gh-40240: Fix a bug in khuri-makdisi small model
    
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Fixes #40237.

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URL: #40240
Reported by: Kwankyu Lee
Reviewer(s): Kwankyu Lee, Vincent Macri

Author: Release Manager

src/sage/rings/function_field/khuri_makdisi.pyx

@@ -819,13 +819,34 @@ cdef class KhuriMakdisi_small(KhuriMakdisi_base):
             sage: q2 = G.point(pl2 - b)
             sage: G.point(af.divisor()) == q1.addflip(p2)
             True
+
+        Check that :issue:`40237` is fixed::
+
+            sage: K = GF(2)
+            sage: F.<x> = FunctionField(K)
+            sage: t = polygen(F)
+            sage: E.<y> = F.extension(t^3 + (x^2 + x + 1)*t^2 + (x^3 + x + 1)*t + x^5 + x^4)
+            sage: O = E.maximal_order()
+            sage: Oinf = E.maximal_order_infinite()
+            sage: D1 = (-5*O.ideal(x, y).divisor() + O.ideal(x + 1, y^2 + y + 1).divisor()
+            ....:   + O.ideal(x^3 + x^2 + 1, y + x + 1).divisor())
+            sage: D2 = (Oinf.ideal(1/x, y/x^2 + 1).divisor() - 5*O.ideal(x, y).divisor()
+            ....:   + O.ideal(x^4 + x^3 + 1, y + x).divisor())
+            sage: J = E.jacobian('km_small', base_div=5*O.ideal(x, y).divisor())
+            sage: JD1 = J(D1)
+            sage: JD2 = J(D2)
+            sage: JD1 + JD2 == JD2 + JD1
+            True
         """
         cdef int d0 = self.d0
         cdef int g = self.g
         cdef Matrix w1, w2, w3, w4, w5
 
         w1 = self.mu_image(wd1, wd2, self.mu_mat33, 4*d0 - g + 1)
-        w2 = self.mu_preimage(self.wV3, w1, self.mu_mat33, 2*d0)
+        # The row space of w2 represents H^0(O(3D_0 - D1 - D2)), whose
+        # dimension is at least d0 - g + 1. Hence the codimension is at most
+        # 2*d0, and we cannot provide an expected_codim argument for mu_preimage.
+        w2 = self.mu_preimage(self.wV3, w1, self.mu_mat33)
         w3 = self.mu_preimage(self.wV2, w1, self.mu_mat42, 2*d0)
         # efficient than
         #   wf = matrix(w2[0])
@@ -872,8 +893,8 @@ cdef class KhuriMakdisi_small(KhuriMakdisi_base):
 
         w1 = self.mu_image(self.wV2, wd, self.mu_mat23, 4*d0 - g + 1)
         # The row space of w2 represents H^0(O(2D_0 - D)), whose dimension is
-        # at least d0 - g + 1, and hence the codimension is at most d0. Thus,
-        # we cannot provide an expected_codim argument for mu_preimage.
+        # at least d0 - g + 1. Hence the codimension is at most d0, and we
+        # cannot provide an expected_codim argument for mu_preimage.
         w2 = self.mu_preimage(self.wV3, w1, self.mu_mat23)
         # efficient than
         #   wf = matrix(w2[0])