Added some documentation, fixed some bugs and partial negative polynomial support

polimani.pl

@@ -84,6 +84,8 @@ term(L * R) :-
 %@ false.
 %% ?- term(a).
 %@ false.
+%% ?- term(-1*x).
+%@ true .
 %% ?- term((-3)*x^2).
 %@ true .
 %% ?- term(3.2*x).
@@ -178,8 +180,17 @@ term_to_list(P, [P2]) :-
 %% Tests:
 %% ?- term_to_list(1, X).
 %@ X = [1] .
+%% ?- term_to_list(-1, X).
+%@ X = [-1] .
 %% ?- term_to_list(1*2*y*z*23*x*y*x^3*x, X).
 %@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2, 1] .
+%% ?- term_to_list(X, [-1]).
+%@ X = -1 .
+%% ?- term_to_list(X, [x^1, -1]).
+%@ X = -1*x .
+%% ?- term_to_list(X, [- 1, x^1]).
+%@ false.
+%@ X = x* -1 .
 %% ?- term_to_list(X, [y^1, x^1]).
 %@ X = x*y .
 %% ?- term_to_list(X, [x^4]).
@@ -268,13 +279,16 @@ simplify_polynomial(0, 0) :-
 simplify_polynomial(P, P2) :-
     polynomial_to_list(P, L),
     maplist(term_to_list, L, L2),
-    maplist(join_similar_parts_of_term, L2, L3),
-    maplist(sort(0, @=<), L3, L4),
-    join_similar_terms(L4, L5),
-    transform_list(sort(0, @>=), L5, L6),
-    transform_list(term_to_list, L7, L6),
-    delete(L7, 0, L8),
-    polynomial_to_list(P2, L8),
+    maplist(sort(0, @>=), L2, L3),
+    sort(0, @>=, L3, L4),
+    maplist(join_similar_parts_of_term, L4, L5),
+    maplist(sort(0, @=<), L5, L6),
+    join_similar_terms(L6, L7),
+    maplist(reverse, L7, L8),
+    maplist(term_to_list, L9, L8),
+    delete(L9, 0, L10),
+    sort(0, @=<, L10, L11),
+    polynomial_to_list(P2, L11),
     !.
 %% Tests:
 %% ?- simplify_polynomial(1, X).
@@ -285,19 +299,43 @@ simplify_polynomial(P, P2) :-
 %@ X = x.
 %% ?- simplify_polynomial(x*x, X).
 %@ X = x^2.
+%% ?- simplify_polynomial(2 + 2, X).
+%@ X = 2*2.
+%% ?- simplify_polynomial(x + x, X).
+%@ X = 2*x.
 %% ?- simplify_polynomial(0 + x*x, X).
 %@ X = x^2.
 %% ?- simplify_polynomial(x^2*x + 3*x^3, X).
 %@ X = 4*x^3.
 %% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*x, X).
 %@ X = 6*x^3.
+%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*4 + z, X).
+%@ X = 5*x^3+4*x^2+z.
+%% ?- 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.
 
+%% join_similar_terms(+P:ListList, -P2:ListList) is det
+%
+%  Joins similar sublists representing terms by using
+%  `add_terms` to check if they can be merged and perform
+%  the addition. Requires the list of list be sorted with
+%    `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`
+%
 join_similar_terms([TL, TR | L], L2) :-
+    %% Check if terms can be added and add them
     add_terms(TL, TR, T2),
+    %% Recurse, accumulation on the first element
     join_similar_terms([T2 | L], L2),
     %% Give only first result. Red cut
     !.
 join_similar_terms([X | L], [X | L2]) :-
+    %% If a pair of elements can't be added, skip one
+    %% and recurse
     join_similar_terms(L, L2),
     %% Give only first result. Red cut
     !.
@@ -306,107 +344,118 @@ join_similar_terms([], []).
 %% ?- join_similar_terms([[2, x^3], [3, x^3], [x^3]], L).
 %@ L = [[6, x^3]].
 
-term_to_canon([T], [1, T]) :-
+%% term_to_canon(+T:List, -T2:List) is det
+%
+%  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, @=<)`
+%
+term_to_canon([T | TS], [1, T | TS]) :-
+    %% Since the list is sorted, if the first element
+    %% is not a number, then we need to add the 1
+    not(number(T)),
     %% Give only first result. Red cut
     !.
 term_to_canon(L, L).
 %% Tests:
+%% ?- term_to_canon([2], T).
+%@ T = [2].
 %% ?- term_to_canon([x^3], T).
 %@ T = [1, x^3].
+%% ?- term_to_canon([x^3, z], T).
+%@ T = [1, x^3, z].
 %% ?- term_to_canon([2, x^3], T).
 %@ T = [2, x^3].
 
+%% add_terms(+L:List, +R:List, -Result:List) is det
+%
+%  Adds two terms represented as list by adding
+%  the coeficients if the power is the same.
+%  Requires the list of terms to be simplified.
+%
 add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
     term_to_canon([NL | TL], [NL2 | TL2]),
     term_to_canon([NR | TR], [NR2 | TR2]),
     TL2 == TR2,
-    number(NL2),
-    number(NR2),
     N2 is NL2 + NR2.
 %% Tests
+%% ?- add_terms([1], [1], R).
+%@ R = [2].
+%% ?- add_terms([x], [x], R).
+%@ R = [2, x].
 %% ?- add_terms([2, x^3], [x^3], R).
 %@ R = [3, x^3].
 %% ?- add_terms([2, x^3], [3, x^3], R).
 %@ R = [5, x^3].
 
