template class VpsMap<class> : public Vps<class>

(Return to index)

Truncate power series map.

This class includes substitution operations. The input and output dimensions need not be the same.

Type:	Instantiable
Superclasses:	public Vps<class>
Include file:	./Algebra/VpsMap.hh

Inheritance

Synopsis (including inherited members):

• Public members:
  • VpsMap (int,int) ;
  • VpsMap (const Vps<T>&) ;
  • VpsMap (int,const Tps<T>[]) ;
  • VpsMap (const Matrix<T>&) ;
  • VpsMap (const Vector<T>&) ;
  • VpsMap () ;
  • VpsMap (const VpsMap<T>&) ;
  • ~VpsMap () ;
  • VpsMap<T>& operator= (const VpsMap<T>&) ;
  • VpsMap<T> substitute (const VpsMap<T>&)const ;
  • VpsMap<T> substitute (const Matrix<T>&)const ;
  • VpsMap<T> substitute (const VpsMap<T>&,int)const ;
  • VpsMap<T> substituteInto (const Matrix<T>&)const ;
  • Vector<T> constantTerm (const Vector<T>&)const ;
  • Vector<T> constantTerm ()const ;
  • Matrix<T> linearTerms (const Vector<T>&)const ;
  • Matrix<T> linearTerms ()const ;
  • VpsMap<T> derivative (int)const ;
  • VpsMap<T> integral (int)const ;
  • Vps<T>& operator= (const Vps<T>&) ;
  • const Tps<T>& getComponent (int)const ;
  • void setComponent (int,const Tps<T>&) ;
  • Tps<T>& operator[] (int) ;
  • const Tps<T>& operator[] (int)const ;
  • void check ()const ;
  • Vps<T> operator+ ()const ;
  • Vps<T> operator- ()const ;
  • Vps<T>& operator*= (const Tps<T>&) ;
  • Vps<T>& operator/= (const Tps<T>&) ;
  • Vps<T>& operator*= (const T&) ;
  • Vps<T>& operator/= (const T&) ;
  • Vps<T>& operator+= (const Vps<T>&) ;
  • Vps<T>& operator-= (const Vps<T>&) ;
  • Vps<T>& operator+= (const Vector<T>&) ;
  • Vps<T>& operator-= (const Vector<T>&) ;
  • std::istream& get (std::istream&) ;
  • std::ostream& put (std::ostream&)const ;
  • int getDimension ()const ;
  • int getTopOrder ()const ;
  • int getTruncOrder ()const ;
  • int getVariables ()const ;
  • Vps<T> filter (int,int)const ;
  • Vps<T> truncate (int) ;

Documentation:

• Public members:

  VpsMap (int,int) ;

  Constructor.
  Construct nDim series in nVar variables each.

  VpsMap (const Vps<T>&) ;

  Convert.

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

  Constructor.
  Assign the nDim components from rhs.

  VpsMap (const Matrix<T>&) ;

  Convert.
  The constant terms are zero. The linear terms are taken from M.

  VpsMap (const Vector<T>&) ;

  Convert.
  The constant terms are taken from V. The linear terms are zero.

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

  Evaluate map at point.
  Return the point y mapped by the map.

  Vector<T> constantTerm ()const ;

  Evaluate map at origin.
  Extract constant part.

  VpsMap<T> derivative (int)const ;

  Derivative with respect to variable var.

  VpsMap<T> integral (int)const ;

  Integral with respect to variable var.

  Matrix<T> linearTerms (const Vector<T>&)const ;

  Extract linear terms at point.
  Return the linear terms of the map around the point y, i.e. the linear part of the partial differentials at y.

  Matrix<T> linearTerms ()const ;

  Extract linear terms at origin.
  Return the linear part.

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

  Substitute.

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

  Substitute.

  VpsMap<T> substitute (const VpsMap<T>&,int)const ;

  Substitute and truncate.

  VpsMap<T> substituteInto (const Matrix<T>&)const ;

  Substitute.