restart projection when found a non-trivial nullified polynomial, and remove is_square_free

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

src/nlsat/nlsat_explain.cpp

@@ -25,6 +25,8 @@ Revision History:
 
 namespace nlsat {
 
+    struct add_all_coeffs_restart {};
+
     typedef polynomial::polynomial_ref_vector polynomial_ref_vector;
     typedef ref_buffer<poly, pmanager> polynomial_ref_buffer;
 
@@ -463,9 +465,13 @@ namespace nlsat {
                     // and were added as assumptions.
                     p = m_pm.mk_zero();
                     TRACE(nlsat_explain, tout << "all coefficients of p vanished\n";);
-                    VERIFY(m_add_all_coeffs); // need to fall back to Collins projection otherwise
+                    if (m_add_all_coeffs) {
                         return;
                     }
+                    TRACE(nlsat_explain, tout << "falling back to add-all-coeffs projection\n";);
+                    m_add_all_coeffs = true;
+                    throw add_all_coeffs_restart();
+                }
                 k--;
                 p = reduct;
             }
@@ -716,35 +722,6 @@ namespace nlsat {
             }
         }
 
-// The monomials have to be square free according to
-//"An improved projection operation for cylindrical algebraic decomposition of three-dimensional space", by McCallum, Scott
-            
-        bool is_square_free(polynomial_ref_vector &ps, var x) {
-            if (m_add_all_coeffs)
-                return false;
-            polynomial_ref p(m_pm);
-            polynomial_ref lc_poly(m_pm);
-            polynomial_ref disc_poly(m_pm); 
-
-            for (unsigned i = 0; i < ps.size(); i++) {
-                p = ps.get(i);
-                unsigned k_deg = m_pm.degree(p, x); 
-                if (k_deg == 0)
-                    continue;
-                // p depends on x
-                disc_poly = discriminant(p, x); // Use global helper
-                if (sign(disc_poly) == 0) { // Discriminant is zero
-                    TRACE(nlsat_explain, tout << "p is not square free:\n ";
-                          display(tout, p); tout << "\ndiscriminant: "; display(tout, disc_poly) << "\n";
-                          m_solver.display_assignment(tout) << '\n';
-                          m_solver.display_var(tout << "x:", x) << '\n';
-                        );
-
-                    return false;
-                }
-            }
-            return true;
-        }
         
      	// If each p from ps is square-free then add the leading coefficents to the projection. 
 	// Otherwise, add each coefficient of each p to the projection.
@@ -752,7 +729,6 @@ namespace nlsat {
             polynomial_ref p(m_pm);
             polynomial_ref coeff(m_pm);
 
-            bool only_lc = !m_add_all_coeffs && is_square_free(ps, x);
             // Add the leading or all coeffs, depening on being square-free
             for (unsigned i = 0; i < ps.size(); i++) {
                 p = ps.get(i);
@@ -764,7 +740,7 @@ namespace nlsat {
                     coeff = m_pm.coeff(p, x, j_coeff_deg);
                     TRACE(nlsat_explain, tout << "    coeff deg " << j_coeff_deg << ": "; display(tout, coeff) << "\n";);
                     insert_fresh_factors_in_todo(coeff);
-                    if (only_lc)
+                    if (!m_add_all_coeffs)
                         break;
                 }
             }
@@ -1731,17 +1707,32 @@ namespace nlsat {
                 result.reset();
                 return;
             }
+            unsigned base = result.size();
+            while (true) {
+                try {
                     m_result = &result;
                     process(num, ls);
                     reset_already_added();
                     m_result = nullptr;
                     TRACE(nlsat_explain, display(tout << "[explain] result\n", result) << "\n";);
                     CASSERT("nlsat", check_already_added());
+                    break;
+                }
+                catch (add_all_coeffs_restart const&) {
+                    TRACE(nlsat_explain, tout << "restarting explanation with all coefficients\n";);
+                    reset_already_added();
+                    result.shrink(base);
+                    m_result = nullptr;
+                }
+            }
         }
 
 
         void project(var x, unsigned num, literal const * ls, scoped_literal_vector & result) {
-            
+            unsigned base = result.size();
+            while (true) {
+                bool reordered = false;
+                try {
                     m_result = &result;
                     svector<literal> lits;
                     TRACE(nlsat, tout << "project x" << x << "\n"; 
@@ -1766,6 +1757,7 @@ namespace nlsat {
                             }
                             std::swap(renaming[x], renaming[mx_var]);
                             m_solver.reorder(renaming.size(), renaming.data());
+                            reordered = true;
                             TRACE(qe, tout << "x: " << x << " max: " << mx_var << " num_vars: " << m_solver.num_vars() << "\n";
                                   m_solver.display(tout););
                         }
@@ -1773,7 +1765,7 @@ namespace nlsat {
                         project(m_ps, mx_var);
                         reset_already_added();
                         m_result = nullptr;
-                if (x != mx_var) {
+                        if (reordered) {
                             m_solver.restore_order();
                         }
                     }
@@ -1791,6 +1783,19 @@ namespace nlsat {
                         SASSERT(l_true == m_solver.value(l));
                     }
 #endif                
+                    break;
+                }
+                catch (add_all_coeffs_restart const&) {
+                    TRACE(nlsat_explain, tout << "restarting projection with all coefficients\n";);
+                    reset_already_added();
+                    if (reordered) {
+                        m_solver.restore_order();
+                    }
+                    result.shrink(base);
+                    m_result = nullptr;
+                    std::cout << "switch\n";
+                }
+            }
         }
 
         void split_literals(var x, unsigned n, literal const* ls, svector<literal>& lits) {

src/nlsat/nlsat_params.pyg

@@ -20,6 +20,6 @@ def_module_params('nlsat',
                           ('inline_vars', BOOL, False, "inline variables that can be isolated from equations (not supported in incremental mode)"),
                           ('seed', UINT, 0, "random seed."),
                           ('factor', BOOL, True, "factor polynomials produced during conflict resolution."),
-                          ('add_all_coeffs', BOOL, True, "add all polynomial coefficients during projection."),
+                          ('add_all_coeffs', BOOL, False, "add all polynomial coefficients during projection."),
                           ('known_sat_assignment_file_name', STRING, "", "the file name of a known solution: used for debugging only")
                           ))