Refactor conic curves

src/sage/schemes/plane_conics/con_field.py

@@ -8,21 +8,21 @@
 - Nick Alexander (2008-01-08)
 
 """
-#*****************************************************************************
-#       Copyright (C) 2008 Nick Alexander <ncalexander@gmail.com>
-#       Copyright (C) 2009/2010 Marco Streng <marco.streng@gmail.com>
+# *****************************************************************************
+#        Copyright (C) 2008 Nick Alexander <ncalexander@gmail.com>
+#        Copyright (C) 2009/2010 Marco Streng <marco.streng@gmail.com>
 #
-#  Distributed under the terms of the GNU General Public License (GPL)
+#   Distributed under the terms of the GNU General Public License (GPL)
 #
-#    This code is distributed in the hope that it will be useful,
-#    but WITHOUT ANY WARRANTY; without even the implied warranty of
-#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-#    General Public License for more details.
+#     This code is distributed in the hope that it will be useful,
+#     but WITHOUT ANY WARRANTY; without even the implied warranty of
+#     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+#     General Public License for more details.
 #
-#  The full text of the GPL is available at:
+#   The full text of the GPL is available at:
 #
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                   http://www.gnu.org/licenses/
+# *****************************************************************************
 
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
@@ -35,12 +35,12 @@
 from sage.matrix.constructor import Matrix
 from sage.structure.element import is_Matrix
 
-from sage.schemes.curves.projective_curve import ProjectivePlaneCurve
+from sage.schemes.curves.projective_curve import ProjectivePlaneCurve_field
 
 from sage.categories.fields import Fields
 _Fields = Fields()
 
-class ProjectiveConic_field(ProjectivePlaneCurve):
+class ProjectiveConic_field(ProjectivePlaneCurve_field):
     r"""
     Create a projective plane conic curve over a field.
     See ``Conic`` for full documentation.
@@ -68,17 +68,14 @@ def __init__(self, A, f):
             sage: c = Conic([1, 1, 1]); c
             Projective Conic Curve over Rational Field defined by x^2 + y^2 + z^2
         """
-        ProjectivePlaneCurve.__init__(self, A, f)
+        super().__init__(A, f)
         self._coefficients = [f[(2,0,0)], f[(1,1,0)], f[(1,0,1)],
                                 f[(0,2,0)], f[(0,1,1)], f[(0,0,2)]]
         self._parametrization = None
         self._diagonal_matrix = None
 
         self._rational_point = None
 
-
-
-
     def _repr_type(self):
         r"""
         Returns ``'Projective Conic'``, which is the first part of the
@@ -128,7 +125,7 @@ def base_extend(self, S):
                     # if (and only if) there is no point in the cache.
                     pt = con.point(pt)
             return con
-        return ProjectivePlaneCurve.base_extend(self, S)
+        return super().base_extend(S)
 
     def cache_point(self, p):
         r"""
@@ -168,7 +165,6 @@ def coefficients(self):
         """
         return self._coefficients
 
-
     def derivative_matrix(self):
         r"""
         Gives the derivative of the defining polynomial of
@@ -702,7 +698,7 @@ def hom(self, x, Y=None):
                                  (x, self, Y))
             x = Sequence(x*vector(self.ambient_space().gens()))
             return self.Hom(Y)(x, check = False)
-        return ProjectivePlaneCurve.hom(self, x, Y)
+        return super().hom(x, Y)
 
     def is_diagonal(self):
         r"""
@@ -743,7 +739,6 @@ def is_smooth(self):
             return self.defining_polynomial()([e, c, b]) != 0
         return self.determinant() != 0
 
-
     def _magma_init_(self, magma):
         """
         Internal function. Returns a string to initialize this
@@ -782,7 +777,6 @@ def _magma_init_(self, magma):
         magma_coeffs = [coeffs[i]._magma_init_(magma) for i in [0, 3, 5, 1, 4, 2]]
         return 'Conic([%s|%s])' % (kmn,','.join(magma_coeffs))
 
-
     def matrix(self):
         r"""
         Returns a matrix `M` such that `(x, y, z) M (x, y, z)^t`
@@ -959,12 +953,11 @@ def point(self, v, check=True):
         """
         if is_Vector(v):
             v = Sequence(v)
-        p = ProjectivePlaneCurve.point(self, v, check=check)
+        p = super().point(v, check=check)
         if self._rational_point is None:
             self._rational_point = p
         return p
 
-
     def random_rational_point(self, *args1, **args2):
         r"""
         Return a random rational point of the conic ``self``.
@@ -1013,7 +1006,6 @@ def random_rational_point(self, *args1, **args2):
             y = B.random_element(*args1, **args2)
         return par[0]([x,y])
 
-
     def rational_point(self, algorithm = 'default', read_cache = True):
         r"""
         Return a point on ``self`` defined over the base field.
@@ -1135,7 +1127,6 @@ def rational_point(self, algorithm = 'default', read_cache = True):
         raise ValueError("Conic %s has no rational points over %s!" % \
                           (self, self.ambient_space().base_ring()))
 
-
     def singular_point(self):
         r"""
         Returns a singular rational point of ``self``
@@ -1192,7 +1183,6 @@ def symmetric_matrix(self):
                        [ b/2,  d , e/2 ],
                        [ c/2, e/2,  f  ]])
 
-
     def upper_triangular_matrix(self):
         r"""
         The upper-triangular matrix `M` such that `(x y z) M (x y z)^t`

src/sage/schemes/projective/projective_morphism.py

@@ -2252,7 +2252,7 @@ def __call__(self, x):
 
         - ``x`` -- a point in the domain of definition
 
-        OUTPUT: a point in the codomain
+        OUTPUT: the image of the point ``x`` under the morphism
 
         TESTS::
 
@@ -2266,7 +2266,12 @@ def __call__(self, x):
             sage: _ == C([0, -1, 2])
             True
         """
-        for m in self.representatives():
+        try:
+            reprs = self.representatives()
+        except NotImplementedError:
+            reprs = [self.defining_polynomials()]
+
+        for m in reprs:
             try:
                 return super(SchemeMorphism_polynomial_projective_subscheme_field, m).__call__(x)
             except ValueError: