Aim: Represents a multivariate polynomial, i.e. an element of \( K[X_0, ..., X_{n-1}] \), where K is some ring or field. More...

#include <DGtal/math/MPolynomial.h>

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

[legend]

Public Types
typedef TRing	Ring

typedef TAlloc	Alloc

typedef MPolynomial< n - 1, Ring, Alloc >	MPolyNM1

typedef IVector< MPolyNM1, typename Alloc::template rebind< MPolyNM1 >::other,(n >1) >	Storage

typedef Storage::Size	Size

Public Member Functions
void	normalize ()

	MPolynomial (const Alloc &allocator=Alloc())

	MPolynomial (const Ring &v, const Alloc &allocator=Alloc())

	MPolynomial (const MPolyNM1 &pdm1, const Alloc &)

template<typename Ring2 , typename Alloc2 >
	MPolynomial (const MPolynomial< n, Ring2, Alloc2 > &p, const Alloc &allocator=Alloc())

template<typename Ring2 , typename Alloc2 >
MPolynomial &	operator= (const MPolynomial< n, Ring2, Alloc2 > &p)

void	swap (MPolynomial &p)

Alloc	getAllocator () const

int	degree () const

const MPolyNM1 &	leading () const

bool	isZero () const

MPolyNM1 &	operator[] (Size i)

const MPolyNM1 &	operator[] (Size i) const

MPolynomialEvaluator< n, Ring, Alloc, Ring >	operator() (const Ring &x) const

template<typename Ring2 >
MPolynomialEvaluator< n, Ring, Alloc, Ring2 >	operator() (const Ring2 &x) const

MPolynomial	operator* (const Ring &v) const

MPolynomial	operator/ (const Ring &v) const

MPolynomial &	operator*= (const MPolynomial &p)

MPolynomial &	operator*= (const Ring &v)

MPolynomial &	operator/= (const Ring &v)

MPolynomial	operator- () const

MPolynomial	operator+ (const MPolynomial &q) const

MPolynomial	operator- (const MPolynomial &q) const

MPolynomial &	operator+= (const MPolynomial &q)

MPolynomial &	operator-= (const MPolynomial &q)

MPolynomial	operator+ (const MPolyNM1 &q) const

MPolynomial	operator- (const MPolyNM1 &q) const

MPolynomial	operator+ (const Ring &v) const

MPolynomial	operator- (const Ring &v) const

MPolynomial &	operator+= (const MPolyNM1 &q)

MPolynomial &	operator-= (const MPolyNM1 &q)

MPolynomial &	operator+= (const Ring &v)

MPolynomial &	operator-= (const Ring &v)

MPolynomial	operator* (const MPolynomial &p) const

bool	operator== (const MPolynomial &q) const

bool	operator!= (const MPolynomial &q) const

bool	operator== (const Ring &v) const

bool	operator!= (const Ring &v) const

void	selfDisplay (std::ostream &s, int N=n) const

bool	isValid () const

Private Member Functions
	MPolynomial (bool, Size s, const Alloc &)

Private Attributes
Storage	myValue

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

Friends
template<int NN, int nn, typename TT , typename AA >
class	MPolynomialDerivativeComputer

template<int nn, typename TT , typename AA , typename SS >
class	MPolynomialEvaluator

template<int nn, typename TT , typename HLHL , typename AA , typename SS >
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)

MPolynomial	operator* (const Ring &v, const MPolynomial &p)

Detailed Description

template<int n, typename TRing, class TAlloc>
class DGtal::MPolynomial< n, TRing, TAlloc >

Aim: Represents a multivariate polynomial, i.e. an element of \( K[X_0, ..., X_{n-1}] \), where K is some ring or field.

Description of template class 'MPolynomial'

Monomials are products of power of variables, like xy^2z^3. Polynomials in n variables are constructed recursively with polynomials in n - 1 variables.

There is a specialization for polynomials with no indeterminates, i.e. constants.

