Aim: Specialization of MPolynomial for degree 0. More...

#include <DGtal/math/MPolynomial.h>

Inheritance diagram for DGtal::MPolynomial< 0, TRing, TAlloc >:

Public Types
typedef TRing	Ring
typedef TAlloc	Alloc
typedef MPolynomial< n - 1, Ring, Alloc >	MPolyNM1
typedef IVector< MPolyNM1, typename std::allocator_traits< Alloc >::template rebind_alloc< MPolyNM1 >,(n > 1) >	Storage
typedef Storage::Size	Size

Public Member Functions
	MPolynomial (const Ring &v=0, const Alloc &allocator=Alloc())
	MPolynomial (const Alloc &allocator)
bool	isZero () const
	operator const Ring & () const
MPolynomial &	operator= (const Ring &v)
Ring	operator() () const
MPolynomial	operator* (const Ring &v) const
MPolynomial	operator/ (const Ring &v) const
MPolynomial	operator+ (const Ring &v) const
MPolynomial	operator- (const Ring &v) const
MPolynomial	operator- () const
MPolynomial &	operator*= (const Ring &v)
MPolynomial &	operator/= (const Ring &v)
MPolynomial &	operator+= (const Ring &v)
MPolynomial &	operator-= (const Ring &v)
bool	operator== (const Ring &v) const
bool	operator!= (const Ring &v) const
void	selfDisplay (std::ostream &s, int) const
void	swap (MPolynomial &p)
Alloc	getAllocator () const
void	normalize ()
int	degree () const
const MPolyNM1 &	leading () const
MPolyNM1 &	operator[] (Size i)
bool	isValid () const

Private Attributes
Alloc	myAllocator
Ring	myValue

Static Private Attributes
static MPolyNM1	myZeroPolynomial
	The zero polynomial of n-1 variables for a n-multivariate polynomial.

Friends
class	MPolynomialDerivativeComputer
class	MPolynomialEvaluator
class	MPolynomialEvaluatorImpl
void	euclidDiv (const MPolynomial< 1, TRing, TAlloc > &f, const MPolynomial< 1, TRing, TAlloc > &g, MPolynomial< 1, TRing, TAlloc > &q, MPolynomial< 1, TRing, TAlloc > &r)

Detailed Description

template<typename TRing, typename TAlloc>
class DGtal::MPolynomial< 0, TRing, TAlloc >

Aim: Specialization of MPolynomial for degree 0.

Description of template class 'MPolynomial'

Stores a polynomial of degree 0, i.e. a scalar of type T. We assume that the type T is not "too" complex, otherwise this class will be partially not very effective.

Template Parameters

TRing	the type chosen for the polynomial, defines also the type of the coefficents (generally int, float or double).
TAlloc	is an allocator for TRing, for example std::allocator<TRing>; this is also the default parameter. Usually this parameter does not needs to be changed.

This class is a backport from Spielwiese.

Author: Felix Fontein (felix.nosp@m.@fon.nosp@m.tein..nosp@m.de), University of Zurich, Switzerland

Definition at line 507 of file MPolynomial.h.

Member Typedef Documentation

◆ Alloc

template<typename TRing, typename TAlloc>

typedef TAlloc DGtal::MPolynomial< 0, TRing, TAlloc >::Alloc

Definition at line 511 of file MPolynomial.h.

◆ MPolyNM1

typedef MPolynomial< n - 1, Ring, Alloc > DGtal::MPolynomial< n, TRing, TAlloc >::MPolyNM1

Definition at line 991 of file MPolynomial.h.

◆ Ring

template<typename TRing, typename TAlloc>

typedef TRing DGtal::MPolynomial< 0, TRing, TAlloc >::Ring

Definition at line 510 of file MPolynomial.h.

◆ Size

typedef Storage::Size DGtal::MPolynomial< n, TRing, TAlloc >::Size

Definition at line 1001 of file MPolynomial.h.

◆ Storage

typedef IVector< MPolyNM1, typename std::allocator_traits<Alloc>::template rebind_alloc<MPolyNM1>, (n > 1) > DGtal::MPolynomial< n, TRing, TAlloc >::Storage

The type for the vector storing polynomials coefficients. For 0 or 1 variables, uses a standard vector, for more variables, uses a specific vector of pointers to polynomials, with adequate allocators. This is for efficiency purposes.

Definition at line 1000 of file MPolynomial.h.

