Fix comparison for divisors of curves (and FormalSum commutativity)

src/sage/schemes/generic/divisor.py

@@ -45,6 +45,7 @@
 from sage.misc.repr import repr_lincomb
 from sage.misc.search import search
 from sage.rings.integer_ring import ZZ
+from sage.sets.set import Set
 from sage.structure.formal_sum import FormalSum
 
 from .morphism import is_SchemeMorphism
@@ -121,6 +122,29 @@ def is_Divisor(x):
 class Divisor_generic(FormalSum):
     r"""
     A Divisor.
+
+    TESTS::
+
+        sage: E = EllipticCurve([1, 2])
+        sage: P = E(-1, 0)
+        sage: Q = E(1, 2)
+        sage: Pd = E.divisor(P)
+        sage: Qd = E.divisor(Q)
+        sage: Pd + Qd == Qd + Pd
+        True
+        sage: Pd != Qd
+        True
+        sage: C = EllipticCurve([2, 1])
+        sage: R = C(1, 2)
+        sage: Rd = C.divisor(R)
+        sage: Qd == Rd
+        False
+        sage: Rd == Qd
+        False
+        sage: Qd == (2 * (Qd * 1/2))
+        True
+        sage: Qd == 1/2 * Qd
+        False
     """
 
     def __init__(self, v, parent, check=True, reduce=True):
@@ -363,14 +387,15 @@ def _repr_(self):
         """
         return repr_lincomb([(tuple(I.gens()), c) for c, I in self])
 
-    def support(self):
+    def support(self) -> list:
         """
         Return the support of this divisor, which is the set of points that
         occur in this divisor with nonzero coefficients.
 
         EXAMPLES::
 
-            sage: x,y = AffineSpace(2, GF(5), names='xy').gens()
+            sage: A = AffineSpace(2, GF(5), names='xy')
+            sage: x, y = A.gens()
             sage: C = Curve(y^2 - x^9 - x)
             sage: pts = C.rational_points(); pts
             [(0, 0), (2, 2), (2, 3), (3, 1), (3, 4)]
@@ -384,6 +409,7 @@ def support(self):
         This checks that :issue:`10732` is fixed::
 
             sage: R.<x, y, z> = GF(5)[]
+            sage: PS = ProjectiveSpace(R)
             sage: C = Curve(x^7 + y^7 + z^7)
             sage: pts = C.rational_points()
             sage: D = C.divisor([(2, pts[0])])

src/sage/schemes/generic/divisor_group.py

@@ -190,6 +190,33 @@ def _element_constructor_(self, x, check=True, reduce=True):
         else:
             return Divisor_generic([(self.base_ring()(1), x)], check=False, reduce=False, parent=self)
 
+    def _coerce_map_from_(self, other):
+        r"""
+        Check if there is a coercion from ``other`` to ``self``.
+        This is used to prevent divisors on different schemes from comparing as equal to each other.
+
+        TESTS::
+
+            sage: C = EllipticCurve([2, 1])
+            sage: E = EllipticCurve([1, 2])
+            sage: C.divisor_group()._coerce_map_from_(E.divisor_group())
+            False
+            sage: E.divisor_group()._coerce_map_from_(C.divisor_group())
+            False
+            sage: E.divisor_group()._coerce_map_from_(E.divisor_group())
+            True
+            sage: C.divisor_group()._coerce_map_from_(C.divisor_group())
+            True
+            sage: D = 1/2 * E.divisor(E(1, 2))
+            sage: D.parent()._coerce_map_from_(E.divisor_group())
+            True
+            sage: E.divisor_group()._coerce_map_from_(D.parent())
+            False
+        """
+        return (isinstance(other, DivisorGroup_generic)
+                and self.scheme() == other.scheme()
+                and super()._coerce_map_from_(other))
+
     def scheme(self):
         r"""
         Return the scheme supporting the divisors.

src/sage/structure/formal_sum.py

@@ -95,6 +95,11 @@ def __init__(self, x, parent=None, check=True, reduce=True):
         - ``reduce`` -- reduce (default: ``True``) if ``False``, do not
           combine common terms
 
+        .. WARNING::
+
+            Setting ``reduce`` to ``False`` can cause issues when comparing
+            equal sums but with different orders and/or cancellations.
+
         EXAMPLES::
 
             sage: FormalSum([(1,2/3), (3,2/3), (-5, 7)])
@@ -230,8 +235,19 @@ def _richcmp_(self, other, op):
             True
             sage: a == 0          # 0 is coerced into a.parent()(0)
             False
+
+        TESTS::
+
+            sage: a = FormalSum([(1, 3), (2, 5)])
+            sage: b = FormalSum([(2, 5), (1, 3)])
+            sage: a == b
+            True
+            sage: b == a
+            True
         """
-        return richcmp(self._data, other._data, op)
+        self_data = [(c, x) for (x, c) in sorted(self._data, key=str)]
+        other_data = [(c, x) for (x, c) in sorted(other._data, key=str)]
+        return richcmp(self_data, other_data, op)
 
     def _neg_(self):
         """