[symbolic] Fix SparseMatrix<Expression> data loss (#18219)

common/symbolic/expression/BUILD.bazel

@@ -176,6 +176,14 @@ drake_cc_googletest(
     ],
 )
 
+drake_cc_googletest(
+    name = "sparse_test",
+    deps = [
+        ":expression",
+        "//common/test_utilities:symbolic_test_util",
+    ],
+)
+
 drake_cc_googletest(
     name = "substitution_test",
     deps = [

common/symbolic/expression/boxed_cell.cc

@@ -17,6 +17,9 @@ void BoxedCell::ConstructCopy(const BoxedCell& other) {
 }
 
 void BoxedCell::AssignCopy(const BoxedCell& other) {
+  if (this == &other) {
+    return;
+  }
   // Decrement the use_count of our currently-managed cell.
   Release();
   if (other.is_constant()) {

common/symbolic/expression/test/boxed_cell_test.cc

@@ -187,6 +187,16 @@ TEST_F(BoxedCellTest, CopyAssignCellOntoCell) {
   EXPECT_EQ(dut.cell().use_count(), 1);
 }
 
+TEST_F(BoxedCellTest, CopyAssignCellOntoSelf) {
+  BoxedCell dut;
+  dut.SetSharedCell(MakeVarCell());
+  BoxedCell& self = dut;
+  dut = self;
+  EXPECT_EQ(dut.get_kind(), ExpressionKind::Var);
+  EXPECT_TRUE(dut.trivially_equals(dut));
+  EXPECT_EQ(dut.cell().use_count(), 1);
+}
+
 TEST_F(BoxedCellTest, CopyAssignCellOntoConstant) {
   auto original = std::make_unique<BoxedCell>();
   original->SetSharedCell(MakeVarCell());

common/symbolic/expression/test/sparse_test.cc

@@ -0,0 +1,33 @@
+/* clang-format off to disable clang-format-includes */
+#include "drake/common/symbolic/expression/all.h"
+/* clang-format on */
+
+#include <vector>
+
+#include <Eigen/Sparse>
+#include <gtest/gtest.h>
+
+#include "drake/common/test_utilities/symbolic_test_util.h"
+
+namespace drake {
+namespace symbolic {
+namespace {
+
+using test::ExprEqual;
+
+// This is a regression test for drake#18218.
+GTEST_TEST(SymbolicMatricesTest, SparseMatrices) {
+  const Variable x("x");
+  std::vector<Eigen::Triplet<Expression>> triplets;
+  triplets.push_back(Eigen::Triplet<Expression>(1, 1, 1.1));
+  triplets.push_back(Eigen::Triplet<Expression>(2, 2, x*2.0));
+  Eigen::SparseMatrix<Expression> M(3, 3);
+  M.setFromTriplets(triplets.begin(), triplets.end());
+  EXPECT_PRED2(ExprEqual, M.coeff(0, 0), 0.0);
+  EXPECT_PRED2(ExprEqual, M.coeff(1, 1), 1.1);
+  EXPECT_PRED2(ExprEqual, M.coeff(2, 2), x*2.0);
+}
+
+}  // namespace
+}  // namespace symbolic
+}  // namespace drake