See also: dgtal_multivariate_polynomial

Template Parameters

n	the number of variables or indeterminates.
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

Examples: math/polynomial-derivative.cpp, math/polynomial-read.cpp, math/polynomial2-derivative.cpp, and topology/trackImplicitPolynomialSurfaceToOFF.cpp.

Definition at line 964 of file MPolynomial.h.

Member Typedef Documentation

◆ Alloc

template<int n, typename TRing , class TAlloc >

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

Definition at line 985 of file MPolynomial.h.

◆ MPolyNM1

template<int n, typename TRing , class TAlloc >

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

Definition at line 986 of file MPolynomial.h.

◆ Ring

template<int n, typename TRing , class TAlloc >

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

Definition at line 984 of file MPolynomial.h.

◆ Size

template<int n, typename TRing , class TAlloc >

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

Definition at line 996 of file MPolynomial.h.

◆ Storage

template<int n, typename TRing , class TAlloc >

typedef IVector< MPolyNM1, typename Alloc::template rebind<MPolyNM1 >::other, (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 995 of file MPolynomial.h.

Constructor & Destructor Documentation

◆ MPolynomial() [1/5]

template<int n, typename TRing , class TAlloc >

DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial	(	bool	,
		Size	s,
		const Alloc &	)

inlineprivate

Private constructor for initializing an array of size s.

Definition at line 1014 of file MPolynomial.h.

1015 : myValue(s)

1016 {}

DGtal::MPolynomial::myValue

Storage myValue

Definition MPolynomial.h:1008

Referenced by DGtal::MPolynomial< 0, TRing, TAlloc >::operator*(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator+(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator-(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator-(), and DGtal::MPolynomial< 0, TRing, TAlloc >::operator/().

◆ MPolynomial() [2/5]

template<int n, typename TRing , class TAlloc >

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

inline

Constructs a zero polynomial

Definition at line 1045 of file MPolynomial.h.

1046 : myValue( allocator )

1047 {}

◆ MPolynomial() [3/5]

template<int n, typename TRing , class TAlloc >

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

inline

Constructs a constant polynomial with constant term v.

Definition at line 1052 of file MPolynomial.h.

1053 : myValue( 1, MPolyNM1( v ), allocator )

1054 {}

DGtal::MPolynomial::MPolyNM1

MPolynomial< n - 1, Ring, Alloc > MPolyNM1

Definition MPolynomial.h:986

◆ MPolynomial() [4/5]

template<int n, typename TRing , class TAlloc >

DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial	(	const MPolyNM1 &	pdm1,
		const Alloc &	)

inline

Constructs a polynomial of type MPolynomial<n, Ring> which is initialized with a polynomial of type MPolynomial<n-1, Ring>.

Definition at line 1060 of file MPolynomial.h.

1062 : myValue( 1, pdm1 )

1063 {}

◆ MPolynomial() [5/5]

template<int n, typename TRing , class TAlloc >

template<typename Ring2 , typename Alloc2 >

DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial	(	const MPolynomial< n, Ring2, Alloc2 > &	p,
		const Alloc &	allocator = Alloc() )

inline

Casts a polynomial of type MPolynomial<n, Ring2, Alloc2> to a polynomial of type MPolynomial<n, Ring, Alloc>.

Definition at line 1070 of file MPolynomial.h.

      : myValue( p.degree() + 1, MPolyNM1(), allocator )
    {
      for ( Size i = 0; i < myValue.size(); ++i )
        myValue[i] = p[i];
      normalize();
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

Member Function Documentation

◆ degree()

template<int n, typename TRing , class TAlloc >

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 1119 of file MPolynomial.h.

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

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

Referenced by DGtal::EhrhartPolynomial< TSpace, TInteger >::countInterior(), DGtal::MPolynomial< n, TRing, TAlloc >::operator*(), DGtal::EhrhartPolynomial< TSpace, TInteger >::remainderInterior(), and testMPolynomial().