Constructor & Destructor Documentation

◆ MPolynomial() [1/2]

template<typename TRing, typename TAlloc>

DGtal::MPolynomial< 0, TRing, TAlloc >::MPolynomial	(	const Ring &	v = 0,
		const Alloc &	allocator = Alloc() )

inline

Constructor (default, or from ring value). Creates the constant polynomial v.

Parameters

v	any value in the ring.
allocator	an allocator for the polynomial.

Definition at line 526 of file MPolynomial.h.

527 : myAllocator(allocator), myValue(v)

528 {}

DGtal::MPolynomial< 0, TRing, TAlloc >::myValue

Ring myValue

Definition MPolynomial.h:515

DGtal::MPolynomial< 0, TRing, TAlloc >::myAllocator

Alloc myAllocator

Definition MPolynomial.h:514

DGtal::MPolynomial

Aim: Represents a multivariate polynomial, i.e. an element of , where K is some ring or field.

Definition MPolynomial.h:970

References myAllocator, and myValue.

Referenced by operator*(), operator*=(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator/=(), operator=(), and swap().

◆ MPolynomial() [2/2]

template<typename TRing, typename TAlloc>

DGtal::MPolynomial< 0, TRing, TAlloc >::MPolynomial ( const Alloc & allocator )

inline

Allocator constructor. Creates the constant polynomial 0, where 0 is the default value of the ring.

Parameters

allocator an allocator for the polynomial.

Definition at line 537 of file MPolynomial.h.

538 : myAllocator(allocator), myValue( Ring() )

539 {}

DGtal::MPolynomial< 0, TRing, TAlloc >::Ring

TRing Ring

Definition MPolynomial.h:510

References myAllocator, and myValue.

Member Function Documentation

◆ degree()

int DGtal::MPolynomial< n, TRing, TAlloc >::degree ( ) const

inline

Returns: the degree of this polynomial. If this is the zero polynomial, the degree is -1.

Definition at line 1124 of file MPolynomial.h.

    {
      return (int)(myValue.size() - 1);
    }

◆ getAllocator()

template<typename TRing, typename TAlloc>

Alloc DGtal::MPolynomial< 0, TRing, TAlloc >::getAllocator ( ) const

inline

Returns: the allocator for this object.

Definition at line 712 of file MPolynomial.h.

    {
      return myAllocator;
    }

References myAllocator.

◆ isValid()

bool DGtal::MPolynomial< n, TRing, TAlloc >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ isZero()

template<typename TRing, typename TAlloc>

bool DGtal::MPolynomial< 0, TRing, TAlloc >::isZero ( ) const

inline

Returns: true if the polynomial is 0.

Definition at line 544 of file MPolynomial.h.

    {
      return myValue == 0;
    }

References myValue.

◆ leading()

const MPolyNM1 & DGtal::MPolynomial< n, TRing, TAlloc >::leading ( ) const

inline

Returns: the leading term (of type MPolynomial<n-1, Ring>) of the first indeterminate. Returns 0 (of type MPolynomial<n-1, Ring>) in case of the zero polynomial.

Definition at line 1134 of file MPolynomial.h.

    {
      return myValue.size() ? myValue.back() : myZeroPolynomial;
    }

◆ normalize()

void DGtal::MPolynomial< n, TRing, TAlloc >::normalize ( )

inline

Adjusts the size of myValue that the leading term and degree can be computed trivially. This must be called only after calls to the non-const operator[], in which the degree of the polynomial has potentially been changed.

Definition at line 1030 of file MPolynomial.h.

    {
      Size dp1 = myValue.size();
      while ( dp1 )
        {
          if (myValue[dp1 - 1].isZero())
            --dp1;
          else
            break;
        }
      if (dp1 < myValue.size())
        myValue.resize(dp1);
    }

◆ operator const Ring &()

template<typename TRing, typename TAlloc>

DGtal::MPolynomial< 0, TRing, TAlloc >::operator const Ring & ( ) const

inline

Const cast operator to Ring value. Returns the coefficient value of this constant polynomial.

Definition at line 553 of file MPolynomial.h.

    {
        return myValue;
    }

References myValue.

◆ operator!=()

template<typename TRing, typename TAlloc>

bool DGtal::MPolynomial< 0, TRing, TAlloc >::operator!= ( const Ring & v ) const

inline

Difference operator.

Parameters

v	any value in the ring.

Returns: true iff myValue is different from v.

Definition at line 686 of file MPolynomial.h.

    {
        return myValue != v;
    }

References myValue.

