Class for polynomials in the semiring E[[d]]. More...

#include <polyEd.h>

Inheritance diagram for etvo::polyEd:

Public Member Functions
	polyEd ()
	default initialization to Epsilon

	polyEd (bool TopNotE)
	specific initialization : polyEd(true) set to Top, polyEd(false) set to E

	polyEd (const Ed &m)
	initialisation to a polynomial with one Ed term w.d^t

	polyEd (const std::vector< Ed > &v)

bool	isCanon () const
	Check if a polyEd is in canonical form, say for a sum w_id^t_i, w_i and t_i are strictly ordered.

void	canon ()
	set to the canonical form

bool	isE () const
	check if is equal to E()=g0.d0

polyEd	oplus (const polyEd &p) const
	Sum of polynomials in E[[d]].

polyEd	operator+ (const polyEd &p) const
	Sum of polynomials in E[[d]].

polyEd	oplusCD (const polyEd &p) const
	Sum of polynomials in E[[d]] via a Core Decomposition (see J.Trunk Thesis)

polyEd	operator+ (const Ed &m) const
	Sum of a polynomial in E[[d]] with a monomial in E[[d]].

void	add (const Ed &m)
	The current polynomial pcur is modified as pcur=pcur+m.

polyEd	operator+= (const Ed &m)
	Lies on polyEd::add(const Ed & m) method.

polyEd	operator* (const polyEd &p) const
	Product of polynomials in E[[d]].

polyEd	otimes (const polyEd &p) const
	Product of polynomials in E[[d]].

polyEd	operator* (const Ed &m) const
	Product of one polynomial by one monomial in E[[d]].

polyEd	otimesCD (const polyEd &p) const
	Product of polynomials in E[[d]] via a Core Decomposition (see j.Trunk thesis)

polyEd	inf (const polyEd &p) const
	Infimum of two polynomials in E[[d]] : p1.inf(p2) = greatest x s.t. x<=p1 and x<=p2.

polyEd	infCD (const polyEd &p) const

seriesEd	star () const

polyEd	lfrac (const polyEd &) const
	Computation of the left-multiplication residuation: p1.lfrac(p2) =p2= greatest x s.t. p2.x <= p1.

polyEd	lfracCD (const polyEd &) const

polyEd	lfrac (const Ed &m) const
	Computation of the left-multiplication residuation: p1.lfrac(m) =m= greatest x s.t. m.x <= p1.

polyEd	rfrac (const polyEd &) const
	Computation of the right-multiplication residuation: p1.rfrac(p2) =p1/p2= greatest x s.t. x.p2 <= p1.

polyEd	rfracCD (const polyEd &) const

polyEd	rfrac (const Ed &m) const
	Computation of the right-multiplication residuation: p1.rfrac(m) =p1/m= greatest x s.t. x.m <= p1.

bool	operator== (const polyEd &) const
	Check equality.

bool	operator!= (const polyEd &) const
	Check difference.

bool	operator<= (const polyEd &) const
	Check order on polynomials in E[[d]].

bool	operator>= (const polyEd &) const
	Check order on polynomials in E[[d]].

poly	toPoly () const
	The zero-slice polynomial in MinMax[[g,d]].

Ed	getFirstDif (const polyEd &p) const

polyEd	transientStar (int Tmax) const
	Do not use it. Use polyEd::star(). Only for DEBUGGING purpose.

void	getMaxGain (unsigned int &mu, unsigned int &beta) const
	Gives the maximal gain.

void	getLcmGain (unsigned int &mu, unsigned int &beta) const
	Gives th Least Common multiple of gains.

std::pair< unsigned int, unsigned int >	getPeriodicity () const
	Returns the periodicity as a pair.

std::vector< Ed >	getTerms () const
	return the monomials as a collection of Ed terms

void	removeTerm (unsigned idx)
	remove term number i in the polynomial

Ed	operator[] (unsigned idx) const
	Returns a copy of monomial in position idx in the polynomial.

unsigned int	size () const
	Returns the size = the number of monomials. For Epsilon and Top, size=0.

std::string	toString () const
	returns a string that gives the description of the current polynomial. Is depending on the canonical form of gNg terms

std::string	toStringAsMuVar () const
	returns a string that gives the description of the current polynomial as a sum of g^n.m<seq>.d^t terms

matrix< poly >	getCore (unsigned ratio=1) const

matrix< poly >	getCoreMax (unsigned ratio=1) const
	returns the maximal Core matrix<poly> (in MinMax[[g,d]]) of the current polynomial

void	toPov (graphicPR::PovRay &pov, graphicPR::PovRay::Color c)
	used in the creation of POV-Ray script for a polyEd object

polyEd	odot (const polyEd &p) const

polyEd	osum (const polyEd &p) const

Public Member Functions inherited from etvo::ISterm
	ISterm (bool isEpsilon=false)
	default constructor : an epsilon term

