20697: Added documentation and made curve string labels match class n…

…ames.

src/sage/schemes/affine/affine_space.py

@@ -946,9 +946,9 @@ def curve(self,F):
 
             sage: A.<x,y,z> = AffineSpace(QQ, 3)
             sage: A.curve([y - x^4, z - y^5])
-            Affine Space Curve over Rational Field defined by -x^4 + y, -y^5 + z
+            Affine Curve over Rational Field defined by -x^4 + y, -y^5 + z
         """
-        from sage.schemes.plane_curves.constructor import Curve
+        from sage.schemes.curves.constructor import Curve
         return Curve(F, self)
 
 class AffineSpace_finite_field(AffineSpace_field):

src/sage/schemes/curves/affine_curve.py

@@ -1,5 +1,19 @@
 """
-Affine plane curves over a general ring
+Affine curves over fields.
+
+EXAMPLES:
+
+We can construct curves in either an affine plane::
+
+    sage: A.<x,y> = AffineSpace(QQ, 2)
+    sage: C = Curve([y - x^2], A); C
+    Affine Plane Curve over Rational Field defined by -x^2 + y
+
+or in higher dimensional affine space::
+
+    sage: A.<x,y,z,w> = AffineSpace(QQ, 4)
+    sage: C = Curve([y - x^2, z - w^3, w - y^4], A); C
+    Affine Curve over Rational Field defined by -x^2 + y, -w^3 + z, -y^4 + w
 
 AUTHORS:
 
@@ -36,9 +50,37 @@
 
 class AffineCurve(Curve_generic, AlgebraicScheme_subscheme_affine):
     def _repr_type(self):
-        return "Affine Space"
+        r"""
+        Return a string representation of the type of this curve.
+
+        EXAMPLES::
+
+            sage: A.<x,y,z,w> = AffineSpace(QQ, 4)
+            sage: C = Curve([x - y, z - w, w - x], A)
+            sage: C._repr_type()
+            'Affine'
+        """
+        return "Affine"
 
     def __init__(self, A, X):
+        r"""
+        Initialization function.
+
+        EXAMPLES::
+
+            sage: R.<v> = QQ[]
+            sage: K.<u> = NumberField(v^2 + 3)
+            sage: A.<x,y,z> = AffineSpace(K, 3)
+            sage: C = Curve([z - u*x^2, y^2], A); C
+            Affine Curve over Number Field in u with defining polynomial v^2 + 3
+            defined by (-u)*x^2 + z, y^2
+
+        ::
+
+            sage: A.<x,y,z> = AffineSpace(GF(7), 3)
+            sage: C = Curve([x^2 - z, z - 8*x], A); C
+            Affine Curve over Finite Field of size 7 defined by x^2 - z, -x + z
+        """
         if not is_AffineSpace(A):
             raise TypeError("A (=%s) must be an affine space"%A)
         Curve_generic.__init__(self, A, X)
@@ -48,12 +90,38 @@ def __init__(self, A, X):
 
 class AffinePlaneCurve(AffineCurve):
     def __init__(self, A, f):
+        r"""
+        Initialization function.
+
+        EXAMPLES::
+
+            sage: A.<x,y> = AffineSpace(QQ, 2)
+            sage: C = Curve([x^3 - y^2], A); C
+            Affine Plane Curve over Rational Field defined by x^3 - y^2
+
+        ::
+
+            sage: A.<x,y> = AffineSpace(CC, 2)
+            sage: C = Curve([y^2 + x^2], A); C
+            Affine Plane Curve over Complex Field with 53 bits of precision defined
+            by x^2 + y^2
+        """
         if not (is_AffineSpace(A) and A.dimension != 2):
             raise TypeError("Argument A (= %s) must be an affine plane."%A)
         Curve_generic.__init__(self, A, [f])
 
     def _repr_type(self):
-        return "Affine"
+        r"""
+        Return a string representation of the type of this curve.
+
+        EXAMPLES::
+
+            sage: A.<x,y> = AffineSpace(QQ, 2)
+            sage: C = Curve([y - 7/2*x^5 + x - 3], A)
+            sage: C._repr_type()
+            'Affine Plane'
+        """
+        return "Affine Plane"
 
