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 std::allocator_traits< Alloc >::template rebind_alloc< MPolyNM1 >,(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 969 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 990 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 991 of file MPolynomial.h.

◆ Ring

template<int n, typename TRing, class TAlloc>

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

Definition at line 989 of file MPolynomial.h.

◆ Size

template<int n, typename TRing, class TAlloc>

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

Definition at line 1001 of file MPolynomial.h.

◆ Storage

template<int n, typename TRing, class TAlloc>

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() [1/5]

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 1019 of file MPolynomial.h.

1020 : myValue(s)

1021 {}

DGtal::MPolynomial

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

Definition MPolynomial.h:970

DGtal::MPolynomial::myValue

Storage myValue

Definition MPolynomial.h:1013

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 1050 of file MPolynomial.h.

1051 : myValue( allocator )

1052 {}

◆ 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 1057 of file MPolynomial.h.

1058 : myValue( 1, MPolyNM1( v ), allocator )

1059 {}

DGtal::MPolynomial::MPolyNM1

MPolynomial< n - 1, Ring, Alloc > MPolyNM1

Definition MPolynomial.h:991

◆ 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 1065 of file MPolynomial.h.

1067 : myValue( 1, pdm1 )

1068 {}

◆ 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 1075 of file MPolynomial.h.

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

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 1124 of file MPolynomial.h.

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

Referenced by DGtal::MPolynomialDerivativeComputer< N, n, Ring, Alloc >::computeDerivative(), DGtal::MPolynomialDerivativeComputer< 0, n, Ring, Alloc >::computeDerivative(), DGtal::MPolynomial< n - 1, Ring, Alloc >::euclidDiv, DGtal::MPolynomial< Space::dimension, Scalar >::operator*(), DGtal::MPolynomial< Space::dimension, Scalar >::operator=(), 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 1112 of file MPolynomial.h.

    {
        return myValue.getAllocator();
    }

Referenced by DGtal::derivative(), DGtal::MPolynomial< n - 1, Ring, Alloc >::euclidDiv, DGtal::gcd(), and DGtal::MPolynomial< Space::dimension, Scalar >::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 1142 of file MPolynomial.h.

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

Referenced by DGtal::gcd(), DGtal::MPolynomial< Space::dimension, Scalar >::normalize(), DGtal::MPolynomial< Space::dimension, Scalar >::operator*(), and DGtal::MPolynomial< Space::dimension, Scalar >::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 1134 of file MPolynomial.h.

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

Referenced by DGtal::MPolynomial< n - 1, Ring, Alloc >::euclidDiv, DGtal::gcd(), and 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 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!=() [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 1510 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 1534 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 1174 of file MPolynomial.h.

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

◆ 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 1188 of file MPolynomial.h.

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

◆ 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.

Definition at line 1472 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;
    }

◆ 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 1201 of file MPolynomial.h.

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

◆ 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 1227 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 1237 of file MPolynomial.h.

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

◆ 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 1351 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 1288 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 1382 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 1413 of file MPolynomial.h.

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

◆ 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 1320 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;
    }

◆ 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 1442 of file MPolynomial.h.

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

◆ 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 1275 of file MPolynomial.h.

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

◆ 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 1367 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 1304 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 1397 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 1428 of file MPolynomial.h.

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

◆ 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 1335 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;
    }

◆ 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 1456 of file MPolynomial.h.

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

◆ 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 1214 of file MPolynomial.h.

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

◆ 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 1250 of file MPolynomial.h.

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

◆ 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 1090 of file MPolynomial.h.

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

◆ 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 1495 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;
    }

◆ 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 1520 of file MPolynomial.h.

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

◆ 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 1152 of file MPolynomial.h.

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

◆ 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 1162 of file MPolynomial.h.

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

◆ 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 1551 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 << ")";
        }
    }

◆ 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 1104 of file MPolynomial.h.

    {
        myValue.swap(p.myValue);
    }

◆ 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 974 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 983 of file MPolynomial.h.

Referenced by DGtal::MPolynomial< Space::dimension, Scalar >::operator()(), and DGtal::MPolynomial< Space::dimension, Scalar >::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 986 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 1264 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 1013 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 1006 of file MPolynomial.h.

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