From 6220fb1aabed87982c71194df0bc5d18bf6ba875 Mon Sep 17 00:00:00 2001
From: Michael Schneeberger <michael.schneeberger@fhnw.ch>
Date: Thu, 4 Aug 2022 15:41:23 +0200
Subject: add a description of the example given in README.md

---
 README.md | 20 ++++++++++++++++----
 1 file changed, 16 insertions(+), 4 deletions(-)

diff --git a/README.md b/README.md
index 6ce4eb8..08e5c9a 100644
--- a/README.md
+++ b/README.md
@@ -25,6 +25,18 @@ Some aspects of the library:
 
 ## Example
 
+In this example, two polynomial expressions are defined using sympy expressions
+
+$f_1(x_1, x_2) = x_1 + x_2$
+
+$f_2(x_1, x_2) = x_1 + x_1 x_2$
+
+Then, the two expression are combined using the `__add__` (or equivalently `+`) function
+
+$f_3(x_1, x_2) = f_1(x_1, x_2) + f_2(x_1, x_2) = 2 x_1 + x_2 + x_1 x_2$
+
+Finally, different representations of the polynomial are printed.
+
 ``` python
 import sympy
 import polymatrix
@@ -37,19 +49,19 @@ x = polymatrix.from_((x1, x2))
 f1 = polymatrix.from_(x1 + x2)
 f2 = polymatrix.from_(x1 + x1*x2)
 
-expr = f1 + f2          
+f3 = f1 + f2          
 
 # prints the data structure of the expression
 # ExpressionImpl(underlying=AdditionExprImpl(left=FromSympyExprImpl(data=((x1 + x2,),)), right=FromSympyExprImpl(data=((x1*x2 + x1,),))))
-print(expr)
+print(f3)
 
-state, poly_matrix = expr.apply(state)
+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, matrix_repr = polymatrix.to_matrix_repr((expr,), x).apply(state)
+state, matrix_repr = polymatrix.to_matrix_repr((f3,), x).apply(state)
 
 # prints the numpy matrix representations of the polynomial matrix
 # array([[2., 1.]])
-- 
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