◆ operator()()

template<typename TRing, typename TAlloc>

Ring DGtal::MPolynomial< 0, TRing, TAlloc >::operator() ( ) const

inline

Evaluation operator for the polynomial.

Returns: the value of its coefficient.

Definition at line 573 of file MPolynomial.h.

    {
      return myValue;
    }

References myValue.

◆ operator*()

template<typename TRing, typename TAlloc>

MPolynomial DGtal::MPolynomial< 0, TRing, TAlloc >::operator* ( const Ring & v ) const

inline

Multiplication by value v.

Parameters

v	any value in the ring.

Returns: a constant polynomial of coefficient myValue*v.

Definition at line 583 of file MPolynomial.h.

    {
        return MPolynomial(myValue * v);
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial(), MPolynomial(), and myValue.

◆ operator*=()

template<typename TRing, typename TAlloc>

MPolynomial & DGtal::MPolynomial< 0, TRing, TAlloc >::operator*= ( const Ring & v )

inline

Self-multiplication by value v.

Parameters

v	any value in the ring.

Returns: itself

Definition at line 632 of file MPolynomial.h.

    {
      myValue *= v;
      return *this;
    }

References MPolynomial(), and myValue.

◆ operator+()

template<typename TRing, typename TAlloc>

MPolynomial DGtal::MPolynomial< 0, TRing, TAlloc >::operator+ ( const Ring & v ) const

inline

Addition by value v.

Parameters

v	any value in the ring.

Returns: a constant polynomial of coefficient myValue+v.

Definition at line 603 of file MPolynomial.h.

    {
        return MPolynomial(myValue + v);
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial(), MPolynomial(), and myValue.

◆ operator+=()

template<typename TRing, typename TAlloc>

MPolynomial & DGtal::MPolynomial< 0, TRing, TAlloc >::operator+= ( const Ring & v )

inline

Self-addition by value v.

Parameters

v	any value in the ring.

Returns: itself

Definition at line 654 of file MPolynomial.h.

    {
      myValue += v;
      return *this;
    }

References MPolynomial(), and myValue.

◆ operator-() [1/2]

template<typename TRing, typename TAlloc>

MPolynomial DGtal::MPolynomial< 0, TRing, TAlloc >::operator- ( ) const

inline

Unary minus operator.

Returns: a constant polynomial of coefficient -myValue.

Definition at line 622 of file MPolynomial.h.

    {
      return MPolynomial(-myValue);
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial(), MPolynomial(), and myValue.

◆ operator-() [2/2]

template<typename TRing, typename TAlloc>

MPolynomial DGtal::MPolynomial< 0, TRing, TAlloc >::operator- ( const Ring & v ) const

inline

Subtraction by value v.

Parameters

v	any value in the ring.

Returns: a constant polynomial of coefficient myValue-v.

Definition at line 613 of file MPolynomial.h.

    {
        return MPolynomial(myValue - v);
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial(), MPolynomial(), and myValue.

◆ operator-=()

template<typename TRing, typename TAlloc>

MPolynomial & DGtal::MPolynomial< 0, TRing, TAlloc >::operator-= ( const Ring & v )

inline

Self-subtraction by value v.

Parameters

v	any value in the ring.

Returns: itself

Definition at line 665 of file MPolynomial.h.

    {
      myValue -= v;
      return *this;
    }

References MPolynomial(), and myValue.

◆ operator/()

template<typename TRing, typename TAlloc>

MPolynomial DGtal::MPolynomial< 0, TRing, TAlloc >::operator/ ( const Ring & v ) const

inline

Division by value v.

Parameters

v	any value in the ring.

Returns: a constant polynomial of coefficient myValue/v.

Definition at line 593 of file MPolynomial.h.

    {
        return MPolynomial(myValue / v);
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial(), MPolynomial(), and myValue.

◆ operator/=()

template<typename TRing, typename TAlloc>

MPolynomial & DGtal::MPolynomial< 0, TRing, TAlloc >::operator/= ( const Ring & v )

inline

Self-division by value v.

Parameters

v	any value in the ring.

Returns: itself

Definition at line 643 of file MPolynomial.h.

    {
      myValue /= v;
      return *this;
    }

References MPolynomial(), and myValue.

◆ operator=()

template<typename TRing, typename TAlloc>

MPolynomial & DGtal::MPolynomial< 0, TRing, TAlloc >::operator= ( const Ring & v )

inline

Assigment from coefficient in the ring.

Parameters

v	any value in the ring.

