try Lazard project

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

src/nlsat/nlsat_explain.cpp

@@ -47,6 +47,7 @@ namespace nlsat {
         bool                    m_add_all_coeffs;
         bool                    m_signed_project;
         bool                    m_cell_sample;
+        bool                    m_lazard;
 
 
         struct todo_set {
@@ -133,7 +134,7 @@ namespace nlsat {
         evaluator &             m_evaluator;
 
         imp(solver & s, assignment const & x2v, polynomial::cache & u, atom_vector const & atoms, atom_vector const & x2eq,
-            evaluator & ev, bool is_sample):
+            evaluator & ev, bool is_sample, bool use_lazard):
             m_solver(s),
             m_assignment(x2v),
             m_atoms(atoms),
@@ -148,6 +149,7 @@ namespace nlsat {
             m_factors_save(m_pm),
             m_roots_tmp(m_am),
             m_cell_sample(is_sample),
+            m_lazard(use_lazard),
             m_todo(u),
             m_core1(s),
             m_core2(s),
@@ -822,6 +824,61 @@ namespace nlsat {
             }
         }
 
+        void process_projection_polynomial(polynomial_ref & s) {
+            if (is_zero(s)) {
+                TRACE(nlsat_explain, tout << "projection polynomial is zero\n";);
+                return;
+            }
+            if (is_const(s)) {
+                TRACE(nlsat_explain, tout << "projection polynomial is constant: "; display(tout, s) << "\n";);
+                return;
+            }
+            if (is_zero(sign(s))) {
+                TRACE(nlsat_explain, tout << "projection polynomial vanished, adding zero assumption\n"; display(tout, s) << "\n";);
+                add_zero_assumption(s);
+                return;
+            }
+            TRACE(nlsat_explain, tout << "adding projection polynomial\n"; display(tout, s) << "\n";);
+            insert_fresh_factors_in_todo(s);
+        }
+
+        void lazard_discriminant(polynomial_ref_vector & ps, var x) {
+            polynomial_ref p(m_pm);
+            polynomial_ref disc(m_pm);
+            unsigned sz = ps.size();
+            for (unsigned i = 0; i < sz; ++i) {
+                p = ps.get(i);
+                if (max_var(p) != x)
+                    continue;
+                unsigned deg = degree(p, x);
+                if (deg < 2)
+                    continue;
+                disc = discriminant(p, x);
+                TRACE(nlsat_explain, tout << "Lazard discriminant of "; display(tout, p); tout << "\n -> "; display(tout, disc); tout << "\n";);
+                process_projection_polynomial(disc);
+            }
+        }
+
+        void lazard_resultant(polynomial_ref_vector & ps, var x) {
+            polynomial_ref p(m_pm);
+            polynomial_ref q(m_pm);
+            polynomial_ref res(m_pm);
+            unsigned sz = ps.size();
+            for (unsigned i = 0; i < sz; ++i) {
+                p = ps.get(i);
+                if (max_var(p) != x || degree(p, x) == 0)
+                    continue;
+                for (unsigned j = i + 1; j < sz; ++j) {
+                    q = ps.get(j);
+                    if (max_var(q) != x || degree(q, x) == 0)
+                        continue;
+                    res = resultant(p, q, x);
+                    TRACE(nlsat_explain, tout << "Lazard resultant of\n"; display(tout, p); tout << "\nand\n"; display(tout, q); tout << "\n -> "; display(tout, res); tout << "\n";);
+                    process_projection_polynomial(res);
+                }
+            }
+        }
+
         void test_root_literal(atom::kind k, var y, unsigned i, poly * p, scoped_literal_vector& result) {
             m_result = &result;
             add_root_literal(k, y, i, p);
@@ -1222,6 +1279,33 @@ namespace nlsat {
             }
         }
 
+        void project_lazard(polynomial_ref_vector & ps, var max_x) {
+            if (ps.empty())
+                return;
+            m_todo.reset();
+            for (poly* p : ps) {
+                m_todo.insert(p);
+            }
+            var x = m_todo.extract_max_polys(ps);
+            if (x < max_x)
+                add_cell_lits(ps, x);
+            while (true) {
+                if (all_univ(ps, x) && m_todo.empty()) {
+                    m_todo.reset();
+                    break;
+                }
+                TRACE(nlsat_explain, tout << "Lazard project loop, processing var "; display_var(tout, x);
+                      tout << "\npolynomials\n"; display(tout, ps); tout << "\n";);
+                add_lcs(ps, x);
+                lazard_discriminant(ps, x);
+                lazard_resultant(ps, x);
+                if (m_todo.empty())
+                    break;
+                x = m_todo.extract_max_polys(ps);
+                add_cell_lits(ps, x);
+            }
+        }
+
         /**
          * Sample Projection
          * Reference:
@@ -1280,7 +1364,10 @@ namespace nlsat {
         }
 