-%% transform_list(+Pred, +L, -R) is det
-%
-%  Apply predicate to each of the elements of L, producing R
-%
-transform_list(_, [], []).
-transform_list(Pred, [L | LS], [R | RS]) :-
-    call(Pred, L, R),
-    transform_list(Pred, LS, RS),
-    !.
-%% Tests:
-%% ?- transform_list(term_to_list, [x, 2], L).
-%@ L = [[x^1], [2]].
-%% ?- transform_list(term_to_list, [x, x, 2], L).
-%@ L = [[x^1], [x^1], [2]].
-%% ?- transform_list(term_to_list, L, [[x^1], [x^1], [2]]).
-%@ L = [x, x, 2].
-
 %% simplify_polynomial_list(+L1,-L3) is det
 %
 %  Simplifies a list of polynomials
 %
-simplify_polynomial_list([L1], L3) :-
-    simplify_polynomial(L1, L2),
-    L3 = [L2].
-simplify_polynomial_list([L1|L2],L3) :-
-    simplify_polynomial(L1, P1),
-    simplify_polynomial_list(L2, P2),
-    L3 = [P1|P2],
-    % There is nothing further to compute at this point
-    !.
+simplify_polynomial_list(L, L2) :-
+    maplist(simplify_polynomial, L, L2).
 
 %% polynomial_to_list(+P:polynomial, -L:List)
 %
 %  Converts a polynomial in a list.
 %  TODO: not everything is a +, there are -
 %
+polynomial_to_list(L - T, [T2 | LS]) :-
+    term(T),
+    negate_term(T, T2),
+    polynomial_to_list(L, LS).
 polynomial_to_list(L + T, [T | LS]) :-
     term(T),
     polynomial_to_list(L, LS).
-    % The others computations are semantically meaningless
-    %% !.
 polynomial_to_list(T, [T]) :-
     term(T).
 %% Tests:
-%%?- polynomial_to_list(2, S).
+%% ?- polynomial_to_list(2, S).
 %@ S = [2] .
-%%?- polynomial_to_list(x^2, S).
+%% ?- polynomial_to_list(x^2, S).
 %@ S = [x^2] .
-%%?- polynomial_to_list(x^2 + x^2, S).
+%% ?- polynomial_to_list(x^2 + x^2, S).
 %@ S = [x^2, x^2] .
-%%?- polynomial_to_list(2*x^2+5+y*2, S).
+%% ?- polynomial_to_list(2*x^2+5+y*2, S).
 %@ S = [y*2, 5, 2*x^2] .
-%%?- polynomial_to_list(P, [2]).
+%% ?- polynomial_to_list(2*x^2+5-y*2, S).
+%@ S = [-2*y, 5, 2*x^2] .
+%% ?- polynomial_to_list(2*x^2-5-y*2, S).
+%@ S = [-2*y, -5, 2*x^2] .
+%% ?- polynomial_to_list(P, [2]).
 %@ P = 2 .
-%%?- polynomial_to_list(P, [x]).
+%% ?- polynomial_to_list(P, [x]).
 %@ P = x .
-%%?- polynomial_to_list(P, [x^2, x, -2.3]).
+%% ?- polynomial_to_list(P, [x^2, x, 2.3]).
+%@ Action (h for help) ? abort
+%@ % Execution Aborted
 %@ P = -2.3+x+x^2 .
 
-%% %% list_to_polynomial(+P:polynomial, -L:List)
-%% %
-%% %  Converts a list in a polynomial.
-%% %  TODO: not everything is a +, there are -
-%% %
-%% list_to_polynomial([T1|T2], P) :-
-%%     list_to_polynomial(T2, L1),
-%%     (
-%%         not(L1 = []),
-%%         P = L1+T1
-%%     ;
-%%         P = T1
-%%     ),
-%%     % The others computations are semantically meaningless
-%%     !.
-%% list_to_polynomial(T, P) :-
-%%     P = T.
-%% %% Tests:
-%% %% TODO
+%% negate_term(T, T2) is det
+%
+%  Negate the coeficient of a term and return the negated term
+%
+negate_term(T, T2) :-
+    term_to_list(T, L),
+    sort(0, @=<, L, L2),
+    term_to_canon(L2, L3),
+    [N | R] = L3,
+    %% (-)/1 is an operator, needs to be evaluated, otherwise
+    %% it gives a symbolic result, which messes with further processing
+    N2 is -N,
+    reverse([N2 | R], L4),
+    term_to_list(T2, L4),
+    !.
+%% Tests:
+%% ?- negate_term(1, R).
+%@ R = -1.
+%% ?- negate_term(x, R).
+%@ R = -1*x.
+%% ?- negate_term(x^2, R).
+%@ R = -1*x^2.
+%% ?- negate_term(3*x*y^2, R).
+%@ R = -3*x*y^2.
 
 %% append_two_atoms_with_star(+V1, +V2, -R) is det
 %