)-class.

Return type:

int