def __init__(self, poly, ambient=None):
"""
Return the affine hypersurface in the space ambient
defined by the polynomial poly.
If ambient is not given, it will be constructed based on
poly.
EXAMPLES::
sage: A.<x, y, z> = AffineSpace(ZZ, 3)
sage: AffineHypersurface(x*y-z^3, A)
Affine hypersurface defined by -z^3 + x*y in Affine Space of dimension 3 over Integer Ring
::
sage: A.<x, y, z> = QQ[]
sage: AffineHypersurface(x*y-z^3)
Affine hypersurface defined by -z^3 + x*y in Affine Space of dimension 3 over Rational Field
TESTS::
sage: H = AffineHypersurface(x*y-z^3)
sage: H == loads(dumps(H))
True
"""
if not is_MPolynomial(poly):
raise TypeError, "Defining polynomial (= %s) must be a multivariate polynomial"%poly
if ambient == None:
R = poly.parent()
from sage.schemes.affine.affine_space import AffineSpace
ambient = AffineSpace(R.base_ring(), R.ngens())
ambient._coordinate_ring = R
AlgebraicScheme_subscheme_affine.__init__(self, ambient, [poly])
def __init__(self, poly, ambient=None):
"""
Return the affine hypersurface in the space ambient
defined by the polynomial poly.
If ambient is not given, it will be constructed based on
poly.
EXAMPLES::
sage: A.<x, y, z> = AffineSpace(ZZ, 3)
sage: AffineHypersurface(x*y-z^3, A)
Affine hypersurface defined by -z^3 + x*y in Affine Space of dimension 3 over Integer Ring
::
sage: A.<x, y, z> = QQ[]
sage: AffineHypersurface(x*y-z^3)
Affine hypersurface defined by -z^3 + x*y in Affine Space of dimension 3 over Rational Field
TESTS::
sage: H = AffineHypersurface(x*y-z^3)
sage: H == loads(dumps(H))
True
"""
if not is_MPolynomial(poly):
raise TypeError, "Defining polynomial (= %s) must be a multivariate polynomial" % poly
if ambient == None:
R = poly.parent()
from sage.schemes.affine.affine_space import AffineSpace
ambient = AffineSpace(R.base_ring(), R.ngens())
ambient._coordinate_ring = R
AlgebraicScheme_subscheme_affine.__init__(self, ambient, [poly])