     def divisor_of_function(self, r):
         """
@@ -239,7 +307,7 @@ def rational_points(self, algorithm="enum"):
             sage: A.<x,y> = AffineSpace(2,GF(9,'a'))
             sage: C = Curve(x^2 + y^2 - 1)
             sage: C
-            Affine Curve over Finite Field in a of size 3^2 defined by x^2 + y^2 - 1
+            Affine Plane Curve over Finite Field in a of size 3^2 defined by x^2 + y^2 - 1
             sage: C.rational_points()
             [(0, 1), (0, 2), (1, 0), (2, 0), (a + 1, a + 1), (a + 1, 2*a + 2), (2*a + 2, a + 1), (2*a + 2, 2*a + 2)]
         """
@@ -346,7 +414,7 @@ def rational_points(self, algorithm="enum"):
             sage: x, y = (GF(5)['x,y']).gens()
             sage: f = y^2 - x^9 - x
             sage: C = Curve(f); C
-            Affine Curve over Finite Field of size 5 defined by -x^9 + y^2 - x
+            Affine Plane Curve over Finite Field of size 5 defined by -x^9 + y^2 - x
             sage: C.rational_points(algorithm='bn')
             [(0, 0), (2, 2), (2, 3), (3, 1), (3, 4)]
             sage: C = Curve(x - y + 1)

src/sage/schemes/curves/constructor.py

@@ -1,5 +1,5 @@
 """
-Plane curve constructors
+General curve constructors.
 
 AUTHORS:
 
@@ -78,7 +78,7 @@ def Curve(F, A=None):
 
         sage: x,y,z = QQ['x,y,z'].gens()
         sage: C = Curve(x^3 + y^3 + z^3); C
-        Projective Curve over Rational Field defined by x^3 + y^3 + z^3
+        Projective Plane Curve over Rational Field defined by x^3 + y^3 + z^3
         sage: C.genus()
         1
 
@@ -88,20 +88,20 @@ def Curve(F, A=None):
 
         sage: x,y = GF(7)['x,y'].gens()
         sage: C = Curve(y^2 + x^3 + x^10); C
-        Affine Curve over Finite Field of size 7 defined by x^10 + x^3 + y^2
+        Affine Plane Curve over Finite Field of size 7 defined by x^10 + x^3 + y^2
         sage: C.genus()
         0
         sage: x, y = QQ['x,y'].gens()
         sage: Curve(x^3 + y^3 + 1)
-        Affine Curve over Rational Field defined by x^3 + y^3 + 1
+        Affine Plane Curve over Rational Field defined by x^3 + y^3 + 1
 
     EXAMPLE: A projective space curve
 
     ::
 
         sage: x,y,z,w = QQ['x,y,z,w'].gens()
         sage: C = Curve([x^3 + y^3 - z^3 - w^3, x^5 - y*z^4]); C
-        Projective Space Curve over Rational Field defined by x^3 + y^3 - z^3 - w^3, x^5 - y*z^4
+        Projective Curve over Rational Field defined by x^3 + y^3 - z^3 - w^3, x^5 - y*z^4
         sage: C.genus()
         13
 
@@ -111,7 +111,7 @@ def Curve(F, A=None):
 
         sage: x,y,z = QQ['x,y,z'].gens()
         sage: C = Curve([y^2 + x^3 + x^10 + z^7,  x^2 + y^2]); C
-        Affine Space Curve over Rational Field defined by x^10 + z^7 + x^3 + y^2, x^2 + y^2
+        Affine Curve over Rational Field defined by x^10 + z^7 + x^3 + y^2, x^2 + y^2
         sage: C.genus()
         47
 
@@ -123,7 +123,7 @@ def Curve(F, A=None):
         sage: Curve((x-y)*(x+y))
         Projective Conic Curve over Rational Field defined by x^2 - y^2
         sage: Curve((x-y)^2*(x+y)^2)
-        Projective Curve over Rational Field defined by x^4 - 2*x^2*y^2 + y^4
+        Projective Plane Curve over Rational Field defined by x^4 - 2*x^2*y^2 + y^4
 
     EXAMPLE: A union of curves is a curve.
 
