The Lie algebra for the commutative polynomials. More...
#include <poly_lie.h>
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< BASIS > | VECT |
The sparse_vector type. | |
typedef algebra< BASIS > | ALG |
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. |
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.