template class Tps<class>

(Return to index)

Truncated power series.

Truncated power series in n variables of type T. All divide operations throw DivideError, if the constant part of the divisor is zero. All operations throw SizeError, if the operands are not consistent. All operations throw RangeError, if an index is out of range.

Type:	Instantiable
Include file:	./Algebra/Tps.hh

Synopsis (including inherited members):

• Public members:
  • Tps (int,int) ;
  • Tps (const T&) ;
  • Tps (int) ;
  • Tps () ;
  • Tps (const Tps<T>&) ;
  • ~Tps () ;
  • Tps<T>& operator= (const Tps<T>&) ;
  • Tps<T>& operator= (const T&) ;
  • Tps<T> filter (int,int)const ;
  • Tps<T> truncate (int) ;
  • const T getCoefficient (int)const ;
  • void setCoefficient (int,const T&) ;
  • const T getCoefficient (const TpsMonomial&)const ;
  • void setCoefficient (const TpsMonomial&,const T&) ;
  • const T operator[] (int)const ;
  • T& operator[] (int) ;
  • const T operator[] (const TpsMonomial&)const ;
  • T& operator[] (const TpsMonomial&) ;
  • static Tps<T> makeVariable (int,int) ;
  • static Tps<T> makeVarPower (int,int,int) ;
  • static Tps<T> makeMonomial (const TpsMonomial&,const T&) ;
  • Tps<T> operator+ ()const ;
  • Tps<T> operator- ()const ;
  • Tps<T>& operator+= (const Tps<T>&) ;
  • Tps<T>& operator-= (const Tps<T>&) ;
  • Tps<T>& operator*= (const Tps<T>&) ;
  • Tps<T>& operator/= (const Tps<T>&) ;
  • Tps<T>& operator+= (const T&) ;
  • Tps<T>& operator-= (const T&) ;
  • Tps<T>& operator*= (const T&) ;
  • Tps<T>& operator/= (const T&) ;
  • bool operator== (const Tps<T>&)const ;
  • bool operator== (const T&)const ;
  • bool operator!= (const Tps<T>&)const ;
  • bool operator!= (const T&)const ;
  • Tps<T> substitute (const Matrix<T>&)const ;
  • Tps<T> substitute (const VpsMap<T>&)const ;
  • T evaluate (const Vector<T>&)const ;
  • void clear () ;
  • Tps<T> inverse (int)const ;
  • Tps<T> multiply (const Tps<T>&,int)const ;
  • Tps<T> derivative (int)const ;
  • Tps<T> integral (int)const ;
  • Tps<T> multiplyVariable (int)const ;
  • Tps<T> scaleMonomials (const Tps<T>&)const ;
  • Tps<T> Taylor (const T[],int)const ;
  • int getMaxOrder ()const ;
  • int getTruncOrder ()const ;
  • int getVariables ()const ;
  • int getSize ()const ;
  • std::istream& get (std::istream&) ;
  • std::ostream& put (std::ostream&)const ;
  • const TpsMonomial& getExponents (int)const ;
  • int getOrder (int)const ;
  • int getSize (int)const ;
  • bool isConstant ()const ;
  • static int getGlobalTruncOrder () ;
  • static void setGlobalTruncOrder (int) ;
  • static const int EXACT ;

Documentation:

• Public members:

  static const int EXACT ;

  Representation of infinite precision.

  Tps<T> Taylor (const T[],int)const ;

  Taylor series.
  Expand truncated Taylor series with coefficiens series and order n.

  Tps (int,int) ;

  Constructor.
  Define maximum order and number of variables, value = 0.

  Tps (const T&) ;

  Conversion.
  From constant y.

  Tps (int) ;

  Conversion.
  From int y.

  void clear () ;

  Set to zero.

  Tps<T> derivative (int)const ;

  Partial derivative.
  Return partial derivative with respect to variable var. Return zero for a constant.

  T evaluate (const Vector<T>&)const ;

  Substitute.
  Substitute vector v in Tps, giving a constant.

