From adf2dc7f322b0be2ef16ba13f411dd1cac34515e Mon Sep 17 00:00:00 2001
From: Diogo Cordeiro <diogo@fc.up.pt>
Date: Sat, 24 Nov 2018 16:10:44 +0000
Subject: [PATCH] Improved list_to_polynomial and finished documentation.

---
 polymani.pl | 59 ++++++++++++++++++++++++++++-------------------------
 1 file changed, 31 insertions(+), 28 deletions(-)

diff --git a/polymani.pl b/polymani.pl
index ab93cf6..858bb24 100644
--- a/polymani.pl
+++ b/polymani.pl
@@ -289,7 +289,7 @@ power_to_canon(T, T^1) :-
 %
 %  Converts a term to a list and vice versa.
 %  A term is multiplication of a number or a power
-%  and another term
+%  and another term.
 %  Can verify if term and list are compatible.
 %
 term_to_list(L * N, [N | TS]) :-
@@ -330,7 +330,9 @@ term_to_list(P, [P2]) :-
 
 %% simplify_term(+Term_In:term, ?Term_Out:term) is det
 %
-%  Simplifies a term.
+%  Simplifies a given term.
+%  This function can also be be used to verify if
+%  a term is simplified.
 %
 simplify_term(Term_In, Term_Out) :-
     term_to_list(Term_In, L),
@@ -380,7 +382,7 @@ simplify_term(Term_In, Term_Out) :-
 
 %% join_similar_parts_of_term(+List, -List) is det
 %
-%  Combine powers of the same variable in the given list
+%  Combine powers of the same variable in the given list.
 %
 join_similar_parts_of_term([P1, P2 | L], L2) :-
     %% If both symbols are powers
@@ -464,7 +466,7 @@ simplify_polynomial(P, P2) :-
 
 %% simplify_polynomial_as_list(+L1:List,-L3:List) is det
 %
-%  Simplifies a polynomial represented as a list
+%  Simplifies a polynomial represented as a list.
 %
 simplify_polynomial_as_list(L, L11) :-
     %% Convert each term to a list
@@ -502,7 +504,7 @@ simplify_polynomial_as_list(L, L11) :-
 %    `maplist(sort(0, @>=), L, L2),
 %     sort(0, @>=, L2, L3)`
 %  and that the sublists to be sorted with
-%  `sort(0, @=<)` since that is inherited from `add_terms`
+%  `sort(0, @=<)` since that is inherited from `add_terms`.
 %
 join_similar_terms([TL, TR | L], L2) :-
     %% Check if terms can be added and add them
@@ -524,10 +526,10 @@ join_similar_terms([], []).
 
 %% term_to_canon(+T:List, -T2:List) is det
 %
-%  Adds a 1 if there's no number in the list
+%  Adds a 1 if there's no number in the list.
 %  Requires the list to be sorted such that the
-%  numbers come first. For instance with
-%  `sort(0, @=<)`
+%  numbers come first.
+%  For instance with `sort(0, @=<)`.
 %
 term_to_canon([T | TS], [1, T | TS]) :-
     %% Since the list is sorted, if the first element
@@ -610,38 +612,39 @@ polynomial_to_list(T, [T]) :-
 %% ?- polynomial_to_list(2*x^2+3*x+5*x^17-7*x^21+3*x^3-23*x^4+25*x^5-4.3, S).
 %@ S = [-4.3, 25*x^5, -23*x^4, 3*x^3, -7*x^21, 5*x^17, 3*x, 2* ... ^ ...].
 
-%% list_to_polynomial(+P:polynomial, -L:List) is det
+%% list_to_polynomial(+L:List, -P:Polynomial) is det
 %
 %  Converts a list in a polynomial.
+%  An empty list will return false.
 %
 list_to_polynomial([T1|T2], P) :-
+    % Start recursive calls until we are in the
+    % end of the list. We know that the `-` will
+    % always be at the left of a term.
     list_to_polynomial(T2, L1),
     (
-        not(L1 = []),
-        (
-            term_string(T1, S1),
-            string_chars(S1, [First|_]),
-            First = -,
-            term_string(L1, S2),
-            string_concat(S2,S1,S3),
-            term_string(P, S3)
-        ;
-            P = L1+T1
-        )
+        % If this is a negative term
+        term_string(T1, S1),
+        string_chars(S1, [First|_]),
+        First = -,
+        % Concat them
+        term_string(L1, S2),
+        string_concat(S2,S1,S3),
+        term_string(P, S3)
     ;
-        P = T1
+        % Otherwise sum them
+        P = L1+T1
     ),
     % The others computations are semantically meaningless
     !.
-list_to_polynomial(T, P) :-
-    P = T.
+list_to_polynomial([T], T).
 %% Tests:
 %% ?- list_to_polynomial([1, x, x^2], P).
 %@ P = x^2+x+1.
 
 %% negate_term(T, T2) is det
 %
-%  Negate the coeficient of a term and return the negated term
+%  Negate the coeficient of a term and return the negated term.
 %
 negate_term(T, T2) :-
     term_to_list(T, L),
@@ -668,9 +671,9 @@ negate_term(T, T2) :-
 %% ?- negate_term(3*x*y^2, R).
 %@ R = -3*x*y^2.
 
-%% scale_polynomial(+P:polynomial,+C:constant,-S:polynomial) is det
+%% scale_polynomial(+P:Polynomial,+C:Constant,-S:Polynomial) is det
 %
-%  Multiplies a polynomial by a scalar
+%  Multiplies a polynomial by a scalar.
 %
 scale_polynomial(P, C, S) :-
     polynomial_to_list(P, L),
@@ -690,13 +693,13 @@ scale_polynomial(P, C, S) :-
 
 %% cons(+C:atom, +L:List, -L2:List) is det
 %
-%  Add an atom C to the head of a list L
+%  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
 %
-%  S = P1 + P2
+%  S = P1 + P2.
 %
 add_polynomial(P1, P2, S) :-
     %% Convert both polynomials to lists