add unit test for #2867

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/math/polynomial/algebraic_numbers.cpp

@@ -569,22 +569,26 @@ namespace algebraic_numbers {
             }
         };
 
-        void check_triangle_inequality(numeral_vector& r) {
+        void check_transitivity(numeral_vector& r) {
             lt_proc lt(m_wrapper);
             for (unsigned i = 0; i < r.size(); ++i) {
                 auto& a = r[i];
-                for (unsigned j = i + 1; j < r.size(); ++j) {
+                for (unsigned j = 0; j < r.size(); ++j) {
                     auto& b = r[j];
                     bool ltab = lt(a, b);
-                    for (unsigned k = j + 1; k < r.size(); ++k) {
+                    for (unsigned k = 0; k < r.size(); ++k) {
                         auto& c = r[k];
-                        CTRACE("algebraic", (lt(b, a) && lt(a, c) && !lt(b, c)),
+                        bool b_lt_a = lt(b, a);
-                            display_root(tout << "b ", b) << "\n";
+                        bool c_lt_b = lt(c, b);
-                        display_root(tout << "a ", a) << "\n";
+                        bool c_lt_a = lt(c, a);
-                        display_root(tout << "c ", c) << "\n";);
+                        // (a <= b & b <= c) => a <= c
-                        SASSERT(!lt(a, b) || !lt(b, c) || lt(a, c));
+                        // b < a or c < b or !(c < a)
-                        SASSERT(!lt(a, b) || !lt(c, a) || lt(c, b));
+                        CTRACE("algebraic_bug", 
-                        SASSERT(!lt(b, a) || !lt(a, c) || lt(b, c));
+                               (!b_lt_a && !c_lt_b && c_lt_a),
+                               display_root(tout << "a ", a) << "\n";
+                               display_root(tout << "b ", b) << "\n";
+                               display_root(tout << "c ", c) << "\n";);
+                        SASSERT(b_lt_a || c_lt_b || !c_lt_a);
                     }
                 }
             }
@@ -592,7 +596,7 @@ namespace algebraic_numbers {
 
         void sort_roots(numeral_vector & r) {
             if (m_limit.inc()) {
-                //DEBUG_CODE(check_triangle_inequality(r););
+                // DEBUG_CODE(check_transitivity(r););
                 std::sort(r.begin(), r.end(), lt_proc(m_wrapper));
             }
         }
@@ -2782,8 +2786,8 @@ namespace algebraic_numbers {
             // the precision on refine is base 2
             return upm().refine(c->m_p_sz, c->m_p, bqm(), l, u, precision * 4);
         }
-
+        
-        void display_decimal(std::ostream & out, numeral const & a, unsigned precision) {
+        std::ostream& display_decimal(std::ostream & out, numeral const & a, unsigned precision) {
             if (a.is_basic()) {
                 qm().display_decimal(out, basic_value(a), precision);
             }
@@ -2798,6 +2802,7 @@ namespace algebraic_numbers {
                     bqm().display_decimal(out, l, precision);
                 }
             }
+            return out;
         }
 
         void get_lower(numeral const & a, mpq & l, unsigned precision) {
@@ -3102,24 +3107,24 @@ namespace algebraic_numbers {
         return m_imp->eval_sign_at(p, x2v);
     }
 
-    void manager::display_interval(std::ostream & out, numeral const & a) const {
+    std::ostream& manager::display_interval(std::ostream & out, numeral const & a) const {
-        m_imp->display_interval(out, a);
+        return m_imp->display_interval(out, a);
     }
 
-    void manager::display_decimal(std::ostream & out, numeral const & a, unsigned precision) const {
+    std::ostream& manager::display_decimal(std::ostream & out, numeral const & a, unsigned precision) const {
-        m_imp->display_decimal(out, a, precision);
+        return m_imp->display_decimal(out, a, precision);
     }
 
-    void manager::display_root(std::ostream & out, numeral const & a) const {
+    std::ostream& manager::display_root(std::ostream & out, numeral const & a) const {
-        m_imp->display_root(out, a);
+        return m_imp->display_root(out, a);
     }
 
-    void manager::display_mathematica(std::ostream & out, numeral const & a) const {
+    std::ostream& manager::display_mathematica(std::ostream & out, numeral const & a) const {
-        m_imp->display_mathematica(out, a);
+        return m_imp->display_mathematica(out, a);
     }
 
-    void manager::display_root_smt2(std::ostream & out, numeral const & a) const {
+    std::ostream& manager::display_root_smt2(std::ostream & out, numeral const & a) const {
-        m_imp->display_root_smt2(out, a);
+        return m_imp->display_root_smt2(out, a);
     }
 
     void manager::reset_statistics() {

src/math/polynomial/algebraic_numbers.h

@@ -326,32 +326,32 @@ namespace algebraic_numbers {
            \brief Display algebraic number as a rational if is_rational(n)
            Otherwise, display it as an interval.
         */
-        void display_interval(std::ostream & out, numeral const & a) const;
+        std::ostream& display_interval(std::ostream & out, numeral const & a) const;
 
