Fix up decomposition_info.

src/AlgebraicGeometry/Schemes/Covering/Objects/Attributes.jl

@@ -107,18 +107,22 @@ function inherit_decomposition_info!(
 
   for V in patches(orig_cov)
     # Collect the patches in `ref_cov` refining V
-    V_ref = [U for U in patches(ref_cov) if decomp_dict[U][1] === V]
-    # Collect the corresponding complement equations
-    comp_eqns = [decomp_dict[U][2] for U in V_ref]
+    V_ref = [(U, (UV, h)) for (U, (UV, h)) in decomp_dict if UV === V]
+    _compl(a) = sum(length(lifted_numerator(b)) + length(lifted_denominator(b)) for b in a[2][2]; init=0)
+    V_ref = sort!(V_ref, by=_compl)
     # Start out from the original decomposition info
     dec_inf = copy(decomposition_info(orig_cov)[V])
-    for (i, U) in enumerate(V_ref)
+    for (i, (U, (_, h))) in enumerate(V_ref)
       # Cast the already made decomposition info down to U
       tmp = elem_type(OO(U))[OX(V, U)(i) for i in dec_inf] # help the compiler
       # Append the equations for the previously covered patches
       for j in 1:i-1
-        W = V_ref[j]
-        surplus = OX(V, U).(decomp_dict[W][2])
+        (_, (_, hh)) = V_ref[j]
+        if is_empty(hh) # The patch for hh already covered everything; this one can hence be discarded.
+          push!(tmp, one(OO(U)))
+          break
+        end
+        surplus = OX(V, U).(hh)
         push!(tmp, prod(surplus; init=one(OO(U))))
       end
       set_decomposition_info!(ref_cov, U, tmp)

src/AlgebraicGeometry/Schemes/Sheaves/CoherentSheaves.jl

@@ -784,19 +784,6 @@ end
   return C
 end
 
-function inherit_decomposition_info!(C::Covering, X::AbsCoveredScheme)
-  D = default_covering(X)
-  OOX = OO(X)
-  if has_decomposition_info(D)
-    for U in patches(C)
-      V = __find_chart(U, D)
-      phi = OOX(V, U)
-      set_decomposition_info!(C, U, phi.(decomposition_info(D)[V]))
-    end
-  end
-  return C
-end
-
 @attr Covering function trivializing_covering(M::HomSheaf)
   X = scheme(M)
   OOX = OO(X)