◆ getAllocator()

template<int n, typename TRing , class TAlloc >

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

inline

Returns: the allocator for this object.

Definition at line 1107 of file MPolynomial.h.

    {
        return myValue.getAllocator();
    }

References DGtal::IVector< T, TAlloc, usePointers >::getAllocator(), and DGtal::MPolynomial< n, TRing, TAlloc >::myValue.

Referenced by DGtal::MPolynomialEvaluator< n, TRing, TAlloc, TX >::operator MPolyNM1(), DGtal::MPolynomial< n, TRing, TAlloc >::operator*(), and DGtal::MPolynomial< n, TRing, TAlloc >::operator-().

◆ isValid()

template<int n, typename TRing , class TAlloc >

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<int n, typename TRing , class TAlloc >

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

inline

Tests whether this polynomial is the zero polynomial.

Definition at line 1137 of file MPolynomial.h.

    {
      return myValue.size() == 0;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

Referenced by DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::MPolynomial< n, TRing, TAlloc >::operator*(), and DGtal::MPolynomial< n, TRing, TAlloc >::selfDisplay().

◆ leading()

template<int n, typename TRing , class TAlloc >

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 1129 of file MPolynomial.h.

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

References DGtal::IVector< T, TAlloc, usePointers >::back(), DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::myZeroPolynomial, and DGtal::IVector< T, TAlloc, usePointers >::size().

Referenced by testMPolynomial().

◆ normalize()

template<int n, typename TRing , class TAlloc >

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 1025 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);
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::isZero(), DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator!=() [1/2]

template<int n, typename TRing , class TAlloc >

bool DGtal::MPolynomial< n, TRing, TAlloc >::operator!= ( const MPolynomial< n, TRing, TAlloc > & q ) const

inline

Inequality operator.

Parameters

q	any polynomial of the same type as this.

Returns: 'true' iff this polynomial is different from q.

Definition at line 1505 of file MPolynomial.h.

    {
      return !(*this == q);
    }

◆ operator!=() [2/2]

template<int n, typename TRing , class TAlloc >

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

inline

Inequality operator with a constant.

Parameters

v	any value in the ring.

Returns: 'true' iff this polynomial is different from v.

Definition at line 1529 of file MPolynomial.h.

    {
      return !(*this == v);
    }

◆ operator()() [1/2]

template<int n, typename TRing , class TAlloc >

MPolynomialEvaluator< n, Ring, Alloc, Ring > DGtal::MPolynomial< n, TRing, TAlloc >::operator() ( const Ring & x ) const

inline

Evaluation in x.

Parameters

x	a value in the ring.

Returns: a functor for performing this evaluation

Definition at line 1169 of file MPolynomial.h.

    {
      return MPolynomialEvaluator<n, Ring, Alloc, Ring>( *this, x );
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomialEvaluator.

◆ operator()() [2/2]

template<int n, typename TRing , class TAlloc >

template<typename Ring2 >

MPolynomialEvaluator< n, Ring, Alloc, Ring2 > DGtal::MPolynomial< n, TRing, TAlloc >::operator() ( const Ring2 & x ) const

inline

Evaluation in x of type Ring2.

Template Parameters

Ring2 another ring (like a polynomial with less variables).

Parameters

x	a value in this ring.

Returns: a functor for performing this evaluation

Definition at line 1183 of file MPolynomial.h.

    {
      return MPolynomialEvaluator<n, Ring, Alloc, Ring2>( *this, x );
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomialEvaluator.

◆ operator*() [1/2]

template<int n, typename TRing , class TAlloc >

MPolynomial DGtal::MPolynomial< n, TRing, TAlloc >::operator* ( const MPolynomial< n, TRing, TAlloc > & p ) const

inline

Multiplies the polynomial with another polynomial.

Parameters

p	any polynomial of the same type.

Returns: the corresponding polynomial.

Todo: Multiplication could be optimized for monovariate polynomials.

