def __init__(self, C):
"""
Initialize.
TESTS::
sage: from sage.schemes.jacobians.abstract_jacobian import Jacobian_generic
sage: P2.<x, y, z> = ProjectiveSpace(QQ, 2)
sage: C = Curve(x^3 + y^3 + z^3)
sage: J = Jacobian_generic(C); J
Jacobian of Projective Plane Curve over Rational Field defined by x^3 + y^3 + z^3
sage: type(J)
<class 'sage.schemes.jacobians.abstract_jacobian.Jacobian_generic_with_category'>
Note: this is an abstract parent, so we skip element tests::
sage: TestSuite(J).run(skip =["_test_an_element",\
"_test_elements",\
"_test_elements_eq_reflexive",\
"_test_elements_eq_symmetric",\
"_test_elements_eq_transitive",\
"_test_elements_neq",\
"_test_some_elements"])
::
sage: Jacobian_generic(ZZ)
Traceback (most recent call last):
...
TypeError: Argument (=Integer Ring) must be a scheme.
sage: Jacobian_generic(P2)
Traceback (most recent call last):
...
ValueError: C (=Projective Space of dimension 2 over Rational Field)
must have dimension 1.
::
sage: P2.<x, y, z> = ProjectiveSpace(Zmod(6), 2)
sage: C = Curve(x + y + z, P2)
sage: Jacobian_generic(C)
Traceback (most recent call last):
...
TypeError: C (=Projective Plane Curve over Ring of integers modulo 6
defined by x + y + z) must be defined over a field.
"""
if not is_Scheme(C):
raise TypeError("Argument (=%s) must be a scheme." % C)
if C.base_ring() not in _Fields:
raise TypeError("C (=%s) must be defined over a field." % C)
if C.dimension() != 1:
raise ValueError("C (=%s) must have dimension 1." % C)
self.__curve = C
Scheme.__init__(self, C.base_scheme())
def __init__(self, n, R=ZZ):
"""
TESTS::
sage: from sage.schemes.generic.ambient_space import AmbientSpace
sage: A = AmbientSpace(5, ZZ)
sage: TestSuite(A).run() # not tested (abstract scheme with no elements?)
"""
if not isinstance(R, CommutativeRing):
raise TypeError("R (={}) must be a commutative ring".format(R))
if n < 0:
raise ValueError("n (={}) must be nonnegative".format(n))
self._dimension_relative = Integer(n)
Scheme.__init__(self, R)
def __init__(self, n, R=ZZ):
"""
TEST::
sage: from sage.schemes.generic.ambient_space import AmbientSpace
sage: A = AmbientSpace(5, ZZ)
sage: TestSuite(A).run() # not tested (abstract scheme with no elements?)
"""
if not is_CommutativeRing(R):
raise TypeError, "R (=%s) must be a commutative ring" % R
n = Integer(n)
if n < 0:
raise ValueError, "n (=%s) must be nonnegative" % n
self._dimension_relative = n
Scheme.__init__(self, R)
def __init__(self, n, R=ZZ):
"""
TEST::
sage: from sage.schemes.generic.ambient_space import AmbientSpace
sage: A = AmbientSpace(5, ZZ)
sage: TestSuite(A).run() # not tested (abstract scheme with no elements?)
"""
if not is_CommutativeRing(R):
raise TypeError, "R (=%s) must be a commutative ring"%R
n = Integer(n)
if n < 0:
raise ValueError, "n (=%s) must be nonnegative"%n
self._dimension_relative = n
Scheme.__init__(self, R)
def __init__(self, C):
"""
TESTS::
sage: from sage.schemes.jacobians.abstract_jacobian import Jacobian_generic
sage: P2.<x, y, z> = ProjectiveSpace(QQ, 2)
sage: C = Curve(x^3 + y^3 + z^3)
sage: J = Jacobian_generic(C); J
Jacobian of Projective Plane Curve over Rational Field defined by x^3 + y^3 + z^3
sage: type(J)
<class 'sage.schemes.jacobians.abstract_jacobian.Jacobian_generic_with_category'>
Note: this is an abstract parent, so we skip element tests::
sage: TestSuite(J).run(skip =["_test_an_element",\
"_test_elements",\
"_test_elements_eq_reflexive",\
"_test_elements_eq_symmetric",\
"_test_elements_eq_transitive",\
"_test_elements_neq",\
"_test_some_elements"])
::
sage: Jacobian_generic(ZZ)
Traceback (most recent call last):
...
TypeError: Argument (=Integer Ring) must be a scheme.
sage: Jacobian_generic(P2)
Traceback (most recent call last):
...
ValueError: C (=Projective Space of dimension 2 over Rational Field) must have dimension 1.
sage: P2.<x, y, z> = ProjectiveSpace(Zmod(6), 2)
sage: C = Curve(x + y + z)
sage: Jacobian_generic(C)
Traceback (most recent call last):
...
TypeError: C (=Projective Plane Curve over Ring of integers modulo 6 defined by x + y + z) must be defined over a field.
"""
if not is_Scheme(C):
raise TypeError("Argument (=%s) must be a scheme."%C)
if C.base_ring() not in _Fields:
raise TypeError("C (=%s) must be defined over a field."%C)
if C.dimension() != 1:
raise ValueError("C (=%s) must have dimension 1."%C)
self.__curve = C
Scheme.__init__(self, C.base_scheme())