Green's relations¶

This page contains information about the methods of the Konieczny class related to Green's relations.

Konieczny.is_regular_element(self: Konieczny, x: Element) → bool¶

Test regularity of an element.

Parameters: x (Element) -- a possible element.
Returns: A bool.

Konieczny.D_class_of_element(self: Konieczny, x: Element) → DClass¶

Returns the \(\mathscr{D}\)-class containing an element.

Raises: RuntimeError if x is not an element of self.
Note: This function computes as many frames for \(\mathscr{D}\)-classes as necessary (this is all of them in the case that x is not an element of self).
Parameters: x (Element) -- a possible element.
Returns: A DClass.

Konieczny.D_classes(self: Konieczny) → Iterator¶

Returns an iterator pointing to the first \(\mathscr{D}\)-class.

Note: This function does not trigger any enumeration; the iterator returned may be invalidated by any call to a method of the Konieczny class.
Parameters: None
Returns: An iterator.

Konieczny.regular_D_classes(self: Konieczny) → Iterator¶

Returns an iterator pointing to the first regular \(\mathscr{D}\)-class.

Note: This function does not trigger any enumeration; the iterator returned may be invalidated by any call to a method of the Konieczny class.
Parameters: None
Returns: An iterator.

Konieczny.number_of_D_classes(self: Konieczny) → int¶

Returns the number of \(\mathscr{D}\)-classes.

Note: This function triggers a full enumeration of the frames of every \(\mathscr{D}\)-class.
Parameters: None
Returns: An integer.

Konieczny.number_of_R_classes(self: Konieczny) → int¶

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

Note: This function triggers a full enumeration of the frames of every \(\mathscr{D}\)-class.
Parameters: None
Returns: An integer.

Konieczny.number_of_L_classes(self: Konieczny) → int¶

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

Note: This function triggers a full enumeration of the frames of every \(\mathscr{D}\)-class.
Parameters: None
Returns: An integer.

Konieczny.number_of_H_classes(self: Konieczny) → int¶

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

Note: This function triggers a full enumeration of the frames of every \(\mathscr{D}\)-class.
Parameters: None
Returns: An integer.

Konieczny.current_number_of_D_classes(self: Konieczny) → int¶

Returns the current number of \(\mathscr{D}\)-classes.

Note: This function triggers no enumeration.
Parameters: None
Returns: An integer.

Konieczny.current_number_of_R_classes(self: Konieczny) → int¶

Returns the current number of \(\mathscr{R}\)-classes.

Note: This function triggers no enumeration.
Parameters: None
Returns: An integer.

Konieczny.current_number_of_L_classes(self: Konieczny) → int¶

Returns the current number of \(\mathscr{L}\)-classes.

Note: This function triggers no enumeration.
Parameters: None
Returns: An integer.

Konieczny.current_number_of_H_classes(self: Konieczny) → int¶

Returns the current number of \(\mathscr{L}\)-classes.

Note: This function triggers no enumeration.
Parameters: None
Returns: An integer.

Konieczny.number_of_regular_D_classes(self: Konieczny) → int¶

Returns the number of regular \(\mathscr{D}\)-classes.

Note: This function triggers a full enumeration of the frames of every \(\mathscr{D}\)-class.
Parameters: None
Returns: An integer.

Konieczny.number_of_regular_R_classes(self: Konieczny) → int¶

Returns the number of regular \(\mathscr{R}\)-classes.

Note: This function triggers a full enumeration of the frames of every \(\mathscr{D}\)-class.
Parameters: None
Returns: An integer.

Konieczny.number_of_regular_L_classes(self: Konieczny) → int¶

Returns the number of regular \(\mathscr{L}\)-classes.

Note: This function triggers a full enumeration of the frames of every \(\mathscr{D}\)-class.
Parameters: None
Returns: An integer.

Konieczny.current_number_of_regular_D_classes(self: Konieczny) → int¶

Returns the current number of regular \(\mathscr{D}\)-classes.

Note: This function triggers no enumeration.
Parameters: None
Returns: An integer.

Konieczny.current_number_of_regular_R_classes(self: Konieczny) → int¶

Returns the current number of regular \(\mathscr{R}\)-classes.

Note: This function triggers no enumeration.
Parameters: None
Returns: An integer.

Konieczny.current_number_of_regular_L_classes(self: Konieczny) → int¶

Returns the current number of regular \(\mathscr{L}\)-classes.

Note: This function triggers no enumeration.
Parameters: None
Returns: An integer.