DGtal  1.2.0
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DGtal::MPolynomial< n, TRing, TAlloc > Class Template Reference

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 >:
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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. More...
 

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 > &, const MPolynomial< 1, TRing, TAlloc > &, MPolynomial< 1, TRing, TAlloc > &, MPolynomial< 1, TRing, TAlloc > &)
 
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
nthe number of variables or indeterminates.
TRingthe type chosen for the polynomial, defines also the type of the coefficents (generally int, float or double).
TAllocis 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 954 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 975 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 976 of file MPolynomial.h.

◆ Ring

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

Definition at line 974 of file MPolynomial.h.

◆ Size

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

Definition at line 986 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 985 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 1004 of file MPolynomial.h.

1005  : myValue(s)
1006  {}

Referenced by 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 1035 of file MPolynomial.h.

1036  : myValue( allocator )
1037  {}

◆ 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 1042 of file MPolynomial.h.

1043  : myValue( 1, MPolyNM1( v ), allocator )
1044  {}
DGtal::MPolynomial::MPolyNM1
MPolynomial< n - 1, Ring, Alloc > MPolyNM1
Definition: MPolynomial.h:976

◆ 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 1050 of file MPolynomial.h.

1052  : myValue( 1, pdm1 )
1053  {}

◆ 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 1060 of file MPolynomial.h.

1062  : myValue( p.degree() + 1, MPolyNM1(), allocator )
1063  {
1064  for ( Size i = 0; i < myValue.size(); ++i )
1065  myValue[i] = p[i];
1066  normalize();
1067  }
DGtal::IVector::size
Size size() const
Definition: MPolynomial.h:742
Size
HalfEdgeDataStructure::Size Size
Definition: testHalfEdgeDataStructure.cpp:50

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 1109 of file MPolynomial.h.

1110  {
1111  return (int)(myValue.size() - 1);
1112  }

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

Referenced by DGtal::MPolynomial< n, TRing, TAlloc >::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 1097 of file MPolynomial.h.

1098  {
1099  return myValue.getAllocator();
1100  }
DGtal::IVector::getAllocator
Alloc getAllocator() const
Definition: MPolynomial.h:782

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 1127 of file MPolynomial.h.

1128  {
1129  return myValue.size() == 0;
1130  }

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 1119 of file MPolynomial.h.

1120  {
1121  return myValue.size() ? myValue.back() : myZeroPolynomial;
1122  }
DGtal::IVector::back
const T & back() const
Definition: MPolynomial.h:762
DGtal::MPolynomial::myZeroPolynomial
static MPolyNM1 myZeroPolynomial
The zero polynomial of n-1 variables for a n-multivariate polynomial.
Definition: MPolynomial.h:991

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 1015 of file MPolynomial.h.

1016  {
1017  Size dp1 = myValue.size();
1018  while ( dp1 )
1019  {
1020  if (myValue[dp1 - 1].isZero())
1021  --dp1;
1022  else
1023  break;
1024  }
1025  if (dp1 < myValue.size())
1026  myValue.resize(dp1);
1027  }
DGtal::IVector::resize
void resize(Size aSize, const T &entry=T())
Definition: MPolynomial.h:747
DGtal::MPolynomial::isZero
bool isZero() const
Definition: MPolynomial.h:1127

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().

Referenced by DGtal::MPolynomialDerivativeComputer< 0, n, Ring, Alloc >::computeDerivative(), DGtal::MPolynomialDerivativeComputer< N, n, Ring, Alloc >::computeDerivative(), DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial(), DGtal::MPolynomial< n, TRing, TAlloc >::operator+=(), DGtal::MPolynomial< n, TRing, TAlloc >::operator-=(), and DGtal::MPolynomial< n, TRing, TAlloc >::operator=().

◆ 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
qany polynomial of the same type as this.
Returns
'true' iff this polynomial is different from q.

Definition at line 1495 of file MPolynomial.h.

1496  {
1497  return !(*this == q);
1498  }

◆ 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
vany value in the ring.
Returns
'true' iff this polynomial is different from v.

Definition at line 1519 of file MPolynomial.h.

1520  {
1521  return !(*this == v);
1522  }

◆ 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
xa value in the ring.
Returns
a functor for performing this evaluation

Definition at line 1159 of file MPolynomial.h.

