minor cleanup

Author: pogudingleb

src/primality_check.jl

@@ -61,34 +61,24 @@ function check_primality(
     ring = parent(leaders[1])
 
     Rspec, vspec = Nemo.polynomial_ring(Nemo.QQ, [var_to_str(l) for l in leaders])
-    # Generic degree of each generator in its leader. Specializing the other
-    # variables must preserve these degrees; the ideal is considered on the
-    # open set where the leading coefficients (w.r.t. the leaders) do not
-    # vanish, so a specialization that drops a degree corresponds to leaving
-    # that set and would collapse the quotient ring, yielding a spurious result.
-    leader_degrees = Dict(l => Nemo.degree(p, l) for (l, p) in polys)
+    leader_degrees = Dict(lead => Nemo.degree(poly, lead) for (lead, poly) in polys)
 
     local zerodim_ideal
     attempts = 0
     while true
         attempts += 1
-        eval_point = [v in keys(polys) ? v : ring(rand(1:100)) for v in gens(ring)]
-        specialized = Dict(l => evaluate(polys[l], eval_point) for l in leaders)
-        if all(Nemo.degree(specialized[l], l) == leader_degrees[l] for l in leaders)
+        eval_point = [v in keys(polys) ? v : ring(rand(1:(100 * attempts))) for v in gens(ring)]
+        specialized = Dict(lead => evaluate(polys[lead], eval_point) for lead in leaders)
+        # Checks if the degrees in leaders drop, restarts if they do
+        if all(Nemo.degree(specialized[lead], lead) == leader_degrees[lead] for lead in leaders)
             all_polys = vcat(
-                [specialized[l] for l in leaders],
+                [specialized[lead] for lead in leaders],
                 [evaluate(p, eval_point) for p in extra_relations],
             )
             zerodim_ideal =
                 collect(map(p -> parent_ring_change(p, Rspec), all_polys))
             break
         end
-        if attempts >= 100
-            error(
-                "Failed to find a generic specialization for the primality check " *
-                    "after $attempts attempts (the leading coefficients keep vanishing).",
-            )
-        end
     end
 
     return check_primality_zerodim(zerodim_ideal)