diff --git a/src/math/polynomial/algebraic_numbers.cpp b/src/math/polynomial/algebraic_numbers.cpp
index 42cfd7469..4cdf9c4b8 100644
--- a/src/math/polynomial/algebraic_numbers.cpp
+++ b/src/math/polynomial/algebraic_numbers.cpp
@@ -2772,9 +2772,12 @@ namespace algebraic_numbers {
             return out;
         }
 
-        std::ostream& display_root_smt2(std::ostream & out, numeral const & a) {
+        template<typename Printer>
+        std::ostream& display_root_common(std::ostream & out, numeral const & a, char const* var_name, bool no_power, Printer&& printer) {
+            SASSERT(var_name != nullptr);
             if (is_zero(a)) {
-                out << "(root-obj x 1)";
+                auto poly_printer = [&](std::ostream& dst) { dst << var_name; };
+                return printer(out, poly_printer, 1u);
             }
             else if (a.is_basic()) {
                 mpq const & v = basic_value(a);
@@ -2782,25 +2785,53 @@ namespace algebraic_numbers {
                 qm().set(neg_n, v.numerator());
                 qm().neg(neg_n);
                 mpz coeffs[2] = { std::move(neg_n), qm().dup(v.denominator()) };
-                out << "(root-obj ";
-                upm().display_smt2(out, 2, coeffs, "x");
-                out << " 1)"; // first root of the polynomial d*# - n
+                auto poly_printer = [&](std::ostream& dst) {
+                    if (no_power)
+                        upm().display_smt2_no_power(dst, 2, coeffs, var_name);
+                    else
+                        upm().display_smt2(dst, 2, coeffs, var_name);
+                };
+                std::ostream& r = printer(out, poly_printer, 1u); // first root of d*x - n
                 qm().del(coeffs[0]);
                 qm().del(coeffs[1]);
+                return r;
             }
             else {
                 algebraic_cell * c = a.to_algebraic();
-                out << "(root-obj ";
-                upm().display_smt2(out, c->m_p_sz, c->m_p, "x");
+                auto poly_printer = [&](std::ostream& dst) {
+                    if (no_power)
+                        upm().display_smt2_no_power(dst, c->m_p_sz, c->m_p, var_name);
+                    else
+                        upm().display_smt2(dst, c->m_p_sz, c->m_p, var_name);
+                };
                 if (c->m_i == 0) {
                     // undefined
                     c->m_i = upm().get_root_id(c->m_p_sz, c->m_p, lower(c)) + 1;
                 }
                 SASSERT(c->m_i > 0);
-                out << " " << c->m_i;
-                out << ")";
+                return printer(out, poly_printer, c->m_i);
             }
-            return out;
+        }
+
+        std::ostream& display_root_smt2(std::ostream & out, numeral const & a) {
+            auto printer = [&](std::ostream& dst, auto const& poly_printer, unsigned idx) -> std::ostream& {
+                dst << "(root-obj ";
+                poly_printer(dst);
+                dst << " " << idx << ")";
+                return dst;
+            };
+            return display_root_common(out, a, "x", false, printer);
+        }
+
+        std::ostream& display_root_smtrat(std::ostream & out, numeral const & a, char const* var_name) {
+            SASSERT(var_name != nullptr);
+            auto printer = [&](std::ostream& dst, auto const& poly_printer, unsigned idx) -> std::ostream& {
+                dst << "(root ";
+                poly_printer(dst);
+                dst << " " << idx << " " << var_name << ")";
+                return dst;
+            };
+            return display_root_common(out, a, var_name, true, printer);
         }
 
         std::ostream& display_interval(std::ostream & out, numeral const & a) {
@@ -3167,6 +3198,10 @@ namespace algebraic_numbers {
         return m_imp->display_root_smt2(out, a);
     }
 