1160  {
1161  return MPolynomialEvaluator<n, Ring, Alloc, Ring>( *this, x );
1162  }

◆ 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
Ring2another ring (like a polynomial with less variables).
Parameters
xa value in this ring.
Returns
a functor for performing this evaluation

Definition at line 1173 of file MPolynomial.h.

1174  {
1175  return MPolynomialEvaluator<n, Ring, Alloc, Ring2>( *this, x );
1176  }

◆ 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
pany polynomial of the same type.
Returns
the corresponding polynomial.
Todo:
Multiplication could be optimized for monovariate polynomials.

Definition at line 1457 of file MPolynomial.h.

1458  {
1459  int d = p.degree() + degree();
1460  if (d < -1)
1461  d = -1;
1462  MPolynomial r( true, d + 1, getAllocator() );
1463  if (!isZero() && !p.isZero())
1464  for ( Size i = 0; i < r.myValue.size(); ++i )
1465  for ( Size j = 0; j < myValue.size(); ++j )
1466  if (i < j + p.myValue.size())
1467  r[i] += myValue[j] * p[i - j];
1468  r.normalize();
1469  return r;
1470  }
DGtal::MPolynomial::getAllocator
Alloc getAllocator() const
Definition: MPolynomial.h:1097
DGtal::MPolynomial::degree
int degree() const
Definition: MPolynomial.h:1109
DGtal::MPolynomial::MPolynomial
MPolynomial(bool, Size s, const Alloc &)
Definition: MPolynomial.h:1004

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
vany value in the ring.
Returns
the corresponding polynomial.

Definition at line 1186 of file MPolynomial.h.

1187  {
1188  MPolynomial r(*this);
1189  for ( Size i = 0; i < myValue.size(); ++i )
1190  r[i] *= v;
1191  return r;
1192  }

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
pany polynomial of the same type.
Returns
a reference to this.

Definition at line 1212 of file MPolynomial.h.

1213  {
1214  return *this = *this * p;
1215  }

◆ 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
vany value in the ring.
Returns
a reference to this.

Definition at line 1222 of file MPolynomial.h.

1223  {
1224  MPolynomial r( *this );
1225  for ( Size i = 0; i < myValue.size(); ++i )
1226  myValue[i] *= v;
1227  return *this;
1228  }

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
qany polynomial with n-1 indeterminates in the same ring.
Returns
the corresponding polynomial.

Definition at line 1336 of file MPolynomial.h.

1337  {
1338  MPolynomial r(*this);
1339  if (r.myValue.size() < 1)
1340  r.myValue.resize(1);
1341  r[0] += q;
1342  r.normalize();
1343  return r;
1344  }

◆ 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
qany polynomial of this type.
Returns
the corresponding polynomial.

Definition at line 1273 of file MPolynomial.h.

1274  {
1275  MPolynomial r(*this);
1276  if (r.myValue.size() < q.myValue.size())
1277  r.myValue.resize(q.myValue.size());
1278  for ( Size i = 0; i < q.myValue.size(); ++i )
1279  r[i] += q[i];
1280  r.normalize();
1281  return r;
1282  }

◆ 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
vany value in the ring.
Returns
the corresponding polynomial.

Definition at line 1367 of file MPolynomial.h.

1368  {
1369  MPolynomial r(*this);
1370  if (r.myValue.size() < 1)
1371  r.myValue.resize(1);
1372  r[0] += v;
1373  r.normalize();
1374  return r;
1375  }

◆ 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
qany polynomial with n-1 indeterminates in the same ring.
Returns
a reference to this.

Definition at line 1398 of file MPolynomial.h.

1399  {
1400  if (myValue.size() < 1)
1401  myValue.resize(1);
1402  myValue[0] += q;
1403  normalize();
1404  return *this;
1405  }

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
qany polynomial of this type.
Returns
a reference to this.

Definition at line 1305 of file MPolynomial.h.

1306  {
1307  if (myValue.size() < q.myValue.size())
1308  myValue.resize(q.myValue.size());
1309  for ( Size i = 0; i < q.myValue.size(); ++i )
1310  myValue[i] += q[i];
1311  normalize();
1312  return *this;
1313  }

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
vany value in the ring.
Returns
a reference to this.

Definition at line 1427 of file MPolynomial.h.

1428  {
1429  if (myValue.size() < 1)
1430  myValue.resize(1);
1431  myValue[0] += v;
1432  normalize();
1433  return *this;
1434  }

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 1260 of file MPolynomial.h.

