algebraixlib.algebras.couplets module¶
This module contains the algebra of couplets.
-
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.
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static
transpose
(couplet: '(M x M)', _checked=True) → '(M x M)'[source]¶ Return the transposition of
couplet
.Returns: The transposition of couplet
orUndef()
ifcouplet
is not an instance ofCouplet
.
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static
compose
(couplet1: '(M x M)', couplet2: '(M x M)', _checked=True) → '(M x M)'[source]¶ Return the composition of
couplet1
withcouplet2
.Returns: The composition of couplet1
withcouplet2
(which may be undefined, in which case the result isUndef()
) orUndef()
ifcouplet1
orcouplet2
are not instances ofCouplet
.
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static
-
algebraixlib.algebras.couplets.
transpose
(couplet: '(M x M)', _checked=True) → '(M x M)'¶ Return the transposition of
couplet
.Returns: The transposition of couplet
orUndef()
ifcouplet
is not an instance ofCouplet
.
-
algebraixlib.algebras.couplets.
compose
(couplet1: '(M x M)', couplet2: '(M x M)', _checked=True) → '(M x M)'¶ Return the composition of
couplet1
withcouplet2
.Returns: The composition of couplet1
withcouplet2
(which may be undefined, in which case the result isUndef()
) orUndef()
ifcouplet1
orcouplet2
are not instances ofCouplet
.
-
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
True
ifobj
is a member of the ground set of this algebra.Returns: True
ifobj
is an instance ofCouplet
.
-
algebraixlib.algebras.couplets.
is_absolute_member
(obj: algebraixlib.mathobjects.mathobject.MathObject) → bool[source]¶ Return
True
ifobj
is a member of the absolute ground set of this algebra.return: True
ifobj
is an absolute couplet.Note
This function calls
get_ground_set()
onobj
.