Truncated power series. More...

#include <Tps.h>

Collaboration diagram for Tps< T >:

Public Member Functions
	Tps (int maxOrder, int nVar)
	Constructor.
	Tps (const T &y)
	Conversion.
	Tps (int y)
	Conversion.
	Tps ()
	Tps (const Tps< T > &x)
	~Tps ()
Tps< T > &	operator= (const Tps< T > &y)
Tps< T > &	operator= (const T &y)
	Convert and assign.
Tps< T >	filter (int lowOrder, int highOrder) const
	Extract orders.
Tps< T >	truncate (int trunc)
	Truncate.
const T	getCoefficient (int index) const
	Get coefficient.
void	setCoefficient (int index, const T &value)
	Set coefficient.
const T	getCoefficient (const TpsMonomial &monomial) const
	Get coefficient.
void	setCoefficient (const TpsMonomial &monomial, const T &value)
	Set coefficient.
const T	operator[] (int index) const
	Get coefficient.
T &	operator[] (int index)
	Get coefficient.
const T	operator[] (const TpsMonomial &monomial) const
	Get coefficient.
T &	operator[] (const TpsMonomial &monomial)
	Get coefficient.
Tps< T >	operator+ () const
	Unary plus.
Tps< T >	operator- () const
	Unary minus.
Tps< T > &	operator+= (const Tps< T > &y)
	Add and assign.
Tps< T > &	operator-= (const Tps< T > &y)
	Subtract and assign.
Tps< T > &	operator*= (const Tps< T > &y)
	Multiply and assign.
Tps< T > &	operator/= (const Tps< T > &y)
	Divide and assign.
Tps< T > &	operator+= (const T &y)
	Add constant and assign.
Tps< T > &	operator-= (const T &y)
	Subtract constant and assign.
Tps< T > &	operator*= (const T &y)
	Multiply by constant and assign.
Tps< T > &	operator/= (const T &y)
	Divide by constant and assign.
bool	operator== (const Tps< T > &y) const
	Equality operator.
bool	operator== (const T &y) const
	Equlatity with constant.
bool	operator!= (const Tps< T > &y) const
	Inequality operator.
bool	operator!= (const T &y) const
	Inequality with constant.
Tps< T >	substitute (const Matrix< T > &M) const
	Substitute.
Tps< T >	substitute (const VpsMap< T > &m) const
	Substitute.
T	evaluate (const Vector< T > &v) const
	Substitute.
void	clear ()
	Set to zero.
Tps< T >	inverse (int order=truncOrder) const
	Reciprocal value.
Tps< T >	multiply (const Tps< T > &y, int trunc) const
	Truncated multiplication.
Tps< T >	derivative (int var) const
	Partial derivative.
Tps< T >	integral (int var) const
	Partial integral.
Tps< T >	multiplyVariable (int var) const
	Multiply by variable [b]var[/b].
Tps< T >	scaleMonomials (const Tps< T > &y) const
	Multiply monomial-wise.
Tps< T >	Taylor (const T series[], int n) const
	Taylor series.
int	getMaxOrder () const
	Get maximal order.
int	getTruncOrder () const
	Get truncation order.
int	getVariables () const
	Get number of variables.
int	getSize () const
	Get number of coefficients.
std::istream &	get (std::istream &is)
	Get Tps from the stream is.
std::ostream &	put (std::ostream &os) const
	Put Tps to the stream is.
const TpsMonomial &	getExponents (int index) const
	Get exponents.
int	getOrder (int index) const
	Get order.
int	getSize (int order) const
	Size.
bool	isConstant () const
	Test for constant.

Static Public Member Functions
static Tps< T >	makeVariable (int nVar, int var)
	Make variable.
static Tps< T >	makeVarPower (int nVar, int var, int power)
	Make power.
static Tps< T >	makeMonomial (const TpsMonomial &m, const T &t)
	Make monomial.
static int	getGlobalTruncOrder ()
	Get global truncation order.
static void	setGlobalTruncOrder (int order)
	Set global truncation order.

Static Public Attributes
static const int	EXACT = INT_MAX
	Representation of infinite precision.

Private Member Functions
	Tps (TpsRep< T > *)
void	setMaxOrder (int)
void	unique ()

Private Attributes
TpsRep< T > *	rep

Static Private Attributes
static int	truncOrder

Detailed Description

template<class T>
class Tps< T >

Truncated power series.

Definition at line 46 of file Tps.h.

Constructor & Destructor Documentation

◆ Tps() [1/6]

template<class T>

Tps< T >::Tps	(	int	maxOrder,
		int	nVar )

Constructor.

Definition at line 227 of file Tps.hpp.

References EXACT, and rep.

Referenced by derivative(), filter(), get(), integral(), inverse(), makeMonomial(), makeVariable(), makeVarPower(), multiply(), multiplyVariable(), operator!=(), operator*=(), operator*=(), operator+(), operator+=(), operator+=(), operator-(), operator-=(), operator-=(), operator/=(), operator/=(), operator=(), operator=(), operator==(), scaleMonomials(), substitute(), substitute(), Taylor(), Tps(), and truncate().

◆ Tps() [2/6]

template<class T>

Tps< T >::Tps ( const T & y )

Conversion.

Definition at line 239 of file Tps.hpp.

References rep.

◆ Tps() [3/6]

template<class T>

Tps< T >::Tps ( int y )

Conversion.

Definition at line 246 of file Tps.hpp.

References rep.

◆ Tps() [4/6]

template<class T>

Tps< T >::Tps ( )

Definition at line 221 of file Tps.hpp.

References rep.

◆ Tps() [5/6]

template<class T>

Tps< T >::Tps ( const Tps< T > & x )

Definition at line 233 of file Tps.hpp.

References rep, and Tps().

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◆ ~Tps()

template<class T>

Tps< T >::~Tps ( )

Definition at line 253 of file Tps.hpp.

References TpsRep< T >::release(), and rep.

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◆ Tps() [6/6]

template<class T>

Tps< T >::Tps ( TpsRep< T > * d )

inlineprivate

Definition at line 1096 of file Tps.hpp.

References rep.

Member Function Documentation

◆ clear()

template<class T>

void Tps< T >::clear ( )

Set to zero.

Definition at line 714 of file Tps.hpp.

References TpsRep< T >::release(), rep, and TpsRep< T >::zero().

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◆ derivative()

template<class T>

Tps< T > Tps< T >::derivative ( int var ) const

Partial derivative.

Definition at line 920 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getExponents(), getMaxOrder(), getSize(), getTruncOrder(), getVariables(), rep, Tps(), and TpsRep< T >::zero().

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◆ evaluate()

template<class T>

T Tps< T >::evaluate ( const Vector< T > & v ) const

Substitute.

Definition at line 686 of file Tps.hpp.

References getMaxOrder(), getVariables(), TpsSubstitution::index, TpsSubstitution::order, rep, Array1D< T >::size(), TpsSubstitution::skip, and TpsSubstitution::variable.

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◆ filter()

template<class T>

Tps< T > Tps< T >::filter	(	int	lowOrder,
		int	highOrder ) const

Extract orders.

Definition at line 279 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getMaxOrder(), getSize(), getTruncOrder(), getVariables(), rep, and Tps().

Referenced by truncate().

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◆ get()

template<class T>

std::istream & Tps< T >::get ( std::istream & is )

Get Tps from the stream is.

Definition at line 721 of file Tps.hpp.

References TpsRep< T >::create(), TpsMonomial::getIndex(), setMaxOrder(), Tps(), and truncOrder.

Referenced by operator>>().

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◆ getCoefficient() [1/2]

template<class T>

const T Tps< T >::getCoefficient ( const TpsMonomial & monomial ) const

Get coefficient.

Definition at line 355 of file Tps.hpp.

References getCoefficient(), TpsMonomial::getIndex(), getVariables(), and TpsMonomial::getVariables().

