def __eq__(self,other):
"""
TESTS::
sage: P = Poset([["a","b"],["d"],["c"],["d"],[]], facade = False)
sage: Q = Poset([["a","b"],["d"],["c"],[],[]], facade = False)
sage: P(0).__eq__(P(4))
False
sage: from sage.combinat.posets.elements import PosetElement
sage: PosetElement(P,0,"c") == PosetElement(P,0,"c")
True
sage: PosetElement(P,0,"c") == PosetElement(Q,0,"c")
False
sage: PosetElement(P,0,"b") == PosetElement(P,0,"c")
False
.. warning:: as an optimization, this only compares the parent
and vertex, using the invariant that, in a proper poset
element, ``self.element == other.element`` if and only
``self.vertex == other.vertex``::
sage: PosetElement(P,1,"c") == PosetElement(P,0,"c")
True
Test that :trac:`12351` is fixed::
sage: P(0) == int(0)
False
"""
# This should instead exploit unique representation, using
# self is other, or best inherit __eq__ from there. But there
# are issues around pickling and rich comparison functions.
return have_same_parent(self, other) \
and self.vertex == other.vertex
def __eq__(self, other):
"""
Check equality.
TESTS::
sage: R.<x,y,z> = QQ[]
sage: W = DifferentialWeylAlgebra(R)
sage: dx,dy,dz = W.differentials()
sage: dy*(x^3-y*z)*dx == -z*dx + x^3*dx*dy - y*z*dx*dy
True
sage: W.zero() == 0
True
sage: W.one() == 1
True
sage: x == 1
False
sage: x + 1 == 1
False
sage: W(x^3 - y*z) == x^3 - y*z
True
"""
if have_same_parent(self, other):
return self.__monomials == other.__monomials
try:
return get_coercion_model().bin_op(self, other, operator.eq)
except TypeError:
return False
def __mul__(self, right):
r"""
Product of two elements
INPUT::
- ``self``, ``right`` -- two elements
This calls the `_mul_` method of ``self``, if it is
available and the two elements have the same parent.
Otherwise, the job is delegated to the coercion model.
Do not override; instead implement a ``_mul_`` method in the
element class or a ``product`` method in the parent class.
EXAMPLES::
sage: S = Semigroups().example("free")
sage: x = S('a'); y = S('b')
sage: x * y
'ab'
"""
if have_same_parent(self, right) and hasattr(self, "_mul_"):
return self._mul_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(self, right, operator.mul)
def __mul__(self, right):
r"""
Product of two elements
INPUT::
- ``self``, ``right`` -- two elements
This calls the `_mul_` method of ``self``, if it is
available and the two elements have the same parent.
Otherwise, the job is delegated to the coercion model.
Do not override; instead implement a ``_mul_`` method in the
element class or a ``product`` method in the parent class.
EXAMPLES::
sage: S = Semigroups().example("free")
sage: x = S('a'); y = S('b')
sage: x * y
'ab'
"""
if have_same_parent(self, right) and hasattr(self, "_mul_"):
return self._mul_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(self, right, operator.mul)
def __eq__(self, other):
"""
Check equality.