Definition at line 1467 of file MPolynomial.h.

    {
      int d = p.degree() + degree();
      if (d < -1)
        d = -1;
      MPolynomial r( true, d + 1, getAllocator() );
      if (!isZero() && !p.isZero())
        for ( Size i = 0; i < r.myValue.size(); ++i )
          for ( Size j = 0; j < myValue.size(); ++j )
            if (i < j + p.myValue.size())
              r[i] += myValue[j] * p[i - j];
      r.normalize();
      return r;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::degree(), DGtal::MPolynomial< n, TRing, TAlloc >::getAllocator(), DGtal::MPolynomial< n, TRing, TAlloc >::isZero(), DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator*() [2/2]

template<int n, typename TRing , class TAlloc >

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

inline

Multiply by constant.

Parameters

v	any value in the ring.

Returns: the corresponding polynomial.

Definition at line 1196 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      for ( Size i = 0; i < myValue.size(); ++i )
        r[i] *= v;
      return r;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator*=() [1/2]

template<int n, typename TRing , class TAlloc >

MPolynomial & DGtal::MPolynomial< n, TRing, TAlloc >::operator*= ( const MPolynomial< n, TRing, TAlloc > & p )

inline

Self-multiplication by other polynomial.

Parameters

p	any polynomial of the same type.

Returns: a reference to this.

Definition at line 1222 of file MPolynomial.h.

    {
      return *this = *this * p;
    }

◆ operator*=() [2/2]

template<int n, typename TRing , class TAlloc >

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

inline

Self-multiplication by a constant.

Parameters

v	any value in the ring.

Returns: a reference to this.

Definition at line 1232 of file MPolynomial.h.

    {
      MPolynomial r( *this );
      for ( Size i = 0; i < myValue.size(); ++i )
        myValue[i] *= v;
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator+() [1/3]

template<int n, typename TRing , class TAlloc >

MPolynomial DGtal::MPolynomial< n, TRing, TAlloc >::operator+ ( const MPolyNM1 & q ) const

inline

Computes the sum of this polynomial with a polynomial with one less variable.

Parameters

q	any polynomial with n-1 indeterminates in the same ring.

Returns: the corresponding polynomial.

Definition at line 1346 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      if (r.myValue.size() < 1)
        r.myValue.resize(1);
      r[0] += q;
      r.normalize();
      return r;
    }

◆ operator+() [2/3]

template<int n, typename TRing , class TAlloc >

MPolynomial DGtal::MPolynomial< n, TRing, TAlloc >::operator+ ( const MPolynomial< n, TRing, TAlloc > & q ) const

inline

Computes the sum of two polynomials.

Parameters

q	any polynomial of this type.

Returns: the corresponding polynomial.

Definition at line 1283 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      if (r.myValue.size() < q.myValue.size())
        r.myValue.resize(q.myValue.size());
      for ( Size i = 0; i < q.myValue.size(); ++i )
        r[i] += q[i];
      r.normalize();
      return r;
    }

◆ operator+() [3/3]

template<int n, typename TRing , class TAlloc >

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

inline

Addition with a constant.

Parameters

v	any value in the ring.

Returns: the corresponding polynomial.

Definition at line 1377 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      if (r.myValue.size() < 1)
        r.myValue.resize(1);
      r[0] += v;
      r.normalize();
      return r;
    }

◆ operator+=() [1/3]

template<int n, typename TRing , class TAlloc >

MPolynomial & DGtal::MPolynomial< n, TRing, TAlloc >::operator+= ( const MPolyNM1 & q )

inline

Self-addition of this polynomial with a polynomial with one less variable.

Parameters

q	any polynomial with n-1 indeterminates in the same ring.

Returns: a reference to this.

Definition at line 1408 of file MPolynomial.h.