+    std::ostream& manager::display_root_smtrat(std::ostream & out, numeral const & a, char const* var_name) const {
+        return m_imp->display_root_smtrat(out, a, var_name);
+    }
+
     void manager::reset_statistics() {
         m_imp->reset_statistics();
     }
diff --git a/src/math/polynomial/algebraic_numbers.h b/src/math/polynomial/algebraic_numbers.h
index e2e95367c..88792bbc2 100644
--- a/src/math/polynomial/algebraic_numbers.h
+++ b/src/math/polynomial/algebraic_numbers.h
@@ -345,6 +345,12 @@ namespace algebraic_numbers {
         */
         std::ostream& display_root_smt2(std::ostream & out, numeral const & a) const;
 
+        /**
+           \brief Display algebraic number using an SMT-RAT style root expression: (root p i x)
+           where the final argument denotes the variable bound to this root.
+        */
+        std::ostream& display_root_smtrat(std::ostream & out, numeral const & a, char const* var_name) const;
+
         /**
            \brief Display algebraic number in Mathematica format.
         */
@@ -495,4 +501,3 @@ inline std::ostream & operator<<(std::ostream & out, interval_pp const & n) {
     n.m.display_interval(out, n.n);
     return out;
 }
-
diff --git a/src/math/polynomial/upolynomial.cpp b/src/math/polynomial/upolynomial.cpp
index a73d3e5fb..241f48b20 100644
--- a/src/math/polynomial/upolynomial.cpp
+++ b/src/math/polynomial/upolynomial.cpp
@@ -1159,67 +1159,89 @@ namespace upolynomial {
         }
     }
 
+    static void display_smt2_var_power(std::ostream & out, char const * var_name, unsigned k, bool allow_power) {
+        SASSERT(k > 0);
+        if (k == 1) {
+            out << var_name;
+        }
+        else if (allow_power) {
+            out << "(^ " << var_name << " " << k << ")";
+        }
+        else {
+            out << "(*";
+            for (unsigned i = 0; i < k; ++i)
+                out << " " << var_name;
+            out << ")";
+        }
+    }
+
     static void display_smt2_monomial(std::ostream & out, numeral_manager & m, mpz const & n,
-                                      unsigned k, char const * var_name) {
+                                      unsigned k, char const * var_name, bool allow_power) {
         if (k == 0) {
             display_smt2_mumeral(out, m, n);
         }
         else if (m.is_one(n)) {
-            if (k == 1)
-                out << var_name;
-            else
-                out << "(^ " << var_name << " " << k << ")";
+            display_smt2_var_power(out, var_name, k, allow_power);
         }
         else {
             out << "(* ";
             display_smt2_mumeral(out, m, n);
             out << " ";
-            if (k == 1)
-                out << var_name;
-            else
-                out << "(^ " << var_name << " " << k << ")";
+            display_smt2_var_power(out, var_name, k, allow_power);
             out << ")";
         }
     }
 
-    // Display p as an s-expression
-    std::ostream& core_manager::display_smt2(std::ostream & out, unsigned sz, numeral const * p, char const * var_name) const {
+    static std::ostream& display_smt2_core(std::ostream & out, core_manager const& cm, unsigned sz, numeral const * p, char const * var_name, bool allow_power) {
         if (sz == 0) {
             out << "0";
             return out;
         }
 
         if (sz == 1) {
-            display_smt2_mumeral(out, m(), p[0]);
+            display_smt2_mumeral(out, cm.m(), p[0]);
             return out;
         }
 
         unsigned non_zero_idx  = UINT_MAX;
         unsigned num_non_zeros = 0;
         for (unsigned i = 0; i < sz; i++) {
-            if (m().is_zero(p[i]))
+            if (cm.m().is_zero(p[i]))
                 continue;
             non_zero_idx = i;
             num_non_zeros ++;
         }
 
-        if (num_non_zeros == 1) {
-            SASSERT(non_zero_idx != UINT_MAX && non_zero_idx >= 1);
-            display_smt2_monomial(out, m(), p[non_zero_idx], non_zero_idx, var_name);
+        if (num_non_zeros == 1 && non_zero_idx != UINT_MAX) {
+            if (non_zero_idx == 0) {
+                display_smt2_mumeral(out, cm.m(), p[0]);
+                return out;
+            }
+            display_smt2_monomial(out, cm.m(), p[non_zero_idx], non_zero_idx, var_name, allow_power);
+            return out;
         }
 
         out << "(+";
         unsigned i = sz;
         while (i > 0) {
             --i;
-            if (!m().is_zero(p[i])) {
+            if (!cm.m().is_zero(p[i])) {
                 out << " ";
-                display_smt2_monomial(out, m(), p[i], i, var_name);
+                display_smt2_monomial(out, cm.m(), p[i], i, var_name, allow_power);
             }
         }
         return out << ")";
     }
 
