# algebraixlib.algebras.properties module¶

Accessors for the properties of a generic MathObject that redirect to the appropriate algebra.

The accessors here check what algebra a given MathObject belongs to, then call the property function of this algebra.

algebraixlib.algebras.properties.is_functional(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is functional or Undef() if not applicable.

Is implemented for relations, clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of relations.

algebraixlib.algebras.properties.is_right_functional(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is right-functional or Undef() if not applicable.

Is implemented for relations, clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of relations.

algebraixlib.algebras.properties.is_bijective(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is bijective or Undef() if not applicable.

Is implemented for relations, clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of relations.

algebraixlib.algebras.properties.is_reflexive(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is reflexive or Undef() if not applicable.

Is implemented for couplets, relations, clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of relations.

algebraixlib.algebras.properties.is_symmetric(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is symmetric or Undef() if not applicable.

Is implemented for relations, clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of relations.

algebraixlib.algebras.properties.is_transitive(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is transitive or Undef() if not applicable.

Is implemented for relations, clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of relations.

algebraixlib.algebras.properties.is_equivalence_relation(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is an equivalence relation or Undef() if not applicable.

Is implemented for relations, clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of relations.

algebraixlib.algebras.properties.is_regular(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is regular or Undef() if not applicable.

Is implemented for clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of clans.

algebraixlib.algebras.properties.is_right_regular(mo: algebraixlib.mathobjects.mathobject.MathObject, _checked: bool = True) → bool[source]

Return whether mo is right-regular or Undef() if not applicable.

Is implemented for clans, multiclans and sets of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets or multisets of clans.