2 files changed, 45 insertions, 3 deletions

diff --git a/README.md b/README.md
index efbbe55..97c9ebf 100644
--- a/README.md
+++ b/README.md
@@ -61,11 +61,17 @@ state, poly_matrix = f3.apply(state)
 # PolyMatrixImpl(terms={(0, 0): {((0, 1), (1, 1)): 1, ((0, 1),): 2, ((1, 1),): 1}}, shape=(1, 1))
 print(poly_matrix)
 
-state, matrix_repr = polymatrix.to_matrix_repr((f3,), x).apply(state)
+state, sympy_repr = polymatrix.to_sympy(f3,).apply(state)
+
+# prints the sympy representation of the polynomial matrix
+# [[x1*x2 + 2*x1 + x2]]
+print(sympy_repr)
+
+state, dense_repr = polymatrix.to_dense((f3,), x).apply(state)
 
 # prints the numpy matrix representations of the polynomial matrix
 # array([[2., 1.]])
 # array([[0. , 0.5, 0.5, 0. ]])
-print(matrix_repr.data[0][1])               # numpy array
-print(matrix_repr.data[0][2].toarray())     # sparse scipy array
+print(dense_repr.data[0][1])               # numpy array
+print(dense_repr.data[0][2].toarray())     # sparse scipy array
 ```
diff --git a/examples/main.py b/examples/main.py
new file mode 100644
index 0000000..ff81589
--- /dev/null
+++ b/examples/main.py
@@ -0,0 +1,36 @@
+import sympy
+import polymatrix
+
+state = polymatrix.init_expression_state()
+
+x1, x2 = sympy.symbols('x1, x2')
+x = polymatrix.from_((x1, x2))
+
+f1 = polymatrix.from_(x1 + x2)
+f2 = polymatrix.from_(x1 + x1*x2)
+
+f3 = f1 + f2          
+
+# prints the data structure of the expression
+# AdditionExprImpl(left=FromSympyExprImpl(data=((x1 + x2,),)), right=FromSympyExprImpl(data=((x1*x2 + x1,),)))
+print(f3)
+
+state, poly_matrix = f3.apply(state)
+
+# prints the data structure of the polynomial matrix
+# PolyMatrixImpl(terms={(0, 0): {((0, 1), (1, 1)): 1, ((0, 1),): 2, ((1, 1),): 1}}, shape=(1, 1))
+print(poly_matrix)
+
+state, sympy_repr = polymatrix.to_sympy(f3,).apply(state)
+
+# prints the sympy representation of the polynomial matrix
+# [[x1*x2 + 2*x1 + x2]]
+print(sympy_repr)
+
+state, dense_repr = polymatrix.to_dense((f3,), x).apply(state)
+
+# prints the numpy matrix representations of the polynomial matrix
+# array([[2., 1.]])
+# array([[0. , 0.5, 0.5, 0. ]])
+print(dense_repr.data[0][1])               # numpy array
+print(dense_repr.data[0][2].toarray())     # sparse scipy array
\ No newline at end of file