def __init__(self, A, polynomials, embedding_center=None,
embedding_codomain=None, embedding_images=None):
"""
EXAMPLES::
sage: A.<x,y,z> = AffineSpace(QQ, 3)
sage: A.subscheme([y^2-x*z-x*y])
Closed subscheme of Affine Space of dimension 3 over Rational Field defined by:
-x*y + y^2 - x*z
"""
AlgebraicScheme_subscheme.__init__(self, A, polynomials)
if embedding_images is not None:
self._embedding_morphism = self.hom(embedding_images, embedding_codomain)
elif A._ambient_projective_space is not None:
self._embedding_morphism = self.projective_embedding \
(A._default_embedding_index, A._ambient_projective_space)
if embedding_center is not None:
self._embedding_center = self.point(embedding_center)
def union(self, other):
"""
Return the union of ``self`` and ``other``.
EXAMPLES::
sage: x,y,z = PolynomialRing(QQ, 3, names='x,y,z').gens()
sage: C1 = Curve(z - x)
sage: C2 = Curve(y - x)
sage: C1.union(C2).defining_polynomial()
x^2 - x*y - x*z + y*z
"""
from .constructor import Curve
return Curve(AlgebraicScheme_subscheme.union(self, other))
def union(self, other):
"""
Return the union of ``self`` and ``other``.
EXAMPLES::
sage: x,y,z = PolynomialRing(QQ, 3, names='x,y,z').gens()
sage: C1 = Curve(z - x)
sage: C2 = Curve(y - x)
sage: C1.union(C2).defining_polynomial()
x^2 - x*y - x*z + y*z
"""
from constructor import Curve
return Curve(AlgebraicScheme_subscheme.union(self, other))
def union(self, other):
from constructor import Curve
return Curve(AlgebraicScheme_subscheme.union(self, other))
def union(self, other):
from constructor import Curve
return Curve(AlgebraicScheme_subscheme.union(self, other))
