Architecture

Modules

The GALACTIC kernel contains several mathematical algebra modules:

a galactic.algebras.set module for dealing with sets;
a galactic.algebras.relational module for dealing with relational data;
a galactic.algebras.poset module for dealing with partially ordered sets;
a galactic.algebras.lattice module for dealing with lattice and semi-lattices;

Class diagrams

"AbstractFiniteBinaryRelation[_E, _E]" <|-- "AbstractFiniteEndoRelation[_E]"
"AbstractFiniteEndoRelation[_E]" <|-- "AbstractFiniteDirectedAcyclicRelation[_E]"
"AbstractFiniteDirectedAcyclicRelation[_E]" <|-- "AbstractFinitePartiallyOrderedSet[_E]"
"AbstractFinitePartiallyOrderedSet[_E]" <|-- "AbstractFiniteJoinSemiLattice[_E]"
"AbstractFinitePartiallyOrderedSet[_E]" <|-- "AbstractFiniteMeetSemiLattice[_E]"
"AbstractFiniteJoinSemiLattice[_E]" <|-- "AbstractFiniteLattice[_E]"
"AbstractFiniteMeetSemiLattice[_E]" <|-- "AbstractFiniteLattice[_E]"
"AbstractFiniteLattice[_E]" <|-- "FrozenFiniteLattice[_E]"
"FrozenFiniteLattice[_E]" <|-- "ExtensibleFiniteLattice[_E]"

class "ExtensibleFiniteLattice[_E]" {
extend(iterable: Iterable[_E])
}

class "FrozenFiniteLattice[_E]" {
}

abstract class "AbstractFiniteLattice[_E]" {
reduced_context : AbstractFiniteBinaryRelation[_E, _E]
}

abstract class "AbstractFiniteJoinSemiLattice[_E]" {
co_atoms : Collection[_E]
join_irreducible : Collection[_E]
greatest_join_irreducible(element: _E) : Collection[_E]
}

abstract class "AbstractFiniteMeetSemiLattice[_E]" {
atoms : Collection[_E]
meet_irreducible : Collection[_E]
smallest_meet_irreducible(element: _E) : Collection[_E]
}

abstract class "AbstractFinitePartiallyOrderedSet[_E]" {
cover : AbstractFiniteCoveringRelation[_E]
order : AbstractFinitePartialOrder[_E]:
top : Collection[_E]
bottom : Collection[_E]
maximum : Optional[_E]
minimum : Optional[_E]
upper_limit(limit: _E, strict: bool = False) : Collection[_E]
lower_limit(limit: _E, strict: bool = False) : Collection[_E]
filter(element: _E) : AbstractFinitePartiallyOrderedSet[_E]
ideal(element: _E) : AbstractFinitePartiallyOrderedSet[_E]
}

abstract class "AbstractFiniteBinaryRelation[_E, _E]" {
domain : Collection[_E]
co_domain : Collection[_E]
successors(element: _E) : Collection[_E]
predecessors(element: _E) : Collection[_E]
}

abstract class "AbstractFiniteEndoRelation[_E]" {
}

abstract class "AbstractFiniteDirectedAcyclicRelation[_E]" {
sinks : Collection[_E]
sources : Collection[_E]
} — Lattice class