The Lie basis class. More...
#include <libalgebra.h>
Public Types | |
| typedef hall_basis::KEY | KEY |
| Import of the KEY type. | |
| typedef std::map< KEY, SCA > | MAP |
| The MAP type. | |
|
typedef lie< SCA, RAT, n_letters, max_degree > | LIE |
| The Free Lie Associative Algebra element type. | |
| typedef RAT | RATIONAL |
| The rationals. | |
Public Member Functions | |
| lie_basis (void) | |
| Constructs the basis for a finite number of letters. | |
| const LIE & | prod (const KEY &k1, const KEY &k2) |
| Returns the product of two key. | |
| LIE | replace (const KEY &k, const std::vector< LET > &s, const std::vector< LIE * > &v, std::map< KEY, LIE > &table) |
| Replaces letters by lie<> instances in a lie<> instance. | |
Friends | |
| std::ostream & | operator<< (std::ostream &os, const std::pair< lie_basis *, KEY > &t) |
| Outupts an std::pair<lie_basis*, KEY> to an std::ostream. | |
Detailed Description
template<typename SCA, typename RAT, DEG n_letters, DEG max_degree>
class alg::lie_basis< SCA, RAT, n_letters, max_degree >
The Lie basis class.
This is the basis used to implement the lie class as a specialisation of the algebra class. In the current implementation, the Lie basis class is a wrapper for the hall_basis class, with a prod() member function.
Member Function Documentation
| const LIE& alg::lie_basis< SCA, RAT, n_letters, max_degree >::prod | ( | const KEY & | k1, | |
| const KEY & | k2 | |||
| ) | [inline] |
Returns the product of two key.
Returns the LIE instance corresponding to the product of the two basis elements k1 and k2. For performance reasons, the basis is enriched/grown dynamically and the already computed products are stored in a static multiplication table to speed up further calculations. This function returns a constant reference to the suitable table element.
| LIE alg::lie_basis< SCA, RAT, n_letters, max_degree >::replace | ( | const KEY & | k, | |
| const std::vector< LET > & | s, | |||
| const std::vector< LIE * > & | v, | |||
| std::map< KEY, LIE > & | table | |||
| ) | [inline] |
Replaces letters by lie<> instances in a lie<> instance.
Replaces the occurences of s letters in the expression of k by the lie<> elements in v, and returns the recursively expanded result. The already computed replacements are stored in table.
The documentation for this class was generated from the following file:
- libalgebra-demo/libalgebra/lie_basis.h
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