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◆ getCoefficient() [2/2]

template<class T>

const T Tps< T >::getCoefficient ( int index ) const

Get coefficient.

Definition at line 327 of file Tps.hpp.

References rep.

Referenced by getCoefficient().

◆ getExponents()

template<class T>

const TpsMonomial & Tps< T >::getExponents ( int index ) const

Get exponents.

Definition at line 1073 of file Tps.hpp.

References rep.

Referenced by derivative(), integral(), and put().

◆ getGlobalTruncOrder()

template<class T>

int Tps< T >::getGlobalTruncOrder ( )

static

Get global truncation order.

Definition at line 1061 of file Tps.hpp.

References truncOrder.

Referenced by operator/(), and Vps< T >::operator/=().

◆ getMaxOrder()

template<class T>

int Tps< T >::getMaxOrder ( ) const

Get maximal order.

Definition at line 1031 of file Tps.hpp.

References rep.

Referenced by derivative(), evaluate(), filter(), Vps< T >::getTopOrder(), multiply(), operator+=(), operator-(), operator-=(), operator==(), put(), scaleMonomials(), substitute(), and substitute().

◆ getOrder()

template<class T>

int Tps< T >::getOrder ( int index ) const

Get order.

Definition at line 1084 of file Tps.hpp.

References rep.

Referenced by setCoefficient().

◆ getSize() [1/2]

template<class T>

int Tps< T >::getSize ( ) const

Get number of coefficients.

Definition at line 1049 of file Tps.hpp.

References rep.

Referenced by derivative(), filter(), integral(), multiply(), multiplyVariable(), operator+=(), operator-=(), operator==(), operator==(), and put().

◆ getSize() [2/2]

template<class T>

int Tps< T >::getSize ( int order ) const

Size.

Definition at line 1090 of file Tps.hpp.

References rep.

◆ getTruncOrder()

template<class T>

int Tps< T >::getTruncOrder ( ) const

Get truncation order.

Definition at line 1037 of file Tps.hpp.

References rep, and truncOrder.

Referenced by cos(), cosh(), derivative(), exp(), filter(), Vps< T >::getTruncOrder(), inverse(), log(), multiply(), operator+=(), operator-(), operator-=(), operator==(), put(), scaleMonomials(), sin(), sinh(), sqrt(), and substitute().

◆ getVariables()

template<class T>

int Tps< T >::getVariables ( ) const

Get number of variables.

Definition at line 1043 of file Tps.hpp.

References rep.

Referenced by derivative(), evaluate(), filter(), getCoefficient(), integral(), multiply(), multiplyVariable(), operator+=(), operator-(), operator-=(), operator==(), put(), scaleMonomials(), setCoefficient(), setCoefficient(), Vps< T >::setComponent(), substitute(), and substitute().

◆ integral()

template<class T>

Tps< T > Tps< T >::integral ( int var ) const

Partial integral.

Definition at line 946 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getExponents(), getSize(), getVariables(), rep, Tps(), and truncOrder.

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◆ inverse()

template<class T>

Tps< T > Tps< T >::inverse ( int order = truncOrder ) const

Reciprocal value.

Definition at line 897 of file Tps.hpp.

References getTruncOrder(), isConstant(), rep, Taylor(), and Tps().

Referenced by csc(), operator/(), operator/=(), Vps< T >::operator/=(), pow(), and sec().

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◆ isConstant()

template<class T>

bool Tps< T >::isConstant ( ) const

Test for constant.

Definition at line 1055 of file Tps.hpp.

References rep.

Referenced by inverse(), and Taylor().

◆ makeMonomial()

template<class T>

Tps< T > Tps< T >::makeMonomial	(	const TpsMonomial &	m,
		const T &	t )

static

Make monomial.

Definition at line 401 of file Tps.hpp.

References TpsRep< T >::create(), EXACT, TpsMonomial::getOrder(), TpsMonomial::getVariables(), and Tps().

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◆ makeVariable()

template<class T>

Tps< T > Tps< T >::makeVariable	(	int	nVar,
		int	var )

static

Make variable.