         /**
            \brief Display algebraic number in decimal notation.
            A question mark is added based on the precision requested.
         */
-        void display_decimal(std::ostream & out, numeral const & a, unsigned precision = 10) const;
+        std::ostream& display_decimal(std::ostream & out, numeral const & a, unsigned precision = 10) const;
 
         /**
            \brief Display algebraic number as a root object: (p, i)
            That is, 'a' is the i-th root of p.
         */
-        void display_root(std::ostream & out, numeral const & a) const;
+        std::ostream& display_root(std::ostream & out, numeral const & a) const;
         
         /**
            \brief Display algebraic number as a root object in SMT 2.0 style: (root-obj p i)
            That is, 'a' is the i-th root of p.
         */
-        void display_root_smt2(std::ostream & out, numeral const & a) const;
+        std::ostream& display_root_smt2(std::ostream & out, numeral const & a) const;
 
         /**
            \brief Display algebraic number in Mathematica format.
         */
-        void display_mathematica(std::ostream & out, numeral const & a) const;
+        std::ostream& display_mathematica(std::ostream & out, numeral const & a) const;
 
-        void display(std::ostream & out, numeral const & a) { return display_decimal(out, a); }
+        std::ostream& display(std::ostream & out, numeral const & a) { return display_decimal(out, a); }
 
         void reset_statistics();
         

src/sat/sat_probing.cpp

@@ -161,7 +161,6 @@ namespace sat {
 
         if (m_probing_binary) {
             watch_list & wlist = s.get_wlist(~l);
-            unsigned sz0 = wlist.size();
             for (unsigned i = 0; i < wlist.size(); ++i) {
                 watched & w = wlist[i];
                 if (!w.is_binary_clause())

src/smt/theory_seq.cpp

@@ -3474,7 +3474,6 @@ bool theory_seq::solve_ne(unsigned idx) {
 
 bool theory_seq::solve_nc(unsigned idx) {
     nc const& n = m_ncs[idx];
-    dependency* deps = n.deps();    
     literal len_gt = n.len_gt();
     context& ctx = get_context();
     expr_ref c(m);
@@ -3509,6 +3508,7 @@ bool theory_seq::solve_nc(unsigned idx) {
     }
     
 #else
+    dependency* deps = n.deps();    
     if (!canonize(n.contains(), deps, c)) {
         return false;
     }

src/test/algebraic.cpp

@@ -562,7 +562,70 @@ static void tst_root() {
 
 }
 
+static void tst_sturm() {
+    reslimit rl;
+    unsynch_mpq_manager nm;
+    polynomial::manager m(rl, nm);
+    polynomial_ref x(m);
+    x = m.mk_polynomial(m.mk_var());
+    polynomial_ref p(m);
+    polynomial_ref q(m);
+
+#define N(s) (rational(#s).to_mpq())
+
+    p = N(507962865083498496)*(x^10) + 
+        N(102100535881783197696)*(x^9) -
+        N(14783112447185507561472)*(x^8) - 
+        N(2001324733200883839555072)*(x^7) + 
+        N(195168383210843217999079936)*(x^6) + 
+        N(38119811955608999164032)*(x^5) + 
+        N(9215524544769908136049956)*(x^4) - 
+        N(733241058456905205563830332)*(x^3) - 
+        N(15888459782104331950227)*(x^2) - 
+        N(10235992917286431461226534)*x + 
+        N(688689757310708660505387921);    
+
+    q = N(1286741608255488)*(x^6) + 
+        N(129317531629676544)*(x^5) - 
+        N(25384908626459170944)*(x^4) + 
+        N(16014650289587907456)*(x^3) + 
+        N(2042137943326838560)*(x^2) + 
+        N(44729821875714513846)*x - 
+        N(29154410578758924855);
+
+    algebraic_numbers::manager am(rl, nm);
+    scoped_anum_vector rs1(am), rs2(am);
+    std::cout << "p: " << p << "\n";
+    am.isolate_roots(p, rs1);
+    scoped_anum a(am), b(am), c(am);
+    a = rs1[2];
+    b = rs1[3];
+    am.isolate_roots(q, rs2);
+    c = rs2[3];
+    am.display_decimal(std::cout << "a:", a) << "\n";
+    am.display_interval(std::cout << "a:", a) << "\n";
+    am.display_root(std::cout << "a:", a) << "\n";
+
+    am.display_decimal(std::cout << "b:", b) << "\n";
+    am.display_interval(std::cout << "b:", b) << "\n";
+    am.display_root(std::cout << "b:", b) << "\n";
+
+    am.display_decimal(std::cout << "c:", c) << "\n";
+    am.display_interval(std::cout << "c:", c) << "\n";
+    am.display_root(std::cout << "c:", c) << "\n";
+
+    std::cout << "b < a " << am.lt(b, a) << "\n";
+    std::cout << "c < b " << am.lt(c, b) << "\n";
+    std::cout << "c < a " << am.lt(c, a) << "\n";
+    // it should not be the case that b < a == 0, c < b == 0 and c < a == 1.
+}
+
+
+
+
 void tst_algebraic() {
+    tst_sturm();
+
     // enable_trace("resultant_bug");
     // enable_trace("poly_sign");
     disable_trace("algebraic");