template class LieMap<class> : public VpsInvMap<class>

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Lie algebraic map.

LieMap<T> is a truncated Taylor series map with coefficients of type T. It implements operations available only for symplectic maps.

Type:	Instantiable
Superclasses:	public VpsInvMap<class>
Include file:	./Algebra/LieMap.hh

Inheritance

Synopsis (including inherited members):

• Public members:
  • LieMap (int) ;
  • LieMap (const Matrix<T>&) ;
  • LieMap (const Vector<T>&) ;
  • LieMap (const Vps<T>&) ;
  • LieMap () ;
  • LieMap (const LieMap<T>&) ;
  • ~LieMap () ;
  • LieMap<T>& operator= (const LieMap<T>&) ;
  • void check ()const ;
  • static LieMap<T> ExpMap (const Tps<T>&) ;
  • static LieMap<T> ExpMap (const Tps<T>&,const LieMap<T>&) ;
  • VpsInvMap<T>& operator= (const VpsInvMap<T>&) ;
  • VpsInvMap<T> inverse ()const ;
  • static VpsInvMap<T> identity (int) ;
  • 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 ;
  • 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:

  static LieMap<T> ExpMap (const Tps<T>&) ;

  Lie series.
  Build the exponential series exp(:H:)Z from the Tps<T> H, acting on the identity map Z.

  static LieMap<T> ExpMap (const Tps<T>&,const LieMap<T>&) ;

  Lie series.
  Build the exponential series exp(:H:)M from the Tps<T> H, acting on the map M.

  LieMap (int) ;

  Constructor.
  Construct identity with nDim variables.

  LieMap (const Matrix<T>&) ;

  Convert.
  Construct a map from the matrix M, which should be symplectic.

  LieMap (const Vector<T>&) ;

  Convert.
  Construct an identity map with a displacement vector V.

  LieMap (const Vps<T>&) ;

  Conversion.
  Convert possibly non-symplectic map.

  void check ()const ;

  Check consistency.