  Tps<T> filter (int,int)const ;

  Extract orders.
  Return the orders lowOrder through highOrder, both included.

  std::istream& get (std::istream&) ;

  Get Tps from the stream is.

  const T getCoefficient (int)const ;

  Get coefficient.
  Return the coefficient denoted by the Giorgelli index. Throw RangeError, if index is out of range.

  const T getCoefficient (const TpsMonomial&)const ;

  Get coefficient.
  Return the coefficient denoted by monomial exponents. Throw RangeError, if index is out of range.

  const TpsMonomial& getExponents (int)const ;

  Get exponents.
  Return the exponent array for the given Giorgelli index.

  static int getGlobalTruncOrder () ;

  Get global truncation order.

  int getMaxOrder ()const ;

  Get maximal order.

  int getOrder (int)const ;

  Get order.
  Return the order of the monomial with the given Giorgelli index.

  int getSize ()const ;

  Get number of coefficients.

  int getSize (int)const ;

  Size.
  Return the number of monomials required for a Tps of order order.

  int getTruncOrder ()const ;

  Get truncation order.

  int getVariables ()const ;

  Get number of variables.

  Tps<T> integral (int)const ;

  Partial integral.
  Return partial integral with respect to variable var. Throw LogicalError for a constant.

  Tps<T> inverse (int)const ;

  Reciprocal value.

  bool isConstant ()const ;

  Test for constant.

  static Tps<T> makeMonomial (const TpsMonomial&,const T&) ;

  Make monomial.
  Construct the monomial with the exponents in m and coefficient t.

  static Tps<T> makeVarPower (int,int,int) ;

  Make power.
  Construct power of variable var, with total of nVar variables.

  static Tps<T> makeVariable (int,int) ;

  Make variable.
  Construct the variable identified by the index var, with total of nVar variables.

  Tps<T> multiply (const Tps<T>&,int)const ;

  Truncated multiplication.

  Tps<T> multiplyVariable (int)const ;

  Multiply by variable var.
  Throw LogicalError for a constant.

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

  Inequality operator.

  bool operator!= (const T&)const ;

  Inequality with constant.

  Tps<T>& operator*= (const Tps<T>&) ;

  Multiply and assign.

  Tps<T>& operator*= (const T&) ;

  Multiply by constant and assign.

  Tps<T> operator+ ()const ;

  Unary plus.

  Tps<T>& operator+= (const Tps<T>&) ;

  Add and assign.

  Tps<T>& operator+= (const T&) ;

  Add constant and assign.

  Tps<T> operator- ()const ;

  Unary minus.

  Tps<T>& operator-= (const Tps<T>&) ;

  Subtract and assign.

  Tps<T>& operator-= (const T&) ;

  Subtract constant and assign.

  Tps<T>& operator/= (const Tps<T>&) ;

  Divide and assign.

  Tps<T>& operator/= (const T&) ;

  Divide by constant and assign.

  Tps<T>& operator= (const T&) ;

  Convert and assign.

  bool operator== (const Tps<T>&)const ;

  Equality operator.

  bool operator== (const T&)const ;

  Equlatity with constant.

  const T operator[] (int)const ;

  Get coefficient.
  Return the coefficient denoted by the Giorgelli index. Result is undefined, if index is out of range.

  T& operator[] (int) ;

  Get coefficient.
  REturn a reference to the coefficient denoted by the Giorgelli index. Result is undefined, if index is out of range.

  const T operator[] (const TpsMonomial&)const ;

  Get coefficient.
  Return the coefficient denoted by monomial exponents. Result is undefined, if index is out of range.

  T& operator[] (const TpsMonomial&) ;

  Get coefficient.
  Return reference to the coefficient denoted by monomial exponents. Result is undefined, if index is out of range.

  std::ostream& put (std::ostream&)const ;

  Put Tps to the stream is.

  Tps<T> scaleMonomials (const Tps<T>&)const ;

  Multiply monomial-wise.
  Construct new Tps<T> by multipying corresponding monomials pair-wise.

  void setCoefficient (int,const T&) ;

  Set coefficient.
  Assign the coefficient denoted by the Giorgelli index. Expand size if index is out of range.

  void setCoefficient (const TpsMonomial&,const T&) ;

  Set coefficient.
  Assign the coefficient denoted by monomial exponents. Throw RangeError, if index is out of range.

  static void setGlobalTruncOrder (int) ;

  Set global truncation order.

  Tps<T> substitute (const Matrix<T>&)const ;

  Substitute.
  Substitute matrix M in Tps, giving new Tps.

  Tps<T> substitute (const VpsMap<T>&)const ;

  Substitute.
  Substitute map m in Tps, giving new Tps.

  Tps<T> truncate (int) ;

  Truncate.
  Change the maximum order to trunc; may also reserve more space.