# algebraixlib.algebras.couplets module¶

This module contains the algebra of couplets and related functionality.

class algebraixlib.algebras.couplets.Algebra[source]

Bases: object

Provide the operations and relations that are members of the algebra of couplets.

This class contains only static member functions. Its main purpose is to provide a namespace for and highlight the operations and relations that belong to the algebra of couplets. All member functions are also available at the enclosing module scope.

static transpose()[source]

Return the transposition of couplet (right and left components swapped).

Returns: The transposition of couplet or Undef() if couplet is not an instance of Couplet.
static compose()[source]

Return the composition of couplet1 with couplet2.

Returns: The composition of couplet1 with couplet2 (which may be undefined, in which case the result is Undef()) or Undef() if couplet1 or couplet2 are not instances of Couplet.
algebraixlib.algebras.couplets.transpose()

Convenience redirection to Algebra.transpose.

algebraixlib.algebras.couplets.compose()

Convenience redirection to Algebra.compose.

algebraixlib.algebras.couplets.get_name() → str[source]

Return the name and ground set of this algebra in string form.

algebraixlib.algebras.couplets.get_ground_set() → algebraixlib.structure.Structure[source]

Return the ground set of this algebra.

algebraixlib.algebras.couplets.get_absolute_ground_set() → algebraixlib.structure.Structure[source]

Return the absolute ground set of this algebra.

algebraixlib.algebras.couplets.is_member(obj: algebraixlib.mathobjects.mathobject.MathObject) → bool[source]

Return whether obj is a member of the ground set of this algebra.

Returns: True if obj is a couplet (an instance of Couplet), False if not.
algebraixlib.algebras.couplets.is_member_or_undef(obj: algebraixlib.mathobjects.mathobject.MathObject) → bool[source]
Return whether obj is either a member of the ground set of this algebra
or Undef.
Returns: True if obj is either a couplet (an instance of Couplet) or Undef, False if not.
algebraixlib.algebras.couplets.is_absolute_member(obj: algebraixlib.mathobjects.mathobject.MathObject) → bool[source]

Return whether obj is a member of the absolute ground set of this algebra.

Returns: True if obj is an absolute couplet, False if not.
algebraixlib.algebras.couplets.is_reflexive()[source]

Return whether couplet is reflexive.

Returns: True if couplet is reflexive, False if it is not, or Undef() if couplet is not a couplet.