algebraixlib.algebras.multiclans module

This module contains the algebra of multiclans.

class algebraixlib.algebras.multiclans.Algebra

Bases: object

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

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 multiclans. All member functions are also available at the enclosing module scope.

static transpose(multiclan: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the transposition of the multiclan multiclan.

Returns:The unary extension of transposition from the algebra of relations to the algebra of multiclans, applied to multiclan, or Undef() if multiclan is not a multiclan.

static compose(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the composition of multiclan1 with multiclan2.

Returns:The binary multi-extension of composition from the algebra of relations to the algebra of multiclans, applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

static cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the cross-union of multiclan1 and multiclan2.

Returns:The binary multi-extension of union from the algebra of relations (which inherits it from the algebra of multisets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

static functional_cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the left-functional cross-union of multiclan1 and multiclan2.

Returns:The binary multi-extension of the left-functional union from the algebra of relations to the algebra of multiclans, applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

static right_functional_cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the right-functional cross-union of multiclan1 and multiclan2.

Returns:The binary multi-extension of the right-functional union from the algebra of relations to the algebra of multiclans, applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

static cross_intersect(multiclan1: 'P(P(M x M) x N)', multiclan2: 'PP(M x M)', _checked=True) → 'PP(M x M)'

Return the cross-intersection of multiclan1 and multiclan2.

Returns:The binary multi-extension of intersection from the algebra of relations (which inherits it from the algebra of sets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

static substrict(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the binary extension of substriction of multiclan1 and multiclan2.

Returns:The binary multi-extension of substriction from the algebra of relations (which inherits it from the algebra of sets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

static superstrict(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the binary multi-extension of superstriction of multiclan1

and multiclan2.

Returns:The binary multi-extension of superstriction from the algebra of relations (which inherits it from the algebra of sets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.transpose(multiclan: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the transposition of the multiclan multiclan.

Returns:The unary extension of transposition from the algebra of relations to the algebra of multiclans, applied to multiclan, or Undef() if multiclan is not a multiclan.

algebraixlib.algebras.multiclans.compose(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the composition of multiclan1 with multiclan2.

Returns:The binary multi-extension of composition from the algebra of relations to the algebra of multiclans, applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the cross-union of multiclan1 and multiclan2.

Returns:The binary multi-extension of union from the algebra of relations (which inherits it from the algebra of multisets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.functional_cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the left-functional cross-union of multiclan1 and multiclan2.

Returns:The binary multi-extension of the left-functional union from the algebra of relations to the algebra of multiclans, applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.right_functional_cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the right-functional cross-union of multiclan1 and multiclan2.

Returns:The binary multi-extension of the right-functional union from the algebra of relations to the algebra of multiclans, applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.cross_intersect(multiclan1: 'P(P(M x M) x N)', multiclan2: 'PP(M x M)', _checked=True) → 'PP(M x M)'

Return the cross-intersection of multiclan1 and multiclan2.

Returns:The binary multi-extension of intersection from the algebra of relations (which inherits it from the algebra of sets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.substrict(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the binary extension of substriction of multiclan1 and multiclan2.

Returns:The binary multi-extension of substriction from the algebra of relations (which inherits it from the algebra of sets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.superstrict(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)', _checked=True) → 'P(P(M x M) x N)'

Return the binary multi-extension of superstriction of multiclan1

and multiclan2.

Returns:The binary multi-extension of superstriction from the algebra of relations (which inherits it from the algebra of sets) to the algebra of multiclans applied to multiclan1 and multiclan2, or Undef() if multiclan1 or multiclan2 are not multiclans.

algebraixlib.algebras.multiclans.get_name() → str

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

algebraixlib.algebras.multiclans.get_ground_set() → algebraixlib.structure.Structure

Return the ground set of this algebra.

algebraixlib.algebras.multiclans.get_absolute_ground_set() → algebraixlib.structure.Structure

Return the absolute ground set of this algebra.

algebraixlib.algebras.multiclans.is_member(obj: algebraixlib.mathobjects.mathobject.MathObject) → bool

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

Note

This function calls get_ground_set() on obj.

algebraixlib.algebras.multiclans.is_absolute_member(obj: algebraixlib.mathobjects.mathobject.MathObject) → bool

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

return:True if obj is an absolute clan.

Note

This function calls get_ground_set() on obj.