TESTS::
sage: R.<x,y,z> = QQ[]
sage: W = DifferentialWeylAlgebra(R)
sage: dx,dy,dz = W.differentials()
sage: dy*(x^3-y*z)*dx == -z*dx + x^3*dx*dy - y*z*dx*dy
True
sage: W.zero() == 0
True
sage: W.one() == 1
True
sage: x == 1
False
sage: x + 1 == 1
False
sage: W(x^3 - y*z) == x^3 - y*z
True
"""
if have_same_parent(self, other):
return self.__monomials == other.__monomials
try:
return get_coercion_model().bin_op(self, other, operator.eq)
except TypeError:
return False
def __eq__(self, other):
"""
EXAMPLES::
sage: F = GF(3); MS = MatrixSpace(F,2)
sage: gens = [MS([1,0, 0,1]), MS([1,1, 0,1])]
sage: G = MatrixGroup(gens)
sage: H = MatrixGroup(gens)
sage: g = G([1,1, 0,1])
sage: h = H([1,1, 0,1])
sage: g == h
True
"""
return have_same_parent(self, other) and self.__mat == other.__mat
def __eq__(self, other):
"""
EXAMPLES::
sage: F = GF(3); MS = MatrixSpace(F,2)
sage: gens = [MS([1,0, 0,1]), MS([1,1, 0,1])]
sage: G = MatrixGroup(gens)
sage: H = MatrixGroup(gens)
sage: g = G([1,1, 0,1])
sage: h = H([1,1, 0,1])
sage: g == h
True
"""
return have_same_parent(self, other) and self.__mat == other.__mat
def __mul__(self, right):
"""
EXAMPLES::
sage: s = SFASchur(QQ)
sage: a = s([2])
sage: a._mul_(a) #indirect doctest
s[2, 2] + s[3, 1] + s[4]
Todo: use AlgebrasWithBasis(QQ).example()
"""
if have_same_parent(self, right) and hasattr(self, "_mul_"):
return self._mul_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(self, right, operator.mul)
def __mul__(self, right):
"""
EXAMPLES::
sage: s = SFASchur(QQ)
sage: a = s([2])
sage: a._mul_(a) #indirect doctest
s[2, 2] + s[3, 1] + s[4]
Todo: use AlgebrasWithBasis(QQ).example()
"""
if have_same_parent(self, right) and hasattr(self, "_mul_"):
return self._mul_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(self, right, operator.mul)
def __radd__(self, left):
r"""
Handles the sum of two elements, when the left hand side
needs to be coerced first.
EXAMPLES::
sage: F = CommutativeAdditiveSemigroups().example()
sage: (a,b,c,d) = F.additive_semigroup_generators()
sage: a.__radd__(b)
a + b
"""
if have_same_parent(left, self) and hasattr(left, "_add_"):
return left._add_(self)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(left, self, operator.add)
def __radd__(self, left):
r"""
Handles the sum of two elements, when the left hand side
needs to be coerced first.
EXAMPLES::
sage: F = CommutativeAdditiveSemigroups().example()
sage: (a,b,c,d) = F.additive_semigroup_generators()
sage: a.__radd__(b)
a + b
"""
if have_same_parent(left, self) and hasattr(left, "_add_"):
return left._add_(self)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(left, self, operator.add)
def __sub__(left, right):
"""
Top-level subtraction operator
See extensive documentation at the top of element.pyx.
EXAMPLES::
sage: F = CombinatorialFreeModule(QQ, ['a','b'])
sage: a,b = F.basis()
sage: a - b
B['a'] - B['b']
"""
if have_same_parent(left, right) and hasattr(left, "_sub_"):
return left._sub_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(left, right, operator.sub)
def __sub__(left, right):
"""
Return the difference between ``left`` and ``right``, if it exists.
This top-level implementation delegates the work to
the ``_sub_`` method or to coercion. See the extensive
documentation at the top of :ref:`sage.structure.element`.
EXAMPLES::
sage: F = CombinatorialFreeModule(QQ, ['a','b'])
sage: a,b = F.basis()
sage: a - b
B['a'] - B['b']
"""
if have_same_parent(left, right) and hasattr(left, "_sub_"):
return left._sub_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(left, right, operator.sub)
def __add__(self, right):
r"""
Sum of two elements
This calls the `_add_` method of ``self``, if it is
available and the two elements have the same parent.
Otherwise, the job is delegated to the coercion model.
Do not override; instead implement an ``_add_`` method in the
element class or a ``summation`` method in the parent class.
EXAMPLES::
sage: F = CommutativeAdditiveSemigroups().example()
sage: (a,b,c,d) = F.additive_semigroup_generators()
sage: a + b
a + b
"""
if have_same_parent(self, right) and hasattr(self, "_add_"):
return self._add_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(self, right, operator.add)
def __add__(self, right):
r"""
Sum of two elements
This calls the `_add_` method of ``self``, if it is
available and the two elements have the same parent.
Otherwise, the job is delegated to the coercion model.
Do not override; instead implement an ``_add_`` method in the
element class or a ``summation`` method in the parent class.
EXAMPLES::
sage: F = CommutativeAdditiveSemigroups().example()
sage: (a,b,c,d) = F.additive_semigroup_generators()
sage: a + b
a + b
"""
if have_same_parent(self, right) and hasattr(self, "_add_"):
return self._add_(right)
from sage.structure.element import get_coercion_model
import operator
return get_coercion_model().bin_op(self, right, operator.add)