Returns: itself

Definition at line 563 of file MPolynomial.h.

    {
      myValue = v;
      return *this;
    }

References MPolynomial(), and myValue.

◆ operator==()

template<typename TRing, typename TAlloc>

bool DGtal::MPolynomial< 0, TRing, TAlloc >::operator== ( const Ring & v ) const

inline

Equality operator.

Parameters

v	any value in the ring.

Returns: true iff myValue is equal to v.

Definition at line 676 of file MPolynomial.h.

    {
        return myValue == v;
    }

References myValue.

◆ operator[]()

MPolyNM1 & DGtal::MPolynomial< n, TRing, TAlloc >::operator[] ( Size i )

inline

Returns: a reference to the i-th coefficient. If i > degree(), the array myValue is enlarged. Afterwards, one should better call normalize() to make sure future operations are correct.

Definition at line 1152 of file MPolynomial.h.

    {
      if (i >= myValue.size())
        myValue.resize(i + 1);
      return myValue[i];
    }

◆ selfDisplay()

template<typename TRing, typename TAlloc>

void DGtal::MPolynomial< 0, TRing, TAlloc >::selfDisplay	(	std::ostream &	s,
		int	) const

inline

Outputs itself in the stream s.

Parameters

s	any stream

Definition at line 695 of file MPolynomial.h.

    {
      s << myValue;
    }

References myValue.

◆ swap()

template<typename TRing, typename TAlloc>

void DGtal::MPolynomial< 0, TRing, TAlloc >::swap ( MPolynomial< 0, TRing, TAlloc > & p )

inline

Swaps two polynomials.

Parameters

p	any zero-degree polynomial.

Definition at line 704 of file MPolynomial.h.

    {
      std::swap(myValue, p.myValue);
    }

References MPolynomial(), DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and myValue.

◆ euclidDiv

void euclidDiv	(	const MPolynomial< 1, TRing, TAlloc > &	f,
		const MPolynomial< 1, TRing, TAlloc > &	g,
		MPolynomial< 1, TRing, TAlloc > &	q,
		MPolynomial< 1, TRing, TAlloc > &	r )

friend

Forward declaration, to be able to declare this as a friend.

◆ MPolynomialDerivativeComputer

friend class MPolynomialDerivativeComputer

friend

Definition at line 974 of file MPolynomial.h.

◆ MPolynomialEvaluator

friend class MPolynomialEvaluator

friend

Definition at line 983 of file MPolynomial.h.

◆ MPolynomialEvaluatorImpl

friend class MPolynomialEvaluatorImpl

friend

Definition at line 986 of file MPolynomial.h.

Field Documentation

◆ myAllocator

template<typename TRing, typename TAlloc>

Alloc DGtal::MPolynomial< 0, TRing, TAlloc >::myAllocator

private

Definition at line 514 of file MPolynomial.h.

Referenced by getAllocator(), MPolynomial(), and MPolynomial().

◆ myValue

template<typename TRing, typename TAlloc>

Ring DGtal::MPolynomial< 0, TRing, TAlloc >::myValue

private

Definition at line 515 of file MPolynomial.h.

Referenced by isZero(), MPolynomial(), MPolynomial(), operator const Ring &(), operator!=(), operator()(), operator*(), operator*=(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator/=(), operator=(), operator==(), selfDisplay(), and swap().

◆ myZeroPolynomial

MPolyNM1 DGtal::MPolynomial< n, TRing, TAlloc >::myZeroPolynomial

staticprivate

The zero polynomial of n-1 variables for a n-multivariate polynomial.

Definition at line 1006 of file MPolynomial.h.

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

MPolynomial.h

Public Types

Public Member Functions

Private Attributes

Static Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Alloc

◆ MPolyNM1

◆ Ring

◆ Size

◆ Storage

Constructor & Destructor Documentation

◆ MPolynomial() [1/2]

◆ MPolynomial() [2/2]

Member Function Documentation

◆ degree()

◆ getAllocator()

◆ isValid()

◆ isZero()

◆ leading()

◆ normalize()

◆ operator const Ring &()

◆ operator!=()

◆ operator()()

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator[]()

◆ selfDisplay()

◆ swap()

Friends And Related Symbol Documentation

◆ euclidDiv

◆ MPolynomialDerivativeComputer

◆ MPolynomialEvaluator

◆ MPolynomialEvaluatorImpl

Field Documentation

◆ myAllocator

◆ myValue

◆ myZeroPolynomial