Computation of orbits. More...

#include "monoid.h"
#include "monoid_ideals.h"
#include "monoid_sub.h"
#include "sep_group.h"

Classes
struct	orbits
	Type used to represent C-orbits of a morphism. More...

Functions
orbits *	init_orbits (morphism *)
	Initialization of an orbits set.

void	delete_orbits (orbits *)
	Release of an orbits set.

subsemi *	compute_one_ddorb (morphism *, uint)
	Computation of the DD-orbit associated to a given idempotent (local monoid).

orbits *	compute_ddorbits (morphism *)
	Initialization of the DD-orbits set.

subsemi *	compute_one_gplusorb (subsemi *, uint)
	Computes the G⁺-orbit associated to a given idempotent for group class G. The G-kernel needs to be given as an input.

orbits *	compute_gplusorbits (subsemi *)
	Initialization of the G⁺-orbits set.

subsemi *	compute_one_ptorb (morphism *, uint, sub_level)
	Computes the PT-orbit associated to a given idempotent.

orbits *	compute_ptorbits (morphism *, sub_level)
	Initialization of the PT-orbits set.

uint **	compute_jmult (morphism , dequeue , dequeue *)
	Given a monoid, computes the partial multiplication table between all elements within a subset and all elements within a J-class that must contain the subset. Only the products evaluating to an element of the J-class are computed.

bool **	compute_polgpairs (subsemi , dequeue , uint)
	Computes a subset of the Pol(G)-pairs associated to a given morphism. The comutation depends on the G-kernel which is given as input.

subsemi *	compute_one_bpgorb (morphism *M, uint, sub_level, basis)
	Computes the BPol(G)-orbit associated to a given idempotent for group class G. The G-kernel needs to be given as an input.

orbits *	compute_bpgorbits (morphism *M, sub_level, basis)
	Initialization of the BPol(G)-orbits set.

subsemi *	compute_one_orbit_from_pairs (morphism , uint, dequeue , bool **, sub_level)
	Given an idempotent e, computes the associated BPol(C)-orbit from a relevant subset of the Pol(C)-pairs.

subsemi *	compute_one_bpddorb (morphism *M, uint e, sub_level level)
	Computes the BPol(DD)-orbit associated to a given idempotent.

subsemi *	compute_one_bpgplusorb (morphism *, uint, sub_level, basis)
	Computes the BPol(G⁺)-orbit associated to a given idempotent for group class G.

orbits *	compute_bpgplusorbits (morphism *, sub_level, basis)
	Initialization of the BPol(G⁺)-orbits set.

Detailed Description

Computation of orbits.

Function Documentation

◆ compute_bpgorbits()

orbits * compute_bpgorbits	(	morphism *	M,
		sub_level	level,
		basis	type )

Initialization of the BPol(G)-orbits set.

Computes one BPol(G)-orbits per regular J-class.

Remarks: The available computation levels are LV_FULL and LV_GREG. If LV_REG is chosen, the computation defaults to LV_GREG.

Returns: The (partial) set of BPol(G)-orbits.

Parameters

M	The G-kernel.
level	Desired computation level.
type	Type of the BPol(G)-orbit to compute (MOD, AMT or GR).

◆ compute_bpgplusorbits()

orbits * compute_bpgplusorbits	(	morphism *	M,
		sub_level	level,
		basis	type )

Initialization of the BPol(G⁺)-orbits set.

Computes one BPol(G⁺)-orbits per regular J-class.

Remarks: The available computation levels are LV_FULL and LV_GREG. If LV_REG is chosen, the computation defaults to LV_GREG.

Returns: The set of BPol(G⁺)-orbits.

Parameters

M	The morphism.
level	Desired computation level.
type	Type of the BPol(G⁺)-orbit to compute (ST, MOD, AMT or GR).

◆ compute_ddorbits()

orbits * compute_ddorbits ( morphism * M )

Initialization of the DD-orbits set.

Computes one orbit per minimal strict regular J-class.

Remarks: The computation level always defaults to LV_FULL. Hence, it is not a parameter.

Returns: The (partial) set of DD-orbits.

Parameters

M	The morphism.

◆ compute_gplusorbits()

orbits * compute_gplusorbits ( subsemi * S )

Initialization of the G⁺-orbits set.

Computes one orbit per minimal strict regular J-class.

Remarks: The computation level is determined by the G-kernel (which can be either LV_FULL or LV_REG).

Returns: The set of G⁺-orbits.

Parameters

S	The G-kernel.

◆ compute_jmult()

uint ** compute_jmult	(	morphism *	,
		dequeue *	,
		dequeue *	)

Given a monoid, computes the partial multiplication table between all elements within a subset and all elements within a J-class that must contain the subset. Only the products evaluating to an element of the J-class are computed.

Remarks: The returned multiplication table is indexed by the indices of the elements of the subset in the input list (first) and by the indices of the J-class (second). Its cells contain the result of every product in the original monoid. If a product does not fall within the J-class, it is given the value ->M->r_cayley->size_graph (which is not a valid element).

Returns: The multiplication table.

◆ compute_one_bpddorb()

subsemi * compute_one_bpddorb	(	morphism *	M,
		uint	e,
		sub_level	level )

Computes the BPol(DD)-orbit associated to a given idempotent.

Remarks: The available computation levels are LV_FULL and LV_GREG. If LV_REG is chosen, the computation defaults to LV_GREG.; If the monoid has a non-empty neutral element, the BPol(DD)-orbit is the same as the BPol(ST)-orbit and the computation default to the latter as this is much faster.

Returns: The BPol(DD)-orbit.

Parameters

M	The morphism.
e	The idempotent.
level	Desired computation level.