+    // Display p as an s-expression
+    std::ostream& core_manager::display_smt2(std::ostream & out, unsigned sz, numeral const * p, char const * var_name) const {
+        return display_smt2_core(out, *this, sz, p, var_name, true);
+    }
+
+    std::ostream& core_manager::display_smt2_no_power(std::ostream & out, unsigned sz, numeral const * p, char const * var_name) const {
+        return display_smt2_core(out, *this, sz, p, var_name, false);
+    }
+
     bool core_manager::eq(unsigned sz1, numeral const * p1, unsigned sz2, numeral const * p2) {
         if (sz1 != sz2)
             return false;
@@ -3117,4 +3139,3 @@ namespace upolynomial {
         return out;
     }
 };
-
diff --git a/src/math/polynomial/upolynomial.h b/src/math/polynomial/upolynomial.h
index 2afdbb7b3..7f807c0ae 100644
--- a/src/math/polynomial/upolynomial.h
+++ b/src/math/polynomial/upolynomial.h
@@ -468,6 +468,7 @@ namespace upolynomial {
         std::ostream& display_smt2(std::ostream & out, numeral_vector const & p, char const * var_name = "x") const { 
             return display_smt2(out, p.size(), p.data(), var_name); 
         }
+        std::ostream& display_smt2_no_power(std::ostream & out, unsigned sz, numeral const * p, char const * var_name = "x") const;
     };
 
     class scoped_set_z {
@@ -917,4 +918,3 @@ namespace upolynomial {
     };
 
 };
-
diff --git a/src/nlsat/nlsat_explain.cpp b/src/nlsat/nlsat_explain.cpp
index 4a3e947ca..77efb4096 100644
--- a/src/nlsat/nlsat_explain.cpp
+++ b/src/nlsat/nlsat_explain.cpp
@@ -295,14 +295,6 @@ namespace nlsat {
             if (maxx == null_var)
                 return;
             SASSERT(m_assignment.is_assigned(maxx));
-
-            // Make sure its discriminant does not vanish at the model.
-            polynomial_ref disc(m_pm);
-            disc = discriminant(q, maxx);
-            int const disc_sign = sign(disc);
-            SASSERT(disc_sign != 0);
-            if (disc_sign == 0)
-                NOT_IMPLEMENTED_YET();
             
             undef_var_assignment partial(m_assignment, maxx);
             scoped_anum_vector & roots = m_roots_tmp;
@@ -319,7 +311,7 @@ namespace nlsat {
                 }
             if (root_idx == 0) 
                 return; // there are no root functions and therefore no constraints aer generated
-            
+
             TRACE(nlsat_explain,
                   tout << "adding zero-assumption root literal for ";
                   display_var(tout, maxx); tout << " using root[" << root_idx << "] of " << q << "\n";);
diff --git a/src/nlsat/nlsat_solver.cpp b/src/nlsat/nlsat_solver.cpp
index 6b3781daa..e4e29c4ea 100644
--- a/src/nlsat/nlsat_solver.cpp
+++ b/src/nlsat/nlsat_solver.cpp
@@ -3368,6 +3368,12 @@ namespace nlsat {
                         m_am.to_rational(m_assignment.value(x), q);
                         m_am.qm().display_smt2(out, q, false);
                     }
+                    else if (m_log_lemma_smtrat) {
+                        std::ostringstream var_name;
+                        proc(var_name, x);
+                        std::string name = var_name.str();
+                        m_am.display_root_smtrat(out, m_assignment.value(x), name.c_str());
+                    }
                     else {
                         m_am.display_root_smt2(out, m_assignment.value(x));
                     }