diff --git a/README.md b/README.md
new file mode 100644
index 0000000..e824e8e
--- /dev/null
+++ b/README.md
@@ -0,0 +1,44 @@
+
+# How to run
+
+Run
+
+    $ swipl
+
+Inside the REPl, load the file
+   
+    ?- ["polimani.pl"].
+
+> Note: Don't forget the dot at the end of the line.
+
+The user available funtions are:
+  1) poly2list/2
+  2) simpoly_list/2
+  3) simpoly/2
+  4) scalepoly/3
+  5) addpoly/3
+
+> Note: In the docs, `foo/N` means the funciton `foo` has `N` parameters.
+  These names are the ones requested in the assignment.
+
+# Tests
+
+```
+:- ["polimani.pl"].
+%@ true.
+
+?- poly2list(2*x^2+3*x+5*x^17-7*x^21+3*x^3+25*x^5-4.3, S).
+%@ S = [-4.3, 25*x^5, 3*x^3, -7*x^21, 5*x^17, 3*x, 2*x^2].
+
+?- simpoly_list([x*x*x, x^3, 5*x^3, 4.2*z, 2, 42.6, 42*y, 5*z, z^7, z*y^1337, 0], L).
+%@ L = [44.6, 7*x^3, 9.2*z, 42*y, y^1337*z, z^7].
+
+?- simpoly(1+x+1+x+1+x+1+x^3+5*x^3+42*x^1337+0, S).
+%@ S = 42*x^1337+6*x^3+3*x+4.
+
+?- scalepoly(2*x^2+3*x+5*x^17-7*x^21+3*x^3-23*x^4+25*x^5-4.3, 42, S).
+%@ S = 1050*x^5+210*x^17+126*x^3+126*x+84*x^2-294*x^21-966*x^4-180.6.
+
+?- addpoly(2*x^2+3*x+5*x^17-x^4+25*x^5-4.3, 42*x^1337+0-5, S).
+%@ S = 42*x^1337+25*x^5+5*x^17+3*x+2*x^2-1*x^4-9.3.
+```
diff --git a/polimani.pl b/polimani.pl
index 9613e65..217e753 100644
--- a/polimani.pl
+++ b/polimani.pl
@@ -26,7 +26,6 @@
  * reversing of a predicate.
  */
 :- use_module(library(clpfd)).
-%% :- use_module(library(clpr)).
 
 
                  /*******************************
@@ -141,6 +140,7 @@ power(X) :-
 %  Returns true if N is a term, false otherwise.
 %
 term(N) :-
+    %% number(N).
     (nonvar(N),
      number(N));
     (not(compound(N)),
@@ -380,7 +380,7 @@ simplify_polynomial(0, 0) :-
 simplify_polynomial(P, P2) :-
     polynomial_to_list(P, L),
     simplify_polynomial_as_list(L, L2),
-    polynomial_to_list(P2, L2),
+    list_to_polynomial(L2, P2),
     !.
 %% Tests:
 %% ?- simplify_polynomial(1, X).
@@ -406,7 +406,7 @@ simplify_polynomial(P, P2) :-
 %% ?- simplify_polynomial(x + 1 + x, X).
 %@ X = 2*x+1.
 %% ?- simplify_polynomial(x + 1 + x + 1 + x + 1 + x, X).
-%@ X = 4*x+3*1.
+%@ X = 4*x+3.
 
 %% join_similar_terms(+P:ListList, -P2:ListList) is det
 %
@@ -598,6 +598,10 @@ scale_polynomial(P, C, S) :-
 %% ?- scale_polynomial(3*x^2, 2, S).
 %@ S = 6*x^2.
 
+%% cons(+C:atom, +L:List, -L2:List) is det
+%
+%  Add an atom C to the head of a list L
+%
 cons(C, L, [C | L]).
 
 %% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det
@@ -607,9 +611,14 @@ cons(C, L, [C | L]).
 add_polynomial(P1, P2, S) :-
     polynomial_to_list(P1, L1),
     polynomial_to_list(P2, L2),
-    append(L1, L2, LA),
-    join_similar_parts_of_term(LA,LJ),
-    list_to_polynomial(LJ, P),
-    simplify_polynomial(P, S).
+    append(L1, L2, L3),
+    simplify_polynomial_as_list(L3, L4),
+    list_to_polynomial(L4, S),
+    !.
 %% Tests:
-%
+%% ?- add_polynomial(2, 2, S).
+%@ S = 4.
+%% ?- add_polynomial(x, x, S).
+%@ S = 2*x.
+%% ?- add_polynomial(2*x+5*z, 2*z+6*x, S).
+%@ S = 8*x+7*z.