1261  {
1262  MPolynomial r( true, myValue.size(), getAllocator() );
1263  for ( Size i = 0; i < myValue.size(); ++i )
1264  r[i] = -myValue[i];
1265  return r;
1266  }

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
qany polynomial with n-1 indeterminates in the same ring.
Returns
the corresponding polynomial.

Definition at line 1352 of file MPolynomial.h.

1353  {
1354  MPolynomial r(*this);
1355  if (r.myValue.size() < 1)
1356  r.myValue.resize(1);
1357  r[0] -= q;
1358  r.normalize();
1359  return r;
1360  }

◆ 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
qany polynomial of this type.
Returns
the corresponding polynomial.

Definition at line 1289 of file MPolynomial.h.

1290  {
1291  MPolynomial r(*this);
1292  if (r.myValue.size() < q.myValue.size())
1293  r.myValue.resize(q.myValue.size());
1294  for ( Size i = 0; i < q.myValue.size(); ++i )
1295  r[i] -= q[i];
1296  r.normalize();
1297  return r;
1298  }

◆ 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
vany value in the ring.
Returns
the corresponding polynomial.

Definition at line 1382 of file MPolynomial.h.

1383  {
1384  MPolynomial r(*this);
1385  if (r.myValue.size() < 1)
1386  r.myValue.resize(1);
1387  r[0] -= v;
1388  r.normalize();
1389  return r;
1390  }

◆ 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
qany polynomial with n-1 indeterminates in the same ring.
Returns
a reference to this.

Definition at line 1413 of file MPolynomial.h.

1414  {
1415  if (myValue.size() < 1)
1416  myValue.resize(1);
1417  myValue[0] -= q;
1418  normalize();
1419  return *this;
1420  }

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
qany polynomial of this type.
Returns
a reference to this.

Definition at line 1320 of file MPolynomial.h.

1321  {
1322  if (myValue.size() < q.myValue.size())
1323  myValue.resize(q.myValue.size());
1324  for ( Size i = 0; i < q.myValue.size(); ++i )
1325  myValue[i] -= q[i];
1326  normalize();
1327  return *this;
1328  }

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
vany value in the ring.
Returns
a reference to this.

Definition at line 1441 of file MPolynomial.h.

1442  {
1443  if (myValue.size() < 1)
1444  myValue.resize(1);
1445  myValue[0] -= v;
1446  normalize();
1447  return *this;
1448  }

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
vany value in the ring.
Returns
the corresponding polynomial.

Definition at line 1199 of file MPolynomial.h.

1200  {
1201  MPolynomial r(*this);
1202  for ( Size i = 0; i < myValue.size(); ++i )
1203  r[i] /= v;
1204  return r;
1205  }

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
vany value in the ring.
Returns
a reference to this.

Definition at line 1235 of file MPolynomial.h.

1236  {
1237  for ( Size i = 0; i < myValue.size(); ++i )
1238  myValue[i] /= v;
1239  return *this;
1240  }

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 1075 of file MPolynomial.h.

1077  {
1078  myValue.resize(p.degree() + 1);
1079  for ( Size i = 0; i < myValue.size(); ++i )
1080  myValue[i] = p[i];
1081  normalize();
1082  return *this;
1083  }

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
qany polynomial of the same type as this.
Returns
'true' iff this polynomial is equal to q.

Definition at line 1480 of file MPolynomial.h.

1481  {
1482  if (myValue.size() != q.myValue.size())
1483  return false;
1484  for (Size i = 0; i < myValue.size(); ++i)
1485  if (myValue[i] != q[i])
1486  return false;
1487  return true;
1488  }

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
vany value in the ring.
Returns
'true' iff this polynomial is equal to v.

Definition at line 1505 of file MPolynomial.h.

1506  {
1507  if ((v == 0) && (myValue.size() == 0))
1508  return true;
1509  if (myValue.size() != 1)
1510  return false;
1511  return myValue[0] == v;
1512  }

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 1137 of file MPolynomial.h.

1138  {
1139  if (i >= myValue.size())
1140  myValue.resize(i + 1);
1141  return myValue[i];
1142  }

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 1147 of file MPolynomial.h.

1148  {
1149  return i < myValue.size() ? myValue[i] : myZeroPolynomial;
1150  }

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
sthe output stream where the object is written.
Nthe number of variables.

Definition at line 1536 of file MPolynomial.h.

