def __init__(self, A, X):
if not is_ProjectiveSpace(A):
raise TypeError, "A (=%s) must be a projective space"%A
Curve_generic_projective.__init__(self, A, X)
d = self.dimension()
if d != 1:
raise ValueError, "defining equations (=%s) define a scheme of dimension %s != 1"%(X,d)
def __init__(self, A, X):
if not is_ProjectiveSpace(A):
raise TypeError, "A (=%s) must be a projective space" % A
Curve_generic_projective.__init__(self, A, X)
d = self.dimension()
if d != 1:
raise ValueError, "defining equations (=%s) define a scheme of dimension %s != 1" % (
X, d)
def __init__(self, parent, polys, check=True):
"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
EXAMPLES::
sage: A2.<x,y> = AffineSpace(QQ,2)
sage: H = A2.Hom(A2)
sage: H([x-y, x*y])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(x - y, x*y)
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError, "polys (=%s) must be a list or tuple" % polys
source_ring = parent.domain().coordinate_ring()
target = parent.codomain().ambient_space()
if len(polys) != target.ngens():
raise ValueError, "there must be %s polynomials" % target.ngens(
)
try:
polys = [source_ring(poly) for poly in polys]
except TypeError:
raise TypeError, "polys (=%s) must be elements of %s" % (
polys, source_ring)
from sage.rings.quotient_ring import QuotientRing_generic
if isinstance(source_ring, QuotientRing_generic):
lift_polys = [f.lift() for f in polys]
else:
lift_polys = polys
from sage.schemes.generic.projective_space import is_ProjectiveSpace
if is_ProjectiveSpace(target):
# if the codomain is a subscheme of projective space,
# then we need to make sure that polys have no common
# zeros
if isinstance(source_ring, QuotientRing_generic):
# if the coordinate ring of the domain is a
# quotient by an ideal, we need to check that the
# gcd of polys and the generators of the ideal is 1
gcd_polys = lift_polys + list(
source_ring.defining_ideal().gens())
else:
# if the domain is affine space, we just need to
# check the gcd of polys
gcd_polys = polys
from sage.rings.arith import gcd
if gcd(gcd_polys) != 1:
raise ValueError, "polys (=%s) must not have common factors" % polys
polys = Sequence(lift_polys)
polys.set_immutable()
# Todo: check that map is well defined (how?)
self.__polys = polys
SchemeMorphism.__init__(self, parent)
def __init__(self, parent, polys, check=True):
"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
EXAMPLES::
sage: A2.<x,y> = AffineSpace(QQ,2)
sage: H = A2.Hom(A2)
sage: H([x-y, x*y])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(x - y, x*y)
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError, "polys (=%s) must be a list or tuple"%polys
source_ring = parent.domain().coordinate_ring()
target = parent.codomain().ambient_space()
if len(polys) != target.ngens():
raise ValueError, "there must be %s polynomials"%target.ngens()
try:
polys = [source_ring(poly) for poly in polys]
except TypeError:
raise TypeError, "polys (=%s) must be elements of %s"%(polys,source_ring)
from sage.rings.quotient_ring import QuotientRing_generic
if isinstance(source_ring, QuotientRing_generic):
lift_polys = [f.lift() for f in polys]
else:
lift_polys = polys
from sage.schemes.generic.projective_space import is_ProjectiveSpace
if is_ProjectiveSpace(target):
# if the codomain is a subscheme of projective space,
# then we need to make sure that polys have no common
# zeros
if isinstance(source_ring, QuotientRing_generic):
# if the coordinate ring of the domain is a
# quotient by an ideal, we need to check that the
# gcd of polys and the generators of the ideal is 1
gcd_polys = lift_polys + list(source_ring.defining_ideal().gens())
else:
# if the domain is affine space, we just need to
# check the gcd of polys
gcd_polys = polys
from sage.rings.arith import gcd
if gcd(gcd_polys) != 1:
raise ValueError, "polys (=%s) must not have common factors"%polys
polys = Sequence(lift_polys)
polys.set_immutable()
# Todo: check that map is well defined (how?)
self.__polys = polys
SchemeMorphism.__init__(self, parent)
def __init__(self, parent, polys, check=True):
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError, "polys (=%s) must be a list or tuple"%polys
source_ring = parent.domain().coordinate_ring()
target = parent.codomain().ambient_space()
if len(polys) != target.ngens():
raise ValueError, "there must be %s polynomials"%target.ngens()
try:
polys = [source_ring(poly) for poly in polys]
except TypeError:
raise TypeError, "polys (=%s) must be elements of %s"%(polys,source_ring)
from sage.rings.quotient_ring import QuotientRing_generic
if isinstance(source_ring, QuotientRing_generic):
lift_polys = [f.lift() for f in polys]
else:
lift_polys = polys
from sage.schemes.generic.projective_space import is_ProjectiveSpace
if is_ProjectiveSpace(target):
# if the codomain is a subscheme of projective space,
# then we need to make sure that polys have no common
# zeros
if isinstance(source_ring, QuotientRing_generic):
# if the coordinate ring of the domain is a
# quotient by an ideal, we need to check that the
# gcd of polys and the generators of the ideal is 1
gcd_polys = lift_polys + list(source_ring.defining_ideal().gens())
else:
# if the domain is affine space, we just need to
# check the gcd of polys
gcd_polys = polys
from sage.rings.arith import gcd
if gcd(gcd_polys) != 1:
raise ValueError, "polys (=%s) must not have common factors"%polys
polys = Sequence(lift_polys)
polys.set_immutable()
# Todo: check that map is well defined (how?)
self.__polys = polys
SchemeMorphism.__init__(self, parent)
def __init__(self, A, f):
if not (is_ProjectiveSpace(A) and A.dimension != 2):
raise TypeError, "Argument A (= %s) must be a projective plane."%A
Curve_generic_projective.__init__(self, A, [f])
def __init__(self, A, f):
if not (is_ProjectiveSpace(A) and A.dimension != 2):
raise TypeError, "Argument A (= %s) must be a projective plane." % A
Curve_generic_projective.__init__(self, A, [f])