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))