1537  {
1538  if (isZero())
1539  s << (Ring) 0;
1540  else
1541  {
1542  Size nonzero = 0;
1543  for (Size i = 0; i < myValue.size(); ++i)
1544  if (!myValue[i].isZero())
1545  ++nonzero;
1546  if (nonzero > 1) s << "(";
1547  bool first = true;
1548  for (Size i = 0; i < myValue.size(); ++i)
1549  if (!myValue[i].isZero())
1550  {
1551  if (first) first = false;
1552  else s << " + ";
1553  myValue[i].selfDisplay(s, N);
1554  if (i > 0)
1555  {
1556  s << " ";
1557  s << "X_" << N - n;
1558  if (i > 1) s << "^" << i;
1559  }
1560  }
1561  if (nonzero > 1)
1562  s << ")";
1563  }
1564  }

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
pthe polynomial to exchange with.

Definition at line 1089 of file MPolynomial.h.

1090  {
1091  myValue.swap(p.myValue);
1092  }
DGtal::IVector::swap
void swap(IVector &v)
Definition: MPolynomial.h:772

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

Friends And Related Function Documentation

◆ euclidDiv

template<int n, typename TRing , class TAlloc >
void euclidDiv ( const MPolynomial< 1, TRing, TAlloc > &  ,
const MPolynomial< 1, TRing, TAlloc > &  ,
MPolynomial< 1, TRing, TAlloc > &  ,
MPolynomial< 1, TRing, TAlloc > &   
)
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 959 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 968 of file MPolynomial.h.

◆ 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 971 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
vany value in the ring.
pany polynomial of this type.
Returns
the corresponding polynomial.

Definition at line 1249 of file MPolynomial.h.

1250  {
1251  MPolynomial r(p);
1252  for ( Size i = 0; i < p.myValue.size(); ++i )
1253  r[i] *= v;
1254  return r;
1255  }

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 998 of file MPolynomial.h.

Referenced by DGtal::MPolynomialDerivativeComputer< 0, n, Ring, Alloc >::computeDerivative(), DGtal::MPolynomialDerivativeComputer< N, n, Ring, Alloc >::computeDerivative(), DGtal::MPolynomial< n, TRing, TAlloc >::degree(), DGtal::MPolynomialEvaluator< n, TRing, TAlloc, TX >::evaluate(), DGtal::MPolynomial< n, TRing, TAlloc >::getAllocator(), DGtal::MPolynomial< 0, TRing, TAlloc >::isZero(), DGtal::MPolynomial< n, TRing, TAlloc >::isZero(), DGtal::MPolynomial< n, TRing, TAlloc >::leading(), DGtal::MPolynomial< n, TRing, TAlloc >::MPolynomial(), DGtal::MPolynomial< n, TRing, TAlloc >::normalize(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator const Ring &(), DGtal::MPolynomialEvaluator< n, TRing, TAlloc, TX >::operator MPolyNM1(), DGtal::MPolynomialEvaluator< 1, TRing, TAlloc, TX >::operator X(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator!=(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator()(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator*(), DGtal::MPolynomial< n, TRing, TAlloc >::operator*(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator*=(), DGtal::MPolynomial< n, TRing, TAlloc >::operator*=(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator+(), DGtal::MPolynomial< n, TRing, TAlloc >::operator+=(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator+=(), DGtal::MPolynomial< n, TRing, TAlloc >::operator-(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator-(), DGtal::MPolynomial< n, TRing, TAlloc >::operator-=(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator-=(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator/(), DGtal::MPolynomial< n, TRing, TAlloc >::operator/(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator/=(), DGtal::MPolynomial< n, TRing, TAlloc >::operator/=(), DGtal::MPolynomial< n, TRing, TAlloc >::operator=(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator=(), DGtal::MPolynomial< n, TRing, TAlloc >::operator==(), DGtal::MPolynomial< 0, TRing, TAlloc >::operator==(), DGtal::MPolynomial< n, TRing, TAlloc >::operator[](), DGtal::MPolynomial< n, TRing, TAlloc >::selfDisplay(), DGtal::MPolynomial< 0, TRing, TAlloc >::selfDisplay(), DGtal::MPolynomial< 0, TRing, TAlloc >::swap(), and DGtal::MPolynomial< n, TRing, TAlloc >::swap().

◆ 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 991 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:
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