Definition at line 383 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), EXACT, and Tps().

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◆ makeVarPower()

template<class T>

Tps< T > Tps< T >::makeVarPower	(	int	nVar,
		int	var,
		int	power )

static

Make power.

Definition at line 391 of file Tps.hpp.

References TpsRep< T >::create(), EXACT, and Tps().

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◆ multiply()

template<class T>

Tps< T > Tps< T >::multiply	(	const Tps< T > &	y,
		int	trunc ) const

Truncated multiplication.

Definition at line 823 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), EXACT, getMaxOrder(), getSize(), getTruncOrder(), getVariables(), prod(), rep, and Tps().

Referenced by operator*=(), operator/=(), and Taylor().

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◆ multiplyVariable()

template<class T>

Tps< T > Tps< T >::multiplyVariable ( int var ) const

Multiply by variable [b]var[/b].

Definition at line 969 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getSize(), getVariables(), rep, Tps(), and truncOrder.

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◆ operator!=() [1/2]

template<class T>

bool Tps< T >::operator!= ( const T & y ) const

Inequality with constant.

Definition at line 608 of file Tps.hpp.

◆ operator!=() [2/2]

template<class T>

bool Tps< T >::operator!= ( const Tps< T > & y ) const

Inequality operator.

Definition at line 602 of file Tps.hpp.

References Tps().

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◆ operator*=() [1/2]

template<class T>

Tps< T > & Tps< T >::operator*= ( const T & y )

Multiply by constant and assign.

Definition at line 527 of file Tps.hpp.

References rep, Tps(), and unique().

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◆ operator*=() [2/2]

template<class T>

Tps< T > & Tps< T >::operator*= ( const Tps< T > & y )

Multiply and assign.

Definition at line 499 of file Tps.hpp.

References multiply(), Tps(), and truncOrder.

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◆ operator+()

template<class T>

Tps< T > Tps< T >::operator+ ( ) const

Unary plus.

Definition at line 411 of file Tps.hpp.

References Tps().

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◆ operator+=() [1/2]

template<class T>

Tps< T > & Tps< T >::operator+= ( const T & y )

Add constant and assign.

Definition at line 511 of file Tps.hpp.

References rep, Tps(), and unique().

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◆ operator+=() [2/2]

template<class T>

Tps< T > & Tps< T >::operator+= ( const Tps< T > & y )

Add and assign.

Definition at line 427 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getMaxOrder(), getSize(), getTruncOrder(), getVariables(), TpsRep< T >::release(), rep, Tps(), and unique().

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◆ operator-()

template<class T>

Tps< T > Tps< T >::operator- ( ) const

Unary minus.

Definition at line 417 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getMaxOrder(), getTruncOrder(), getVariables(), rep, and Tps().

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◆ operator-=() [1/2]

template<class T>

Tps< T > & Tps< T >::operator-= ( const T & y )

Subtract constant and assign.

Definition at line 519 of file Tps.hpp.

References rep, Tps(), and unique().

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◆ operator-=() [2/2]

template<class T>

Tps< T > & Tps< T >::operator-= ( const Tps< T > & y )

Subtract and assign.

Definition at line 462 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getMaxOrder(), getSize(), getTruncOrder(), getVariables(), TpsRep< T >::release(), rep, Tps(), and unique().

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◆ operator/=() [1/2]

template<class T>

Tps< T > & Tps< T >::operator/= ( const T & y )

Divide by constant and assign.

Definition at line 536 of file Tps.hpp.

References rep, and Tps().

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◆ operator/=() [2/2]

template<class T>

Tps< T > & Tps< T >::operator/= ( const Tps< T > & y )

Divide and assign.

Definition at line 505 of file Tps.hpp.

References inverse(), multiply(), Tps(), and truncOrder.

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◆ operator=() [1/2]

template<class T>

Tps< T > & Tps< T >::operator= ( const T & y )

Convert and assign.

Definition at line 270 of file Tps.hpp.

