def __init__(self, poly, ambient=None):
"""
Return the projective hypersurface in the space ambient
defined by the polynomial poly.
If ambient is not given, it will be constructed based on
poly.
EXAMPLES::
sage: P.<x, y, z> = ProjectiveSpace(ZZ, 2)
sage: ProjectiveHypersurface(x-y, P)
Projective hypersurface defined by x - y in Projective Space of dimension 2 over Integer Ring
::
sage: R.<x, y, z> = QQ[]
sage: ProjectiveHypersurface(x-y)
Projective hypersurface defined by x - y in Projective Space of dimension 2 over Rational Field
TESTS::
sage: H = ProjectiveHypersurface(x-y)
sage: H == loads(dumps(H))
True
"""
if not is_MPolynomial(poly):
raise TypeError(
"Defining polynomial (=%s) must be a multivariate polynomial."
% poly)
if not poly.is_homogeneous():
raise TypeError("Defining polynomial (=%s) must be homogeneous." %
poly)
if ambient is None:
R = poly.parent()
from sage.schemes.projective.projective_space import ProjectiveSpace
ambient = ProjectiveSpace(R.base_ring(), R.ngens() - 1)
ambient._coordinate_ring = R
AlgebraicScheme_subscheme_projective.__init__(self, ambient, [poly])
def __init__(self, poly, ambient=None):
"""
Return the projective hypersurface in the space ambient
defined by the polynomial poly.
If ambient is not given, it will be constructed based on
poly.
EXAMPLES::
sage: P.<x, y, z> = ProjectiveSpace(ZZ, 2)
sage: ProjectiveHypersurface(x-y, P)
Projective hypersurface defined by x - y in Projective Space of dimension 2 over Integer Ring
::
sage: R.<x, y, z> = QQ[]
sage: ProjectiveHypersurface(x-y)
Projective hypersurface defined by x - y in Projective Space of dimension 2 over Rational Field
TESTS::
sage: H = ProjectiveHypersurface(x-y)
sage: H == loads(dumps(H))
True
"""
if not is_MPolynomial(poly):
raise TypeError, \
"Defining polynomial (=%s) must be a multivariate polynomial."%poly
if not poly.is_homogeneous():
raise TypeError, "Defining polynomial (=%s) must be homogeneous."%poly
if ambient == None:
R = poly.parent()
from sage.schemes.projective.projective_space import ProjectiveSpace
ambient = ProjectiveSpace(R.base_ring(), R.ngens()-1)
ambient._coordinate_ring = R
AlgebraicScheme_subscheme_projective.__init__(self, ambient, [poly])