	ISterm (int epsNTop)
	constructor to specify the type of ISterm

bool	isEpsilon () const

bool	isTop () const

bool	isExtreme () const

void	setEpsilon ()

void	setTop ()

bool	operator== (const ISterm &) const

Static Public Member Functions
static polyEd	Epsilon ()
	Epsilon element.

static polyEd	E ()
	E element.

static polyEd	Top ()
	Top element.

static polyEd	otimes (const Ed &m, const polyEd &p)

static polyEd	toPolyEd (const poly &p)
	An injection from MinMax[[g,d]] to E[[d]]. More...

static polyEd	toCausal (const polyEd &p)
	returns a causal polynomial in E[[d]]

static polyEd	coreToPolyEd (const matrix< poly > &core)
	computes the recomposition of a polyEd polynomial from a Core Decomposition core.

static etvo::matrix< poly >	getMatN (unsigned size)

Additional Inherited Members
Protected Attributes inherited from etvo::ISterm
char	_epsNTop
	_epsNTop = -1 epsilon 0 not extrem (normal) +1 Top

Detailed Description

Class for polynomials in the semiring E[[d]].

Epsilon and Top element exist

Author: BC LH JT LARIS

Version: 2.0

Constructor & Destructor Documentation

◆ polyEd()

etvo::polyEd::polyEd ( const std::vector< Ed > & v )

initialization to a polynomial created from a collection of Ed terms w.d^t The initialization leads to a canonical form where Ed terms are sorted

Member Function Documentation

◆ getCore()

matrix< poly > etvo::polyEd::getCore ( unsigned ratio = 1 ) const

returns the Core matrix<poly> (in MinMax[[g,d]]) of the current polynomial a polynomial p=Mu_m Q Beta_b with Mu_m=[mu_m g^1mu_m g^2mu_m ... g^(m-1)mu_m] with Beta_b=[beta_b g^(b-1) ... beta_b g^1 beta_b]' and Q in MinMax[[g,d]] Mu_m and Beta_b are implicit from the size of Core

◆ getFirstDif()

Ed etvo::polyEd::getFirstDif ( const polyEd & p ) const

When the current polynomial is different from p, gives the first different monomial Otherwise, if both polynomials are equals, returns Ed::E()=g0.d0

◆ getMatN()

etvo::matrix< poly > etvo::polyEd::getMatN ( unsigned size )

static

returns the specific matrix Beta_N.Mu_N with Mu_m=[mu_m g^1mu_m g^2mu_m ... g^(m-1)mu_m] with Beta_b=[beta_b g^(b-1) ... beta_b g^1 beta_b]'

◆ infCD()

polyEd etvo::polyEd::infCD ( const polyEd & p ) const

Infimum of two polynomials in E[[d]] via a Core Decomposition (see J.Trunk thesis) Note: p1.inf(p2) is supposed to be equal to p1.infCD(p2), with a different algorithm.

◆ lfracCD()

polyEd etvo::polyEd::lfracCD ( const polyEd & p ) const

Computation of the left-multiplication residuation via a Core Decomposition : p1.lfracCD(p2) =p2= greatest x s.t. p2.x <= p1 Note: p1.lfrac(p2) is supposed to be equal to p1.lfracCD(p2) with a different algorithm

◆ rfracCD()

polyEd etvo::polyEd::rfracCD ( const polyEd & p ) const

Computation of the right-multiplication residuation via a Core Decomposition: p1.rfrac(p2) =p1/p2= greatest x s.t. x.p2 <= p1 Note: p1.rfrac(p2) is supposed to be equal to p1.rfracCD(p2), with a different algorithm

◆ star()

seriesEd etvo::polyEd::star ( ) const

Kleene star of a polynomial in E[[d]], the result is a series in E[[d]] The default algorithm is by using a Core Decomposition of the current polynomial, the Kleene star of the Core matrix, and finally the recomposition of a series in E[[d]] Exception : this method can throw a const char * exception (non causal case) or an etvoException when the result is a degenerate matrix (generally, it corresponds to liveness issues for the corresponding WB-TEG)

◆ toPolyEd()

polyEd etvo::polyEd::toPolyEd ( const poly & p )

static

An injection from MinMax[[g,d]] to E[[d]].

Creates a polynomial in E[[d]] from a polynomial in MinMax[[g,d]]

The documentation for this class was generated from the following files:

C:/Users/usrlocal/ownCloud/DevSoft/etvoIII/etvo31/etvo/seriesEd/polyEd.h
C:/Users/usrlocal/ownCloud/DevSoft/etvoIII/etvo31/etvo/seriesEd/polyEd.cpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members