Public Types | Public Member Functions | Friends

poly_lie< SCA, RAT, n_letters, max_degree > Class Template Reference

The Lie algebra for the commutative polynomials. More...

#include <poly_lie.h>

Inheritance diagram for poly_lie< SCA, RAT, n_letters, max_degree >:
algebra< poly_lie_basis< SCA, RAT, n_letters, max_degree > > sparse_vector< poly_lie_basis< SCA, RAT, n_letters, max_degree > > MAP

List of all members.

Public Types

typedef poly_basis< SCA, RAT >::KEY POLYBASISKEY
 The basis elements for the polynomials (monomials).
typedef poly_lie_basis< SCA,
RAT, n_letters, max_degree > 
BASIS
 The basis type.
typedef BASIS::KEY KEY
 Import of the KEY type.
typedef sparse_vector< BASISVECT
 The sparse_vector type.
typedef algebra< BASISALG
 The algebra type.
typedef ALG::iterator iterator
 Import of the iterator type.
typedef ALG::const_iterator const_iterator
 Import of the constant iterator type.

Public Member Functions

 poly_lie (void)
 Default constructor. Zero lie element.
 poly_lie (const poly_lie &l)
 Copy constructor.
 poly_lie (const ALG &a)
 Constructs an instance from an algebra instance.
 poly_lie (const VECT &v)
 Constructs an instance from a sparse_vector instance.
 poly_lie (LET x, LET y, DEG z)
 Constructs a unidimensional instance from a given key (with scalar one).
 poly_lie (const KEY &k)
 Constructs an instance from a basis element.
 poly_lie (LET letter, const SCA &s)
 Constructs a unidimensional instance from a letter and a scalar.

Friends

poly_lie replace (const poly_lie &src, const std::vector< LET > &s, const std::vector< poly_lie * > &v)
 Replaces the occurences of letters in s by Lie elements in v.

Detailed Description

template<typename SCA, typename RAT, DEG n_letters, DEG max_degree>
class poly_lie< SCA, RAT, n_letters, max_degree >

The Lie algebra for the commutative polynomials.

Elements of the algebra are polynomial vector fields (ie linear combinations of pairs of monomials and directions). The product is the Lie bracket for vector fields.


The documentation for this class was generated from the following file: