def __init__(self, parent, iterable):
"""
EXAMPLES::
sage: F = CommutativeAdditiveSemigroups().example()
sage: x = F.element_class(F, (('a',4), ('b', 0), ('a', 2), ('c', 1), ('d', 5)))
sage: x
2*a + c + 5*d
sage: x.value
{'a': 2, 'b': 0, 'c': 1, 'd': 5}
sage: x.parent()
An example of a commutative monoid: the free commutative monoid generated by ('a', 'b', 'c', 'd')
Internally, elements are represented as dense dictionaries which
associate to each generator of the monoid its multiplicity. In
order to get an element, we wrap the dictionary into an element
via :class:`ElementWrapper`::
sage: x.value
{'a': 2, 'b': 0, 'c': 1, 'd': 5}
"""
d = dict((a, 0) for a in parent.alphabet)
for (a, c) in iterable:
d[a] = c
ElementWrapper.__init__(self, parent, d)
def __init__(self, parent, iterable):
"""
EXAMPLES::
sage: F = CommutativeAdditiveSemigroups().example()
sage: x = F.element_class(F, (('a',4), ('b', 0), ('a', 2), ('c', 1), ('d', 5)))
sage: x
2*a + c + 5*d
sage: x.value
{'a': 2, 'b': 0, 'c': 1, 'd': 5}
sage: x.parent()
An example of a commutative monoid: the free commutative monoid generated by ('a', 'b', 'c', 'd')
Internally, elements are represented as dense dictionaries which
associate to each generator of the monoid its multiplicity. In
order to get an element, we wrap the dictionary into an element
via :class:`ElementWrapper`::
sage: x.value
{'a': 2, 'b': 0, 'c': 1, 'd': 5}
"""
d = dict( (a,0) for a in parent.alphabet )
for (a, c) in iterable:
d[a] = c
ElementWrapper.__init__(self, parent, d)
def __init__(self, parent, value):
ElementWrapper.__init__(self, parent=parent, value=value)
# setup methods defined only in special cases
if parent._is_principal:
self.g_vector = MethodType(g_vector, self, self.__class__)
self.is_homogeneous = MethodType(is_homogeneous, self, self.__class__)
self.homogeneous_components = MethodType(homogeneous_components, self, self.__class__)
def __init__(self, parent, value):
ElementWrapper.__init__(self, parent=parent, value=value)
# setup methods defined only in special cases
if parent._is_principal:
self.g_vector = MethodType(g_vector, self, self.__class__)
self.is_homogeneous = MethodType(is_homogeneous, self,
self.__class__)
self.homogeneous_components = MethodType(homogeneous_components,
self, self.__class__)
def __init__(self, parent, x):
"""
TESTS::
sage: W = CoxeterGroup(['A', 3], implementation='coxeter3') # optional - coxeter3
sage: W([2,1,2]) # optional - coxeter3
[1, 2, 1]
"""
if not isinstance(x, CoxGroupElement):
x = CoxGroupElement(parent._coxgroup, x).reduced()
ElementWrapper.__init__(self, parent, x)
def __init__(self, ambient_element, parent):
"""
TESTS::
sage: from sage.monoids.automatic_semigroup import AutomaticSemigroup
sage: R = IntegerModRing(21)
sage: M = AutomaticSemigroup(Family([2]))
sage: m = M(2); m
2
sage: type(m)
<class 'sage.monoids.automatic_semigroup.AutomaticSemigroup_with_category.element_class'>
"""
ElementWrapper.__init__(self, ambient_element, parent)
self._reduced_word = None
def __init__(self, ambient_element, parent):
"""
TESTS::
sage: from sage.monoids.automatic_semigroup import AutomaticSemigroup
sage: R = IntegerModRing(21)
sage: M = AutomaticSemigroup(Family([2]))
sage: m = M(2); m
2
sage: type(m)
<class 'sage.monoids.automatic_semigroup.AutomaticSemigroup_with_category.element_class'>
"""
ElementWrapper.__init__(self, ambient_element, parent)
self._reduced_word = None
def __init__(self, parent, value):
"""
Initialize ``self``.
EXAMPLES::
sage: B = crystals.infinity.Multisegments(2)
sage: mg = B.highest_weight_vector()
sage: TestSuite(mg).run()
"""
def sort_key(x):
return (-x[0], ZZ(x[1]))
ZM = parent._Zn
value = [(k, ZM(i)) for k,i in value]
ElementWrapper.__init__(self, parent, tuple(sorted(value, key=sort_key)))
def __init__(self, parent, x):
r"""
EXAMPLES::
sage: G = QQ^2
sage: EG = GroupExp()(G)
sage: x = EG.an_element(); x
(1, 0)
sage: TestSuite(x).run(skip = "_test_category")
See the documentation of :meth:`sage.structure.element_wrapper.ElementWrapper.__init__`
for the reason behind skipping the category test.
