template class FTps<class,int>

(Return to index)

Truncated power series in N variables of type T.

All divide operations throw DivideError, if the constant part of the divisor is zero.

Type:	Instantiable
Include file:	./FixedAlgebra/FTps.hh

Synopsis (including inherited members):

• Public members:
  • FTps () ;
  • FTps (const T&) ;
  • FTps (int) ;
  • FTps (int,int) ;
  • FTps (const FTps&) ;
  • ~FTps () ;
  • FTps& operator= (const FTps&) ;
  • FTps& operator= (const T&) ;
  • const T getCoefficient (int)const ;
  • void setCoefficient (int,const T&) ;
  • const T getCoefficient (const FMonomial<N>&)const ;
  • void setCoefficient (const FMonomial<N>&,const T&) ;
  • inline const T operator[] (int)const ;
  • inline T& operator[] (int) ;
  • const T operator[] (const FMonomial<N>&)const ;
  • T& operator[] (const FMonomial<N>&) ;
  • T* begin ()const ;
  • T* end ()const ;
  • static const FMonomial<N>& getExponents (int) ;
  • static int getIndex (const FMonomial<N>&) ;
  • static inline const Array1D<int>& getProductArray (int) ;
  • static inline const Array1D<TpsSubstitution>& getSubTable () ;
  • int getMaxOrder ()const ;
  • int getSize ()const ;
  • static int getSize (int) ;
  • int getTruncOrder ()const ;
  • int getVariables ()const ;
  • static void setGlobalTruncOrder (int) ;
  • static int getGlobalTruncOrder () ;
  • FTps filter (int,int)const ;
  • FTps truncate (int) ;
  • static FTps makeVariable (int) ;
  • static FTps makeVarPower (int,int) ;
  • static FTps makeMonomial (const FMonomial<N>&,const T&) ;
  • FTps operator+ ()const ;
  • FTps operator- ()const ;
  • FTps& operator+= (const FTps&) ;
  • FTps& operator-= (const FTps&) ;
  • FTps& operator*= (const FTps&) ;
  • FTps& operator/= (const FTps&) ;
  • FTps& operator+= (const T&) ;
  • FTps& operator-= (const T&) ;
  • FTps& operator*= (const T&) ;
  • FTps& operator/= (const T&) ;
  • bool operator== (const FTps&)const ;
  • bool operator== (const T&)const ;
  • bool operator!= (const FTps&)const ;
  • bool operator!= (const T&)const ;
  • FTps inverse (int)const ;
  • FTps multiply (const FTps&,int)const ;
  • FTps multiplyVariable (int)const ;
  • T evaluate (const FVector<T,N>&)const ;
  • FTps derivative (int)const ;
  • FTps integral (int)const ;
  • FTps scaleMonomials (const FTps&)const ;
  • FTps<T,N> substitute (const FVps<T,N>&)const ;
  • FTps<T,N> substitute (const FMatrix<T,N,N>&)const ;
  • FTps taylor (const Array1D<T>&,int)const ;
  • std::istream& get (std::istream&) ;
  • std::ostream& put (std::ostream&)const ;
  • inline void unique () ;
  • static const int EXACT ;

Documentation:

• Public members:

  static const int EXACT ;

  Representation of infinite precision.

  FTps () ;

  Default constructor.
  Constructs zero value.

  FTps (const T&) ;

  Conversion.

  FTps (int) ;

  Conversion.

  FTps (int,int) ;

  Constructor.
  Define the internal orders.

  T* begin ()const ;

  Return the beginning of the monomial array. Return the end of the monomial array.

  FTps derivative (int)const ;

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

  T* end ()const ;

  Get exponents for given order.

  T evaluate (const FVector<T,N>&)const ;

  Evaluate FTps at point.

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

  Read FTps on the stream is.

  const T getCoefficient (int)const ;

  Get coefficient.
  Return value of the coefficient denoted by the Giorgelli index. Return zero, if index is out of range.

  const T getCoefficient (const FMonomial<N>&)const ;

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

  static int getGlobalTruncOrder () ;

  Return the global truncation order. Extract given range of orders.

  static int getIndex (const FMonomial<N>&) ;

  Get Giorgelli index for monomial.

  int getMaxOrder ()const ;

  Get maximal order. Get number of coefficients.

  static inline const Array1D<int>& getProductArray (int) ;

  Index array for products of monomial "index".

  int getSize ()const ;

  Get number of coefficients for given order.

  static inline const Array1D<TpsSubstitution>& getSubTable () ;

  Return the substitution table.

  int getTruncOrder ()const ;

  Get truncation order. Get number of variables.

  int getVariables ()const ;

  Set the global truncation order.

  FTps integral (int)const ;

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

  FTps inverse (int)const ;

  Reciprocal value 1/(*this).

  static FTps makeMonomial (const FMonomial<N>&,const T&) ;

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

  static FTps makeVarPower (int,int) ;

  Make power.
  Construct power of variable var.

  static FTps makeVariable (int) ;

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

  FTps multiply (const FTps&,int)const ;

  Truncated multiplication.

  FTps multiplyVariable (int)const ;

  Multiply by variable var.

  bool operator!= (const FTps&)const ;

  Inequality operator.

  bool operator!= (const T&)const ;

  Inequality with constant.

  FTps& operator*= (const FTps&) ;

  Multiply and assign.

  FTps& operator*= (const T&) ;

  Multiply by constant and assign.

  FTps operator+ ()const ;

  Unary plus.

  FTps& operator+= (const FTps&) ;

  Add and assign.

  FTps& operator+= (const T&) ;

  Add constant and assign.

  FTps operator- ()const ;

  Unary minus.

  FTps& operator-= (const FTps&) ;

  Subtract and assign.

  FTps& operator-= (const T&) ;

  Subtract constant and assign.

  FTps& operator/= (const FTps&) ;

  Divide and assign.

  FTps& operator/= (const T&) ;

  Divide by constant and assign.

  FTps& operator= (const T&) ;

  Convert and assign.

  bool operator== (const FTps&)const ;

  Equality operator.

  bool operator== (const T&)const ;

  Equality with constant.

  inline const T operator[] (int)const ;

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

  inline 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. Use as a lvalue is only allowed when the FTps is unique().

  const T operator[] (const FMonomial<N>&)const ;

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

  T& operator[] (const FMonomial<N>&) ;

  Get coefficient.
  Return a reference to the coefficient denoted by monomial exponents. Result is undefined, if index is out of range. Use as a lvalue is only allowed when the FTps is unique().

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

  Write FTps on the stream os.

  FTps scaleMonomials (const FTps&)const ;

  Multiply by variable var.
  Throw LogicalError for a constant.

  void setCoefficient (int,const T&) ;

  Set coefficient.
  Assign value of the coefficient denoted by the Giorgelli index. Ignore, if index is out of range.

  void setCoefficient (const FMonomial<N>&,const T&) ;

  Set coefficient.
  Assign value of the coeffient denoted by monomial exponents. Ignore, if index is out of range.

  FTps<T,N> substitute (const FVps<T,N>&)const ;

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

  FTps<T,N> substitute (const FMatrix<T,N,N>&)const ;

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

  FTps taylor (const Array1D<T>&,int)const ;

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

  FTps truncate (int) ;

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

  inline void unique () ;

  Make representation unique.