         void project(polynomial_ref_vector & ps, var max_x) {
-            if (m_cell_sample) {
+            if (m_lazard) {
+                project_lazard(ps, max_x);
+            }
+            else if (m_cell_sample) {
                 project_cdcac(ps, max_x);
             }
             else {
@@ -2110,8 +2197,8 @@ namespace nlsat {
     };
 
     explain::explain(solver & s, assignment const & x2v, polynomial::cache & u, 
-                     atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev, bool use_cell_sample) {
+                     atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev, bool use_cell_sample, bool use_lazard) {
-        m_imp = alloc(imp, s, x2v, u, atoms, x2eq, ev, use_cell_sample);
+        m_imp = alloc(imp, s, x2v, u, atoms, x2eq, ev, use_cell_sample, use_lazard);
     }
 
     explain::~explain() {
@@ -2147,6 +2234,10 @@ namespace nlsat {
         m_imp->m_signed_project = f;
     }
 
+    void explain::set_lazard(bool f) {
+        m_imp->m_lazard = f;
+    }
+
     void explain::main_operator(unsigned n, literal const * ls, scoped_literal_vector & result) {
         (*m_imp)(n, ls, result);
     }

src/nlsat/nlsat_explain.h

@@ -35,7 +35,7 @@ namespace nlsat {
         imp * m_imp;
     public:
         explain(solver & s, assignment const & x2v, polynomial::cache & u, 
-                atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev, bool use_cell_sample_proj);
+                atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev, bool use_cell_sample_proj, bool use_lazard_proj);
 
         ~explain();
 
@@ -46,6 +46,7 @@ namespace nlsat {
         void set_factor(bool f);
         void set_add_all_coeffs(bool f);
         void set_signed_project(bool f);
+        void set_lazard(bool f);
 
         /**
            \brief Given a set of literals ls[0], ... ls[n-1] s.t.

src/nlsat/nlsat_params.pyg

@@ -6,6 +6,7 @@ def_module_params('nlsat',
                           ('simple_check', BOOL, False, "precheck polynomials using variables sign"),
                           ('variable_ordering_strategy', UINT, 0, "Variable Ordering Strategy, 0 for none, 1 for BROWN, 2 for TRIANGULAR, 3 for ONLYPOLY"),
                           ('cell_sample', BOOL, True, "cell sample projection"),
+                          ('lazard', BOOL, False, "Lazard projection"),
                           ('lazy', UINT, 0, "how lazy the solver is."),
                           ('reorder', BOOL, True, "reorder variables."),
                           ('log_lemmas', BOOL, False, "display lemmas as self-contained SMT formulas"),

src/nlsat/nlsat_solver.cpp

@@ -226,6 +226,7 @@ namespace nlsat {
         unsigned m_variable_ordering_strategy;
         bool m_set_0_more;
         bool m_cell_sample;
+        bool m_lazard;
 
         struct stats {
             unsigned               m_simplifications;
@@ -260,7 +261,8 @@ namespace nlsat {
             m_simplify(s, m_atoms, m_clauses, m_learned, m_pm),
             m_display_var(m_perm),
             m_display_assumption(nullptr),
-            m_explain(s, m_assignment, m_cache, m_atoms, m_var2eq, m_evaluator, nlsat_params(c.m_params).cell_sample()),
+            m_explain(s, m_assignment, m_cache, m_atoms, m_var2eq, m_evaluator, 
+                      nlsat_params(c.m_params).cell_sample(), nlsat_params(c.m_params).lazard()),
             m_scope_lvl(0),
             m_lemma(s),
             m_lazy_clause(s),
@@ -301,12 +303,14 @@ namespace nlsat {
             m_debug_known_solution_file_name = p.known_sat_assignment_file_name();
             m_check_lemmas |= !(m_debug_known_solution_file_name.empty());
             m_cell_sample = p.cell_sample();
+            m_lazard = p.lazard();
   
             m_ism.set_seed(m_random_seed);
             m_explain.set_simplify_cores(m_simplify_cores);
             m_explain.set_minimize_cores(min_cores);
             m_explain.set_factor(p.factor());
             m_explain.set_add_all_coeffs(p.add_all_coeffs());
+            m_explain.set_lazard(m_lazard);
             m_am.updt_params(p.p);
         }