◆ compute_one_bpgorb()

subsemi * compute_one_bpgorb	(	morphism *	M,
		uint	e,
		sub_level	level,
		basis	type )

Computes the BPol(G)-orbit associated to a given idempotent for group class G. The G-kernel needs to be given as an input.

Remarks: The available computation levels are LV_FULL and LV_GREG. If LV_REG is chosen, the computation defaults to LV_GREG.

Returns: The BPol(G)-orbit.

Parameters

M	The morphism.
e	The idempotent.
level	Desired computation level.
type	Type of the BPol(G)-orbit to compute (MOD, AMT or GR).

◆ compute_one_bpgplusorb()

subsemi * compute_one_bpgplusorb	(	morphism *	M,
		uint	e,
		sub_level	level,
		basis	type )

Computes the BPol(G⁺)-orbit associated to a given idempotent for group class G.

Remarks: The available computation levels are LV_FULL and LV_GREG. If LV_REG is chosen, the computation defaults to LV_GREG.; If the monoid has a non-empty neutral element, the BPol(G⁺)-orbit is the same as the BPol(G)-orbit and the computation default to the latter as this is much faster.; For G = ST, the BPol(G⁺)-orbit is the BPol(DD)-orbit an the function compute_one_bpddorb is called.

Returns: The BPol(G⁺)-orbit.

Parameters

M	The morphism.
e	The idempotent.
level	Desired computation level.
type	Type of the BPol(G⁺)-orbit to compute (ST, MOD, AMT or GR).

◆ compute_one_ddorb()

subsemi * compute_one_ddorb	(	morphism *	M,
		uint	e )

Computation of the DD-orbit associated to a given idempotent (local monoid).

Remarks: The computation level always defaults to LV_FULL. Hence, it is not a parameter.

Returns: The DD-orbit.

Parameters

M	The morphism.
e	The idempotent.

◆ compute_one_gplusorb()

subsemi * compute_one_gplusorb	(	subsemi *	ker,
		uint	e )

Computes the G⁺-orbit associated to a given idempotent for group class G. The G-kernel needs to be given as an input.

Remarks: The computation level is determined by the G-kernel (which can be either LV_FULL or LV_REG).

Returns: The G⁺-orbit.

Parameters

ker	The G-kernel.
e	The idempotent.

◆ compute_one_orbit_from_pairs()

subsemi * compute_one_orbit_from_pairs	(	morphism *	M,
		uint	e,
		dequeue *	eM,
		bool **	pairs,
		sub_level	level )

Given an idempotent e, computes the associated BPol(C)-orbit from a relevant subset of the Pol(C)-pairs.

Attention: Only the Pol(C)-pairs (s,t) such that s belongs to eM and t R e are given as input (this is enough information to compute the BPol(C)-orbit of e). They are given by a two-dimensional array of Booleans indexed by the indices of the right ideal eM (first) and the indices of the R-class of e (second).

Remarks: The procedure exploits the fact that the BPol(C)-orbites are the same as the co-Pol(C)-orbits.; The available computation levels are LV_FULL and LV_GREG. If LV_REG is chosen, the computation defaults to LV_GREG.

Returns: The BPol(C)-orbit.

Parameters

M	The morphism.
e	The index of the idempotent e.
eM	The right ideal eM associated to e.
pairs	Two-dimensional array indicating the Pol(C)-pairs.
level	Desired computation level.

◆ compute_one_ptorb()

subsemi * compute_one_ptorb	(	morphism *	M,
		uint	e,
		sub_level	level )

Computes the PT-orbit associated to a given idempotent.

Remarks: The computation level always defaults to LV_FULL. Hence, it is not a parameter.

Returns: The PT-orbit.

Parameters

M	The morphism.
e	The idempotent.
level	Desired computation level.

◆ compute_polgpairs()

bool ** compute_polgpairs	(	subsemi *	,
		dequeue *	,
		uint	)

Computes a subset of the Pol(G)-pairs associated to a given morphism. The comutation depends on the G-kernel which is given as input.

Attention: A regular R-class is given as input. Only the Pol(G)-pairs (s,t) such that s is in the right ideal of the R-class and t is in the R-class itself are computed.

Returns: A two-dimensional array of Booleans indexed by the indices of the right ideal (first) and the indices of the R-class (second). It marks the Pol(G)-pairs.

◆ compute_ptorbits()

orbits * compute_ptorbits	(	morphism *	M,
		sub_level	level )

Initialization of the PT-orbits set.

Remarks: The computation level always defaults to LV_FULL. Hence, it is not a parameter.

Computes one PT-orbit per regular J-class.

Returns: The (partial) set of PT-orbits.

Parameters

M	The morphism.
level	Desired computation level.

◆ delete_orbits()

void delete_orbits ( orbits * L )

Release of an orbits set.

Attention: The original morphism and its Green relations are not released.

Parameters

L	The orbits set.

◆ init_orbits()

orbits * init_orbits ( morphism * M )

Initialization of an orbits set.

Returns: The orbits set.

Parameters

M	The morphism.

Classes

Functions

Detailed Description

Function Documentation

◆ compute_bpgorbits()

◆ compute_bpgplusorbits()

◆ compute_ddorbits()

◆ compute_gplusorbits()

◆ compute_jmult()

◆ compute_one_bpddorb()

◆ compute_one_bpgorb()

◆ compute_one_bpgplusorb()

◆ compute_one_ddorb()

◆ compute_one_gplusorb()

◆ compute_one_orbit_from_pairs()

◆ compute_one_ptorb()

◆ compute_polgpairs()

◆ compute_ptorbits()

◆ delete_orbits()

◆ init_orbits()