def _element_constructor_(self, x):
"""
Convert an element into this quotient space `V/W` if there is
a way to make sense of it.
An element converts into self if it can be converted into `V`,
or if not at least if it can be made sense of as a list of
length the dimension of self.
EXAMPLES:
We create a 2-dimensional quotient of a 3-dimension ambient
vector space::
sage: M = QQ^3 / [[1,2,3]]
A list of length 3 converts into ``QQ^3``, so it converts into
`M`::
sage: M([1,2,4]) #indirect doctest
(-1/3, -2/3)
sage: M([1,2,3])
(0, 0)
A list of length 2 converts into M, where here it just gives
the corresponding linear combination of the basis for `M`::
sage: M([1,2])
(1, 2)
sage: M.0 + 2*M.1
(1, 2)
Of course, elements of ``QQ^3`` convert into the quotient
module as well. Here is a different example::
sage: V = QQ^3; W = V.span([[1,0,0]]); Q = V/W
sage: Q(V.0)
(0, 0)
sage: Q(V.1)
(1, 0)
sage: Q.0
(1, 0)
sage: Q.0 + V.1
(2, 0)
Here we start with something that is over ZZ, so it
canonically coerces into ``QQ^3``, hence into ``self``::
sage: Q((ZZ^3)([1,2,3]))
(2, 3)
"""
if isinstance(x, self.element_class) and x.parent() is self:
return x
if isinstance(x, (list, tuple)) and len(x) == self.__domain.rank():
return self.__quo_map(self.__domain(x))
return FreeModule_ambient_field._element_constructor_(self, x)
def _element_constructor_(self, x):
"""
Convert an element into this quotient space `V/W` if there is
a way to make sense of it.
An element converts into self if it can be converted into `V`,
or if not at least if it can be made sense of as a list of
length the dimension of self.
EXAMPLES:
We create a 2-dimensional quotient of a 3-dimension ambient
vector space::
sage: M = QQ^3 / [[1,2,3]]
A list of length 3 converts into ``QQ^3``, so it converts into
`M`::
sage: M([1,2,4]) #indirect doctest
(-1/3, -2/3)
sage: M([1,2,3])
(0, 0)
A list of length 2 converts into M, where here it just gives
the corresponding linear combination of the basis for `M`::
sage: M([1,2])
(1, 2)
sage: M.0 + 2*M.1
(1, 2)
Of course, elements of ``QQ^3`` convert into the quotient
module as well. Here is a different example::
sage: V = QQ^3; W = V.span([[1,0,0]]); Q = V/W
sage: Q(V.0)
(0, 0)
sage: Q(V.1)
(1, 0)
sage: Q.0
(1, 0)
sage: Q.0 + V.1
(2, 0)
Here we start with something that is over ZZ, so it
canonically coerces into ``QQ^3``, hence into ``self``::
sage: Q((ZZ^3)([1,2,3]))
(2, 3)
"""
if isinstance(x, self.element_class) and x.parent() is self:
return x
if isinstance(x, (list, tuple)) and len(x) == self.__domain.rank():
return self.__quo_map(self.__domain(x))
return FreeModule_ambient_field._element_constructor_(self, x)