    {
      if (myValue.size() < 1)
        myValue.resize(1);
      myValue[0] += q;
      normalize();
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator+=() [2/3]

template<int n, typename TRing , class TAlloc >

MPolynomial & DGtal::MPolynomial< n, TRing, TAlloc >::operator+= ( const MPolynomial< n, TRing, TAlloc > & q )

inline

Adds q to this polynomial.

Parameters

q	any polynomial of this type.

Returns: a reference to this.

Definition at line 1315 of file MPolynomial.h.

    {
      if (myValue.size() < q.myValue.size())
        myValue.resize(q.myValue.size());
      for ( Size i = 0; i < q.myValue.size(); ++i )
        myValue[i] += q[i];
      normalize();
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator+=() [3/3]

template<int n, typename TRing , class TAlloc >

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

inline

Self-addition of a constant.

Parameters

v	any value in the ring.

Returns: a reference to this.

Definition at line 1437 of file MPolynomial.h.

    {
      if (myValue.size() < 1)
        myValue.resize(1);
      myValue[0] += v;
      normalize();
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator-() [1/4]

template<int n, typename TRing , class TAlloc >

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

inline

Returns: the additive inverse of the polynomial.

Definition at line 1270 of file MPolynomial.h.

    {
      MPolynomial r( true, myValue.size(), getAllocator() );
      for ( Size i = 0; i < myValue.size(); ++i )
        r[i] = -myValue[i];
      return r;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::getAllocator(), DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator-() [2/4]

template<int n, typename TRing , class TAlloc >

MPolynomial DGtal::MPolynomial< n, TRing, TAlloc >::operator- ( const MPolyNM1 & q ) const

inline

Computes the difference of this polynomial with a polynomial with one less variable.

Parameters

q	any polynomial with n-1 indeterminates in the same ring.

Returns: the corresponding polynomial.

Definition at line 1362 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      if (r.myValue.size() < 1)
        r.myValue.resize(1);
      r[0] -= q;
      r.normalize();
      return r;
    }

◆ operator-() [3/4]

template<int n, typename TRing , class TAlloc >

MPolynomial DGtal::MPolynomial< n, TRing, TAlloc >::operator- ( const MPolynomial< n, TRing, TAlloc > & q ) const

inline

Computes the difference of two polynomials.

Parameters

q	any polynomial of this type.

Returns: the corresponding polynomial.

Definition at line 1299 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      if (r.myValue.size() < q.myValue.size())
        r.myValue.resize(q.myValue.size());
      for ( Size i = 0; i < q.myValue.size(); ++i )
        r[i] -= q[i];
      r.normalize();
      return r;
    }

◆ operator-() [4/4]

template<int n, typename TRing , class TAlloc >

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

inline

Difference to a constant.

Parameters

v	any value in the ring.

Returns: the corresponding polynomial.

Definition at line 1392 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      if (r.myValue.size() < 1)
        r.myValue.resize(1);
      r[0] -= v;
      r.normalize();
      return r;
    }

◆ operator-=() [1/3]

template<int n, typename TRing , class TAlloc >

MPolynomial & DGtal::MPolynomial< n, TRing, TAlloc >::operator-= ( const MPolyNM1 & q )

inline

Self-subtraction of this polynomial with a polynomial with one less variable.

Parameters

q	any polynomial with n-1 indeterminates in the same ring.

Returns: a reference to this.

Definition at line 1423 of file MPolynomial.h.

    {
      if (myValue.size() < 1)
        myValue.resize(1);
      myValue[0] -= q;
      normalize();
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator-=() [2/3]

template<int n, typename TRing , class TAlloc >

MPolynomial & DGtal::MPolynomial< n, TRing, TAlloc >::operator-= ( const MPolynomial< n, TRing, TAlloc > & q )

inline

Subtracts q from this polynomial.

Parameters

q	any polynomial of this type.

Returns: a reference to this.

Definition at line 1330 of file MPolynomial.h.