References TpsRep< T >::release(), rep, Tps(), and TpsRep< T >::zero().

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◆ operator=() [2/2]

template<class T>

Tps< T > & Tps< T >::operator= ( const Tps< T > & y )

Definition at line 259 of file Tps.hpp.

References TpsRep< T >::release(), rep, and Tps().

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◆ operator==() [1/2]

template<class T>

bool Tps< T >::operator== ( const T & y ) const

Equlatity with constant.

Definition at line 588 of file Tps.hpp.

References getSize(), and rep.

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◆ operator==() [2/2]

template<class T>

bool Tps< T >::operator== ( const Tps< T > & y ) const

Equality operator.

Definition at line 545 of file Tps.hpp.

References getMaxOrder(), getSize(), getTruncOrder(), getVariables(), rep, and Tps().

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◆ operator[]() [1/4]

template<class T>

T & Tps< T >::operator[] ( const TpsMonomial & monomial )

Get coefficient.

Definition at line 320 of file Tps.hpp.

References TpsMonomial::getIndex(), rep, and unique().

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◆ operator[]() [2/4]

template<class T>

const T Tps< T >::operator[] ( const TpsMonomial & monomial ) const

Get coefficient.

Definition at line 314 of file Tps.hpp.

References TpsMonomial::getIndex(), and rep.

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◆ operator[]() [3/4]

template<class T>

T & Tps< T >::operator[] ( int index )

Get coefficient.

Definition at line 307 of file Tps.hpp.

References rep, and unique().

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◆ operator[]() [4/4]

template<class T>

const T Tps< T >::operator[] ( int index ) const

Get coefficient.

Definition at line 301 of file Tps.hpp.

References rep.

◆ put()

template<class T>

std::ostream & Tps< T >::put ( std::ostream & os ) const

Put Tps to the stream is.

Definition at line 784 of file Tps.hpp.

References getExponents(), getMaxOrder(), getSize(), getTruncOrder(), getVariables(), and rep.

Referenced by operator<<().

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◆ scaleMonomials()

template<class T>

Tps< T > Tps< T >::scaleMonomials ( const Tps< T > & y ) const

Multiply monomial-wise.

Definition at line 992 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getMaxOrder(), getTruncOrder(), getVariables(), TpsRep< T >::len, rep, and Tps().

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◆ setCoefficient() [1/2]

template<class T>

void Tps< T >::setCoefficient	(	const TpsMonomial &	monomial,
		const T &	value )

Set coefficient.

Definition at line 369 of file Tps.hpp.

References TpsMonomial::getIndex(), getVariables(), TpsMonomial::getVariables(), and setCoefficient().

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◆ setCoefficient() [2/2]

template<class T>

void Tps< T >::setCoefficient	(	int	index,
		const T &	value )

Set coefficient.

Definition at line 337 of file Tps.hpp.

References TpsRep< T >::create(), TpsRep< T >::data(), getOrder(), getVariables(), TpsRep< T >::release(), rep, and unique().

Referenced by setCoefficient().

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◆ setGlobalTruncOrder()

template<class T>

void Tps< T >::setGlobalTruncOrder ( int order )

static

Set global truncation order.

Definition at line 1067 of file Tps.hpp.

References truncOrder.

◆ setMaxOrder()

template<class T>

void Tps< T >::setMaxOrder ( int order )

inlineprivate

Definition at line 49 of file Tps.hpp.

References rep.

Referenced by get().

◆ substitute() [1/2]

template<class T>

Tps< T > Tps< T >::substitute ( const Matrix< T > & M ) const

Substitute.

Definition at line 614 of file Tps.hpp.

References getMaxOrder(), getVariables(), TpsSubstitution::index, Array2D< T >::ncols(), Array2D< T >::nrows(), TpsSubstitution::order, rep, Array1D< T >::size(), TpsSubstitution::skip, Tps(), and TpsSubstitution::variable.

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◆ substitute() [2/2]

template<class T>

Tps< T > Tps< T >::substitute ( const VpsMap< T > & m ) const

Substitute.

