Merge pull request #3 from diogogithub/negatives_in_polynomials

Negatives in polynomials

polimani.pl

@@ -150,6 +150,8 @@ term(L * R) :-
 %@ false.
 %% ?- term(a).
 %@ false.
+%% ?- term(-1*x).
+%@ true .
 %% ?- term((-3)*x^2).
 %@ true .
 %% ?- term(3.2*x).
@@ -244,8 +246,17 @@ 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]).
@@ -327,20 +338,22 @@ join_similar_parts_of_term([], []).
 %% simplify_polynomial(+P:atom, -P2:atom) is det
 %
 %  Simplifies a polynomial.
-%  TODO: not everything is a +, there are -
 %
 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, @>=), L2, L3),
-    maplist(sort(0, @=<), L3, L4),
+    sort(0, @>=, L3, L4),
-    join_similar_terms(L4, L5),
+    maplist(join_similar_parts_of_term, L4, L5),
-    transform_list(sort(0, @>=), L5, L6),
+    maplist(sort(0, @=<), L5, L6),
-    transform_list(term_to_list, L7, L6),
+    join_similar_terms(L6, L7),
-    delete(L7, 0, L8),
+    maplist(reverse, L7, L8),
-    polynomial_to_list(P2, L8),
+    maplist(term_to_list, L9, L8),
+    delete(L9, 0, L10),
+    sort(0, @=<, L10, L11),
+    list_to_polynomial(L11, P2),
     !.
 %% Tests:
 %% ?- simplify_polynomial(1, X).
@@ -351,19 +364,43 @@ 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
     !.
@@ -372,46 +409,51 @@ 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(+L:list, -S:list) is det
 %
 %  Simplifies a polynomial represented as a list
@@ -424,31 +466,91 @@ simplify_polynomial_list(L, S) :-
 %% 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.
+%
+list_to_polynomial([T1|T2], P) :-
+    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
+        )
+    ;
+        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
 %
 %  Returns R = V1 * V2
@@ -481,73 +583,3 @@ scale_polynomial(P, C, S) :-
 %% Tests:
 %% ?- scale_polynomial(3*x^2, 2, S).
 %@ S = 2*3*x^2.
-
-
-
-/* CENAS DO PROF: */
-
-
-
-
-%% monomial_parts(X, Y, Z)
-%
-%  TODO Maybe remove
-%  Separate monomial into it's parts. Given K*X^N, gives K and N
-%
-monomial_parts(X, 1, X)     :-
-    power(X),
-    !.
-monomial_parts(X^N, 1, X^N) :-
-    power(X^N),
-    !.
-monomial_parts(K * M, K, M) :-
-    number(K),
-    !.
-monomial_parts(K, K, indep) :-
-    number(K),
-    !.
-
-
-delete_monomial(M, X, M, 0) :-
-    term(M),
-    monomial_parts(M, _, X),
-    !.
-delete_monomial(M + M2, X, M, M2) :-
-    term(M2),
-    term(M),
-    monomial_parts(M, _, X),
-    !.
-delete_monomial(P + M, X, M, P) :-
-    term(M),
-    monomial_parts(M, _, X),
-    !.
-delete_monomial(P + M2, X, M, P2 + M2) :-
-    delete_monomial(P, X, M, P2).
-
-add_monomial(K1, K2, K3) :-
-    number(K1),
-    number(K2), !,
-    K3 is K1 + K2.
-add_monomial(M1, M2, M3) :-
-    monomial_parts(M1, K1, XExp),
-    monomial_parts(M2, K2, XExp),
-    K3 is K1 + K2,
-    p_aux_add_monomial(K3, XExp, M3).
-
-p_aux_add_monomial(K, indep, K) :-
-    !.
-p_aux_add_monomial(0, _, 0) :-
-    !.
-p_aux_add_monomial(1, XExp, XExp) :-
-    !.
-p_aux_add_monomial(K, XExp, K * XExp).
-
-closure_simplify_polynomial(P, P) :-
-    simplify_polynomial(P, P2),
-    P==P2,
-    !.
-closure_simplify_polynomial(P, P3) :-
-    simplify_polynomial(P, P2),
-    closure_simplify_polynomial(P2, P3),
-    !.
-