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# Algebra

Collaboration diagram for Algebra:

Algebra constructs for Vaucanson. More...

## Files
file | algebra.hh
| Workaround to give Doxygen documentation about the algebra namespace.

file | rational_number.hh
| RationalNumber class declaration.

file | krat_exp_parser.hh
| This file declares the parse() function.

## Namespaces
namespace | vcsn::algebra
| Namespace for algebra constructs in Vaucanson.

namespace | vcsn::algebra::krat_exp_lexing
| Misc. declarations used for rational expression lexing.

## Modules
| Alphabet
| Freemonoid
| Fmp
| Monoid
| Semiring
| Semigroup
| Series
## Classes
struct | AlphabetSetBase
| Base class for structural elements of alphabets. More...
struct | dynamic_traits< algebra::AlphabetSetBase< S > >
| Specialization of `dynamic_traits` for `AlphabetSetBase`. More...
struct | FreeMonoidBase
| Structural element for free monoid. More...
struct | dynamic_traits< algebra::FreeMonoidBase< Self > >
struct | FreeMonoidProduct
| Implementation of a monoid which is a product of two free monoids. More...
struct | dynamic_traits< algebra::FreeMonoidProduct< F, S > >
| Meta information about FreeMonoidProduct. More...
struct | FreeMonoidProductBase
| Structural element for free monoid product. More...
struct | dynamic_traits< algebra::FreeMonoidProductBase< Self > >
struct | MonoidBase
| `The` base class of all structures that are monoids. More...
struct | dynamic_traits< algebra::MonoidBase< Self > >
struct | NumericalSemiring
| The set of semirings implemented with usual operations (+, *). More...
struct | dynamic_traits< algebra::NumericalSemiring >
| Meta information about the NumericalSemiring structural element. More...
struct | mul_kind
| Empty class used as static information to denote the kind of internal operation of a semigroup. More...
struct | dynamic_traits< algebra::SemigroupBase< Self > >
struct | SemiringBase
| Base class for all structures that are semirings. More...
struct | dynamic_traits< algebra::SemiringBase< Self > >
struct | SeriesBase
| Structural element of series K<A*> from a free monoid A* to a semiring K. More...
struct | dynamic_traits< algebra::SeriesBase< Self > >
struct | dynamic_traits< algebra::TropicalSemiring< TropicalKind > >
| Meta information about the tropical semirings. More...
struct | TropicalMin
| Static information about the kind of tropical we are confronted with. More...
struct | MetaElement< algebra::TropicalSemiring< TropicalKind >, T >
| Services of element of a tropical semiring. More...
struct | alphabet_traits< AlphabetSet< L >, std::set< L > >
| Meta information about the mixing of AlphabetSet with std::set. More...
struct | MetaElement< algebra::AlphabetSet< L >, std::set< L > >
| Services of every alphabet implemented with std::set. More...
struct | AlphabetSet
| Static implementation of alphabet structural element. More...
struct | dynamic_traits< algebra::AlphabetSet< L > >
| Meta information about AlphabetSet. More...
class | AlphabetDecorator
| Decorate a given alphabet implementation with meta-symbols. More...
struct | MetaElement< algebra::AlphabetSet< L >, algebra::AlphabetDecorator< L, T > >
| Services of every alphabet implemented with AlphabetDecorator<L, T>. More...
struct | FreeMonoid
| Implementation of a free monoid which aggregates its alphabet. More...
struct | dynamic_traits< algebra::FreeMonoid< A > >
| Meta information about FreeMonoid. More...
class | RationalNumber
| Rational numbers class. More...

## Detailed Description

Algebra constructs for Vaucanson.

This group aggregates the documentation of compounds related to algebraic structures of Vaucanson, such as Monoids, Series, or rational expressions (as implementation of series).

See also:
  - vcsn::algebra
  - vcsn::algebra::AlphabetSet
  - vcsn::algebra::MonoidBase
  - vcsn::algebra::FreeMonoid
  - vcsn::algebra::FreeMonoidProduct
  - vcsn::algebra::SemigroupBase
  - vcsn::algebra::NumericalSemiring
  - vcsn::algebra::TropicalSemiring
  - vcsn::algebra::Series