Definition at line 657 of file Tps.hpp.

References Vps< T >::getDimension(), getMaxOrder(), getTruncOrder(), getVariables(), TpsSubstitution::index, TpsSubstitution::order, rep, Array1D< T >::size(), TpsSubstitution::skip, Tps(), and TpsSubstitution::variable.

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◆ Taylor()

template<class T>

Tps< T > Tps< T >::Taylor	(	const T	series[],
		int	n ) const

Taylor series.

Definition at line 1014 of file Tps.hpp.

References isConstant(), multiply(), and Tps().

Referenced by cos(), cosh(), exp(), inverse(), log(), sin(), sinh(), and sqrt().

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◆ truncate()

template<class T>

Tps< T > Tps< T >::truncate ( int trunc )

Truncate.

Definition at line 295 of file Tps.hpp.

References filter(), and Tps().

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◆ unique()

template<class T>

void Tps< T >::unique ( )

inlineprivate

Definition at line 55 of file Tps.hpp.

References rep.

Referenced by operator*=(), operator+=(), operator+=(), operator-=(), operator-=(), operator[](), operator[](), and setCoefficient().

Member Data Documentation

◆ EXACT

template<class T>

const int Tps< T >::EXACT = INT_MAX

static

Representation of infinite precision.

Definition at line 260 of file Tps.h.

Referenced by makeMonomial(), makeVariable(), makeVarPower(), multiply(), Tps(), and TpsRep< T >::zero().

◆ rep

template<class T>

TpsRep<T>* Tps< T >::rep

private

Definition at line 274 of file Tps.h.

Referenced by clear(), derivative(), evaluate(), filter(), getCoefficient(), getExponents(), getMaxOrder(), getOrder(), getSize(), getSize(), getTruncOrder(), getVariables(), integral(), inverse(), isConstant(), multiply(), multiplyVariable(), operator*=(), operator+=(), operator+=(), operator-(), operator-=(), operator-=(), operator/=(), operator=(), operator=(), operator==(), operator==(), operator[](), operator[](), operator[](), operator[](), put(), scaleMonomials(), setCoefficient(), setMaxOrder(), substitute(), substitute(), Tps(), Tps(), Tps(), Tps(), Tps(), Tps(), unique(), and ~Tps().

◆ truncOrder

template<class T>

int Tps< T >::truncOrder

staticprivate

Definition at line 277 of file Tps.h.

Referenced by get(), getGlobalTruncOrder(), getTruncOrder(), integral(), multiplyVariable(), operator*=(), operator/=(), and setGlobalTruncOrder().

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

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Tps() [1/6]

◆ Tps() [2/6]

◆ Tps() [3/6]

◆ Tps() [4/6]

◆ Tps() [5/6]

◆ ~Tps()

◆ Tps() [6/6]

Member Function Documentation

◆ clear()

◆ derivative()

◆ evaluate()

◆ filter()

◆ get()

◆ getCoefficient() [1/2]

◆ getCoefficient() [2/2]

◆ getExponents()

◆ getGlobalTruncOrder()

◆ getMaxOrder()

◆ getOrder()

◆ getSize() [1/2]

◆ getSize() [2/2]

◆ getTruncOrder()

◆ getVariables()

◆ integral()

◆ inverse()

◆ isConstant()

◆ makeMonomial()

◆ makeVariable()

◆ makeVarPower()

◆ multiply()

◆ multiplyVariable()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator[]() [1/4]

◆ operator[]() [2/4]

◆ operator[]() [3/4]

◆ operator[]() [4/4]

◆ put()

◆ scaleMonomials()

◆ setCoefficient() [1/2]

◆ setCoefficient() [2/2]

◆ setGlobalTruncOrder()

◆ setMaxOrder()

◆ substitute() [1/2]

◆ substitute() [2/2]

◆ Taylor()

◆ truncate()

◆ unique()

Member Data Documentation

◆ EXACT

◆ rep

◆ truncOrder