def __init__(self,
domain,
sub,
quotient_matrix,
lift_matrix,
inner_product_matrix=None):
"""
Create this quotient space, from the given domain, sub-module, and quotient_matrix.
EXAMPLES::
sage: A = QQ^5; V = A.span_of_basis([[1,0,-1,1,1], [1,-1,0,2/3,3/4]]); V
Vector space of degree 5 and dimension 2 over Rational Field
User basis matrix:
[ 1 0 -1 1 1]
[ 1 -1 0 2/3 3/4]
sage: W = V.span_of_basis([V.0 - 2/3*V.1]); W
Vector space of degree 5 and dimension 1 over Rational Field
User basis matrix:
[1/3 2/3 -1 5/9 1/2]
This creates a quotient vector space, which calls the init method::
sage: Q = V / W #indirect doctest
Behold the type of Q::
sage: type(Q)
<class 'sage.modules.quotient_module.FreeModule_ambient_field_quotient_with_category'>
We do some consistency checks on the extra quotient and
lifting structure of Q::
sage: Q(V.0)
(1)
sage: Q( V.0 - 2/3*V.1 )
(0)
sage: v = Q.lift(Q.0); v
(1, 0, -1, 1, 1)
sage: Q( v )
(1)
"""
base_field = domain.base_field()
dimension = quotient_matrix.ncols()
sparse = domain.is_sparse()
self.__sub = sub
self.__domain = domain
self.__hash = hash((domain, sub))
FreeModule_ambient_field.__init__(self, base_field, dimension, sparse)
self.__quo_map = domain.Hom(self)(quotient_matrix)
self.__quo_map.register_as_coercion()
self.__lift_map = self.Hom(domain)(lift_matrix)
def __init__(self, domain, sub, quotient_matrix, lift_matrix, inner_product_matrix = None):
"""
Create this quotient space, from the given domain, sub-module, and quotient_matrix.
EXAMPLES::
sage: A = QQ^5; V = A.span_of_basis([[1,0,-1,1,1], [1,-1,0,2/3,3/4]]); V
Vector space of degree 5 and dimension 2 over Rational Field
User basis matrix:
[ 1 0 -1 1 1]
[ 1 -1 0 2/3 3/4]
sage: W = V.span_of_basis([V.0 - 2/3*V.1]); W
Vector space of degree 5 and dimension 1 over Rational Field
User basis matrix:
[1/3 2/3 -1 5/9 1/2]
This creates a quotient vector space, which calls the init method::
sage: Q = V / W #indirect doctest
Behold the type of Q::
sage: type(Q)
<class 'sage.modules.quotient_module.FreeModule_ambient_field_quotient_with_category'>
We do some consistency checks on the extra quotient and
lifting structure of Q::
sage: Q(V.0)
(1)
sage: Q( V.0 - 2/3*V.1 )
(0)
sage: v = Q.lift(Q.0); v
(1, 0, -1, 1, 1)
sage: Q( v )
(1)
"""
base_field = domain.base_field()
dimension = quotient_matrix.ncols()
sparse = domain.is_sparse()
self.__sub = sub
self.__domain = domain
self.__hash = hash((domain, sub))
FreeModule_ambient_field.__init__(self, base_field, dimension, sparse)
self.__quo_map = domain.Hom(self)(quotient_matrix)
self.__quo_map.register_as_coercion()
self.__lift_map = self.Hom(domain)(lift_matrix)