"""
if x not in parent._G:
raise ValueError("%s is not an element of %s" % (x, parent._G))
ElementWrapper.__init__(self, parent, x)
def __init__(self, parent, value, check=True):
"""
TESTS::
sage: from sage.structure.set_factories_example import XYPairs
sage: P = XYPairs(); p = P.list()[0]
sage: TestSuite(p).run()
"""
if check:
if not isinstance(value, tuple):
raise ValueError("Value {} must be a tuple".format(value))
if len(value) != 2:
raise ValueError("Value must be of length 2")
if not all(int(x) in range(MAX) for x in value):
raise ValueError("numbers must be in range({})".format(MAX))
ElementWrapper.__init__(self, parent, value)
def __init__(self, parent, value, check=True):
"""
TESTS::
sage: from sage.structure.set_factories_example import XYPairs
sage: P = XYPairs(); p = P.list()[0]
sage: TestSuite(p).run()
"""
if check:
if not isinstance(value, tuple):
raise ValueError("Value {} must be a tuple".format(value))
if len(value) != 2:
raise ValueError("Value must be of length 2")
if not all(int(x) in range(MAX) for x in value):
raise ValueError("numbers must be in range({})".format(MAX))
ElementWrapper.__init__(self, parent, value)
def __init__(self, parent, x):
r"""
EXAMPLES::
sage: G = QQ^2
sage: EG = GroupExp()(G)
sage: x = EG.an_element(); x
(1, 0)
sage: TestSuite(x).run(skip = "_test_category")
See the documentation of :meth:`sage.structure.element_wrapper.ElementWrapper.__init__`
for the reason behind skipping the category test.
"""
if x not in parent._G:
raise ValueError("%s is not an element of %s" % (x, parent._G))
ElementWrapper.__init__(self, parent, x)
def __init__(self, parent, value):
"""
Initialize ``self``.
EXAMPLES::
sage: B = crystals.infinity.Multisegments(2)
sage: mg = B.highest_weight_vector()
sage: TestSuite(mg).run()
"""
def sort_key(x):
return (-x[0], ZZ(x[1]))
ZM = parent._Zn
value = [(k, ZM(i)) for k, i in value]
ElementWrapper.__init__(self, parent,
tuple(sorted(value, key=sort_key)))
def __init__(self, parent, x):
"""
TESTS::
sage: W = CoxeterGroup(['A', 3], implementation='coxeter3') # optional - coxeter3
sage: W([2,1,2]) # optional - coxeter3
[1, 2, 1]
Check that :trac:`32266` is fixed::
sage: A3 = CoxeterGroup('A3', implementation='coxeter3') # optional - coxeter3
sage: s1,s2,s3 = A3.simple_reflections() # optional - coxeter3
sage: s1*s3 # optional - coxeter3
[1, 3]
sage: s3*s1 # optional - coxeter3
[1, 3]
sage: s3*s1 == s1*s3 # optional - coxeter3
True
"""
if not isinstance(x, CoxGroupElement):
x = CoxGroupElement(parent._coxgroup, x).reduced()
x = x.normal_form()
ElementWrapper.__init__(self, parent, x)
def _repr_(self):
"""
EXAMPLES::
sage: from sage.monoids.automatic_semigroup import AutomaticSemigroup
sage: R = IntegerModRing(19)
sage: M = AutomaticSemigroup(Family({1: R(3), 2: R(5)}), one=R.one())
sage: a = M.an_element(); a
3
sage: b = M.from_reduced_word([1,2,1]); b
7
sage: M.repr_element_method("reduced_word")
sage: a
[1]
sage: b
7
sage: M.construct(up_to=b)
sage: b
[1, 1, 2]
"""
if self.parent()._repr_element_method == "ambient" or self._reduced_word is None:
return ElementWrapper._repr_(self)
return str(self._reduced_word)
def _repr_(self):
"""
EXAMPLES::
sage: from sage.monoids.automatic_semigroup import AutomaticSemigroup
sage: R = IntegerModRing(19)
sage: M = AutomaticSemigroup(Family({1: R(3), 2: R(5)}), one=R.one())
sage: a = M.an_element(); a
3
sage: b = M.from_reduced_word([1,2,1]); b
7
sage: M.repr_element_method("reduced_word")
sage: a
[1]
sage: b
7
sage: M.construct(up_to=b)
sage: b
[1, 1, 2]
"""
if self.parent()._repr_element_method == "ambient" or self._reduced_word is None:
return ElementWrapper._repr_(self)
return str(self._reduced_word)