@@ -133,7 +133,7 @@ def Curve(F, A=None):
         sage: C = Curve(x^3 + y^3 + z^3)
         sage: D = Curve(x^4 + y^4 + z^4)
         sage: C.union(D)
-        Projective Curve over Rational Field defined by
+        Projective Plane Curve over Rational Field defined by
         x^7 + x^4*y^3 + x^3*y^4 + y^7 + x^4*z^3 + y^4*z^3 + x^3*z^4 + y^3*z^4 + z^7
 
     The intersection is not a curve, though it is a scheme.
@@ -203,24 +203,24 @@ def Curve(F, A=None):
                 raise TypeError("F (=%s) must consist of a single nonconstant polynomial to define a plane curve"%(F,))
         if is_AffineSpace(A):
             if n > 2:
-                return AffineSpaceCurve_generic(A, F)
+                return AffineCurve(A, F)
             k = A.base_ring()
             if is_FiniteField(k):
                 if k.is_prime_field():
-                    return AffineCurve_prime_finite_field(A, F[0])
-                return AffineCurve_finite_field(A, F[0])
-            return AffineCurve_generic(A, F[0])
+                    return AffinePlaneCurve_prime_finite_field(A, F[0])
+                return AffinePlaneCurve_finite_field(A, F[0])
+            return AffinePlaneCurve(A, F[0])
         elif is_ProjectiveSpace(A):
             if not all([f.is_homogeneous() for f in F]):
                 raise TypeError("polynomials defining a curve in a projective space must be homogeneous")
             if n > 2:
-                return ProjectiveSpaceCurve_generic(A, F)
+                return ProjectiveCurve(A, F)
             k = A.base_ring()
             if is_FiniteField(k):
                 if k.is_prime_field():
-                    return ProjectiveCurve_prime_finite_field(A, F[0])
-                return ProjectiveCurve_finite_field(A, F[0])
-            return ProjectiveCurve_generic(A, F[0])
+                    return ProjectivePlaneCurve_prime_finite_field(A, F[0])
+                return ProjectivePlaneCurve_finite_field(A, F[0])
+            return ProjectivePlaneCurve(A, F[0])
 
     if is_AlgebraicScheme(F):
         return Curve(F.defining_polynomials(), F.ambient_space())

src/sage/schemes/curves/curve.py

@@ -1,5 +1,5 @@
 """
-Generic plane curves
+Generic plane curves.
 """
 
 from sage.misc.all import latex
@@ -13,6 +13,8 @@
 
 class Curve_generic(AlgebraicScheme_subscheme):
     r"""
+    Generic curve class.
+
     EXAMPLES::
 
         sage: A.<x,y,z> = AffineSpace(QQ,3)
@@ -23,26 +25,41 @@ class Curve_generic(AlgebraicScheme_subscheme):
 
     def _repr_(self):
         """
+        Return a string representation of this curve.
+
         EXAMPLES::
 
             sage: A.<x,y,z> = AffineSpace(QQ,3)
             sage: C = Curve([x-y,z-2])
             sage: C
-            Affine Space Curve over Rational Field defined by x - y, z - 2
+            Affine Curve over Rational Field defined by x - y, z - 2
 
             sage: P.<x,y,z> = ProjectiveSpace(QQ,2)
             sage: C = Curve(x-y)
             sage: C
-            Projective Curve over Rational Field defined by x - y
+            Projective Plane Curve over Rational Field defined by x - y
         """
         return "%s Curve over %s defined by %s"%(
             self._repr_type(), self.base_ring(), ', '.join([str(x) for x in self.defining_polynomials()]))
 
     def _repr_type(self):
+        r"""
+        Return a string representation of the type of this curve.
+
+        EXAMPLES::
+
+            sage: P.<x,y,z,w> = ProjectiveSpace(QQ, 3)
+            sage: C = Curve([w^3 - z^3, w*x - x^2])
+            sage: from sage.schemes.curves.curve import Curve_generic
+            sage: Curve_generic._repr_type(C)
+            'Generic'
+        """
         return "Generic"
 
     def _latex_(self):
         """
+        Return a latex representation of this curve.
+
         EXAMPLES::
 
             sage: x,y,z = PolynomialRing(QQ, 3, names='x,y,z').gens()