    {
      if (myValue.size() < q.myValue.size())
        myValue.resize(q.myValue.size());
      for ( Size i = 0; i < q.myValue.size(); ++i )
        myValue[i] -= q[i];
      normalize();
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator-=() [3/3]

template<int n, typename TRing , class TAlloc >

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

inline

Self-subtraction of a constant.

Parameters

v	any value in the ring.

Returns: a reference to this.

Definition at line 1451 of file MPolynomial.h.

    {
      if (myValue.size() < 1)
        myValue.resize(1);
      myValue[0] -= v;
      normalize();
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator/()

template<int n, typename TRing , class TAlloc >

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

inline

Divide by constant.

Parameters

v	any value in the ring.

Returns: the corresponding polynomial.

Definition at line 1209 of file MPolynomial.h.

    {
      MPolynomial r(*this);
      for ( Size i = 0; i < myValue.size(); ++i )
        r[i] /= v;
      return r;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator/=()

template<int n, typename TRing , class TAlloc >

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

inline

Self-division by a constant.

Parameters

v	any value in the ring.

Returns: a reference to this.

Definition at line 1245 of file MPolynomial.h.

    {
      for ( Size i = 0; i < myValue.size(); ++i )
        myValue[i] /= v;
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator=()

template<int n, typename TRing , class TAlloc >

template<typename Ring2 , typename Alloc2 >

MPolynomial & DGtal::MPolynomial< n, TRing, TAlloc >::operator= ( const MPolynomial< n, Ring2, Alloc2 > & p )

inline

Copies a polynomial of type MPolynomial<n, Ring2, Alloc2> to this polynomial (of type MPolynomial<n, Ring, Alloc>).

Definition at line 1085 of file MPolynomial.h.

    {
      myValue.resize(p.degree() + 1);
      for ( Size i = 0; i < myValue.size(); ++i )
        myValue[i] = p[i];
      normalize();
      return *this;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator==() [1/2]

template<int n, typename TRing , class TAlloc >

bool DGtal::MPolynomial< n, TRing, TAlloc >::operator== ( const MPolynomial< n, TRing, TAlloc > & q ) const

inline

Equality operator.

Parameters

q	any polynomial of the same type as this.

Returns: 'true' iff this polynomial is equal to q.

Definition at line 1490 of file MPolynomial.h.

    {
      if (myValue.size() != q.myValue.size())
        return false;
      for (Size i = 0; i < myValue.size(); ++i)
        if (myValue[i] != q[i])
          return false;
      return true;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator==() [2/2]

template<int n, typename TRing , class TAlloc >

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

inline

Equality operator with a constant.

Parameters

v	any value in the ring.

Returns: 'true' iff this polynomial is equal to v.

Definition at line 1515 of file MPolynomial.h.

    {
      if ((v == 0) && (myValue.size() == 0))
        return true;
      if (myValue.size() != 1)
        return false;
      return myValue[0] == v;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator[]() [1/2]

template<int n, typename TRing , class TAlloc >

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 1147 of file MPolynomial.h.

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

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::IVector< T, TAlloc, usePointers >::resize(), and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ operator[]() [2/2]

template<int n, typename TRing , class TAlloc >

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

inline

Returns: a reference to the i-th coefficient, or zero if i > degree().

Definition at line 1157 of file MPolynomial.h.

    {
      return i < myValue.size() ? myValue[i] : myZeroPolynomial;
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, DGtal::MPolynomial< n, TRing, TAlloc >::myZeroPolynomial, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ selfDisplay()

template<int n, typename TRing , class TAlloc >

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

inline

Prints this polynomial to the stream s. N gives the number of variables; this is needed for recursive printing.

Parameters

s	the output stream where the object is written.
N	the number of variables.

Definition at line 1546 of file MPolynomial.h.

    {
      if (isZero())
        s << (Ring) 0;
      else
        {
          Size nonzero = 0;
          for (Size i = 0; i < myValue.size(); ++i)
            if (!myValue[i].isZero())
              ++nonzero;
          if (nonzero > 1) s << "(";
          bool first = true;
          for (Size i = 0; i < myValue.size(); ++i)
            if (!myValue[i].isZero())
              {
                if (first) first = false;
                else       s << " + ";
                myValue[i].selfDisplay(s, N);
                if (i > 0)
                  {
                    s << " ";
                    s << "X_" << N - n;
                    if (i > 1) s << "^" << i;
                  }
              }
          if (nonzero > 1)
            s << ")";
        }
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::isZero(), DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::size().

◆ swap()

template<int n, typename TRing , class TAlloc >

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

inline

Swaps two polynomials.

Parameters

p	the polynomial to exchange with.

Definition at line 1099 of file MPolynomial.h.

    {
        myValue.swap(p.myValue);
    }

References DGtal::MPolynomial< n, TRing, TAlloc >::myValue, and DGtal::IVector< T, TAlloc, usePointers >::swap().

Friends And Related Symbol Documentation

◆ euclidDiv

template<int n, typename TRing , class TAlloc >

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

template<int n, typename TRing , class TAlloc >

template<int NN, int nn, typename TT , typename AA >

friend class MPolynomialDerivativeComputer

friend

Definition at line 969 of file MPolynomial.h.

◆ MPolynomialEvaluator

template<int n, typename TRing , class TAlloc >

template<int nn, typename TT , typename AA , typename SS >

friend class MPolynomialEvaluator

friend

Definition at line 978 of file MPolynomial.h.

Referenced by DGtal::MPolynomial< n, TRing, TAlloc >::operator()(), and DGtal::MPolynomial< n, TRing, TAlloc >::operator()().

◆ MPolynomialEvaluatorImpl

template<int n, typename TRing , class TAlloc >

template<int nn, typename TT , typename HLHL , typename AA , typename SS >

friend class MPolynomialEvaluatorImpl

friend

Definition at line 981 of file MPolynomial.h.

◆ operator*

template<int n, typename TRing , class TAlloc >

MPolynomial operator*	(	const Ring &	v,
		const MPolynomial< n, TRing, TAlloc > &	p )

friend

Multiplication by a constant from the left.

Parameters

v	any value in the ring.
p	any polynomial of this type.

Returns: the corresponding polynomial.

Definition at line 1259 of file MPolynomial.h.

    {
      MPolynomial r(p);
      for ( Size i = 0; i < p.myValue.size(); ++i )
        r[i] *= v;
      return r;
    }

Field Documentation

◆ myValue

template<int n, typename TRing , class TAlloc >

Storage DGtal::MPolynomial< n, TRing, TAlloc >::myValue

private

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 1008 of file MPolynomial.h.

◆ myZeroPolynomial

template<int n, typename TRing , class TAlloc >

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

staticprivate

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

Definition at line 1001 of file MPolynomial.h.

Referenced by DGtal::MPolynomial< n, TRing, TAlloc >::leading(), and DGtal::MPolynomial< n, TRing, TAlloc >::operator[]().

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

MPolynomial.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Alloc

◆ MPolyNM1

◆ Ring

◆ Size

◆ Storage

Constructor & Destructor Documentation

◆ MPolynomial() [1/5]

◆ MPolynomial() [2/5]

◆ MPolynomial() [3/5]

◆ MPolynomial() [4/5]

◆ MPolynomial() [5/5]

Member Function Documentation

◆ degree()

◆ getAllocator()

◆ isValid()

◆ isZero()

◆ leading()

◆ normalize()

◆ 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+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator-=() [1/3]

◆ operator-=() [2/3]

◆ operator-=() [3/3]

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ selfDisplay()

◆ swap()

Friends And Related Symbol Documentation

◆ euclidDiv

◆ MPolynomialDerivativeComputer

◆ MPolynomialEvaluator

◆ MPolynomialEvaluatorImpl

◆ operator*

Field Documentation

◆ myValue

◆ myZeroPolynomial