Implemented Horner's scheme for evaluating UnivariatePolynomial

symengine/polynomial.cpp

@@ -468,14 +468,18 @@ Expression UnivariatePolynomial::max_coef() const {
 }
 
 Expression UnivariatePolynomial::eval(const Expression &x) const {
-    //TODO: Use Horner's Scheme
-    Expression ans = 0;
-    for (const auto &p : dict_) {
-        Expression temp;
-        temp = pow_ex(x, Expression(p.first));
-        ans += p.second * temp;
+    int last_deg = dict_.rbegin()->first;
+    Expression result, x_pow;
+
+    for (auto it = dict_.rbegin(); it != dict_.rend(); ++it) {
+        x_pow = pow_ex(x, last_deg - it->first);
+        last_deg = it->first;
+        result = it->second + expand(x_pow * result);
     }
-    return ans;
+    x_pow = pow_ex(x, last_deg);
+    result = expand(result * x_pow);
+
+    return result;
 }
 
 bool UnivariatePolynomial::is_zero() const {

symengine/tests/basic/test_polynomial.cpp

@@ -245,6 +245,12 @@ TEST_CASE("Evaluation of UnivariatePolynomial", "[UnivariatePolynomial]")
     RCP<const UnivariatePolynomial> a = univariate_polynomial(x, 2, {{0, 1}, {1, 2}, {2, symbol("a")}});
 
     REQUIRE(a->eval(2).get_basic()->__str__() == "5 + 4*a");
+
+    a = univariate_polynomial(x, 2, {{-1, 5}, {0, 1}, {1, symbol("a")}, {2, 3}});
+    REQUIRE(a->eval(2).get_basic()->__str__() == "31/2 + 2*a");
+
+    a = univariate_polynomial(x, 2, {{-1, symbol("a")}, {0, 1}, {1, 5}, {2, 3}});
+    REQUIRE(a->eval(3).get_basic()->__str__() == "43 + (1/3)*a");
 }
 
 TEST_CASE("Derivative of UnivariatePolynomial", "[UnivariatePolynomial]")