bugfix in the genus code (addresses #28336

)

src/sage/schemes/curves/curve.py

@@ -19,6 +19,8 @@
 AUTHORS:
 
 - William Stein (2005)
+
+- Katie Ahrens (2024): fixed #28336
 """
 # ****************************************************************************
 #       Copyright (C) 2005 William Stein <[email protected]>
@@ -38,8 +40,10 @@
 from sage.schemes.generic.divisor_group import DivisorGroup
 from sage.schemes.generic.divisor import Divisor_curve
 
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.integer import Integer
-
+from sage.rings.rational_field import is_RationalField
+from sage.rings.qqbar import QQbar
 
 class Curve_generic(AlgebraicScheme_subscheme):
     r"""
@@ -153,8 +157,8 @@ def divisor_group(self, base_ring=None):
 
         INPUT:
 
-        - ``base_ring`` -- the base ring of the divisor group; usually, this is
-          `\ZZ` (default) or `\QQ`
+        - ``base_ring`` -- the base ring of the divisor group. Usually, this is
+          `\ZZ` (default) or `\QQ`.
 
         OUTPUT: the divisor group of the curve
 
@@ -201,16 +205,52 @@ def genus(self):
             sage: C = Curve(y^2*z - x^3 - 17*x*z^2 + y*z^2)
             sage: C.genus()
             1
+
+            Throw an error if the curve is not geometrically irreducible. Addresses issue #28336.
+            sage: x,y = PolynomialRing(QQ, 2, names='x,y').gens()
+            sage: C = Curve(x^2+y^2)
+            sage: C.genus()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: Curve is not geometrically irreducible
+
+            sage: FF.<y> =QQ[]
+            sage: R.<x> = FF[]
+            sage: K = QQ[y, x]
+            sage: poly2 = K(x^2 - y^4)
+            sage: C2 = Curve(poly2)
+            sage: C2.genus()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: Curve is not irreducible over the ground field
+
+
+            Geometric irreducibility is also checked for finite fields.
+            sage: x,y = PolynomialRing(GF(5), 2, names='x,y').gens()
+            sage: C = Curve(x^2+2)
+            sage: C.genus()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: Curve is not geometrically irreducible
         """
+
         return self.geometric_genus()
 
     def geometric_genus(self):
         r"""
         Return the geometric genus of the curve.
 
+        This is by definition the genus of the normalization of the projective
+        closure of the curve over the algebraic closure of the base field; the
+        base field must be a prime field.
+
+        .. NOTE::
+
+            This calls Singular's genus command.
+
         EXAMPLES:
 
-        Examples of projective curves::
+        Examples of projective curves. ::
 
             sage: P2 = ProjectiveSpace(2, GF(5), names=['x','y','z'])
             sage: x, y, z = P2.coordinate_ring().gens()
@@ -224,7 +264,14 @@ def geometric_genus(self):
             sage: C.geometric_genus()
             3
 
-        Examples of affine curves::
+            Addressing issue #28336
+            sage: C = Curve(x^2+y^2)
+            sage: C.geometric_genus()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: Curve is not irreducible over the ground field
+
+        Examples of affine curves. ::
 
             sage: x, y = PolynomialRing(GF(5), 2, 'xy').gens()
             sage: C = Curve(y^2 - x^3 - 17*x + y)
@@ -237,22 +284,31 @@ def geometric_genus(self):
             sage: C.geometric_genus()
             3
 
-        .. WARNING::
-
-            Geometric genus is only defined for `geometrically irreducible curve
-            <https://stacks.math.columbia.edu/tag/0BYE>`_. This method does not
-            check the condition. You may get a nonsensical result if the curve is
-            not geometrically irreducible::
-
-                sage: P2.<x,y,z> = ProjectiveSpace(QQ, 2)
-                sage: C = Curve(x^2 + y^2, P2)
-                sage: C.geometric_genus()  # nonsense!
-                -1
         """
+        k=self.base_ring()
+
+        #handle the rational case
+        if is_RationalField(k):
+            curve_over_closure = self.change_ring(QQbar)
+            if len(curve_over_closure.defining_polynomial().factor()) > 1:
+                if self.is_irreducible():
+                    raise NotImplementedError("Curve is not geometrically irreducible")
+                else:
+                    raise NotImplementedError("Curve is not irreducible over the ground field")
+
+        #handle the finite field case
+        if k.is_finite():
+            if len(self.change_ring(GF(k.characteristic()**self.defining_polynomial().degree())).defining_polynomial().factor()) > 1:
+                if self.is_irreducible():
+                    raise NotImplementedError("Curve is not geometrically irreducible")
+                else:
+                    raise NotImplementedError("Curve is not irreducible over the ground field")
+
         try:
             return self._genus
         except AttributeError:
-            raise NotImplementedError
+            self._genus = self.defining_ideal().genus()
+            return self._genus
 
     def union(self, other):
         """
@@ -275,7 +331,9 @@ def singular_subscheme(self):
         r"""
         Return the subscheme of singular points of this curve.
 
-        OUTPUT: a subscheme in the ambient space of this curve
+        OUTPUT:
+
+        - a subscheme in the ambient space of this curve.
 
         EXAMPLES::
 
@@ -313,10 +371,10 @@ def singular_points(self, F=None):
 
         INPUT:
 
-        - ``F`` -- (default: ``None``) field over which to find the singular
+        - ``F`` -- (default: None) field over which to find the singular
           points; if not given, the base ring of this curve is used
 
-        OUTPUT: list of points in the ambient space of this curve
+        OUTPUT: a list of points in the ambient space of this curve
 
         EXAMPLES::
 
@@ -360,13 +418,13 @@ def is_singular(self, P=None):
 
         INPUT:
 
-        - ``P`` -- (default: ``None``) a point on this curve
+        - ``P`` -- (default: None) a point on this curve
 
         OUTPUT:
 
-        boolean; if a point ``P`` is provided, and if ``P`` lies on this
-        curve, returns ``True`` if ``P`` is a singular point of this curve, and
-        ``False`` otherwise. If no point is provided, returns ``True`` or False
+        A boolean. If a point ``P`` is provided, and if ``P`` lies on this
+        curve, returns True if ``P`` is a singular point of this curve, and
+        False otherwise. If no point is provided, returns True or False
         depending on whether this curve is or is not singular, respectively.
 
         EXAMPLES::
@@ -393,9 +451,9 @@ def intersects_at(self, C, P):
 
         INPUT:
 
-        - ``C`` -- a curve in the same ambient space as this curve
+        - ``C`` -- a curve in the same ambient space as this curve.
 
-        - ``P`` -- a point in the ambient space of this curve
+        - ``P`` -- a point in the ambient space of this curve.
 
         EXAMPLES::
 
@@ -448,11 +506,11 @@ def intersection_points(self, C, F=None):
 
         - ``C`` -- a curve in the same ambient space as this curve
 
-        - ``F`` -- (default: ``None``) field over which to compute the
+        - ``F`` -- (default: None); field over which to compute the
           intersection points; if not specified, the base ring of this curve is
           used
 
-        OUTPUT: list of points in the ambient space of this curve
+        OUTPUT: a list of points in the ambient space of this curve
 
         EXAMPLES::