Simplifying polynomials should now work
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189
polimani.pl
189
polimani.pl
@ -203,7 +203,7 @@ simplify_term(Term_In, Term_Out) :-
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Term_Out = Term_In
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);
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exclude(==(1), L2, L3),
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join_like_terms(L3, L4),
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join_similar_parts_of_term(L3, L4),
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sort(0, @>=, L4, L5),
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term_to_list(Term_Out, L5)
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),
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@ -227,29 +227,35 @@ simplify_term(Term_In, Term_Out) :-
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%% ?- simplify_term(x^(-3), X).
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%@ false.
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%% join_like_terms(+List, -List)
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%% join_similar_parts_of_term(+List, -List)
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%
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% Combine powers of the same variable in the given list
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%
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join_like_terms([P1, P2 | L], [B^N | L2]) :-
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join_similar_parts_of_term([P1, P2 | L], L2) :-
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power(P1),
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power(P2),
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B^N1 = P1,
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B^N2 = P2,
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N is N1 + N2,
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join_like_terms(L, L2).
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join_like_terms([N1, N2 | L], [N | L2]) :-
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join_similar_parts_of_term([B^N | L], L2).
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join_similar_parts_of_term([N1, N2 | L], L2) :-
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number(N1),
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number(N2),
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N is N1 * N2,
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join_like_terms(L, L2).
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join_like_terms([X | L], [X | L2]) :-
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join_like_terms(L, L2).
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join_like_terms([], []).
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join_similar_parts_of_term([N | L], L2).
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join_similar_parts_of_term([X | L], [X | L2]) :-
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join_similar_parts_of_term(L, L2).
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join_similar_parts_of_term([], []).
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%% Tests:
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%% ?- join_like_terms([2, 3, x^1, x^2], T).
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%% ?- join_similar_parts_of_term([3], T).
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%@ T = [3].
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%% ?- join_similar_parts_of_term([x^2], T).
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%@ T = [x^2].
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%% ?- join_similar_parts_of_term([x^1, x^1, x^1, x^1], T).
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%@ T = [x^4] .
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%% ?- join_similar_parts_of_term([2, 3, x^1, x^2], T).
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%@ T = [6, x^3] .
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%% ?- join_like_terms([2, 3, x^1, x^2, y^1, y^6], T).
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%% ?- join_similar_parts_of_term([2, 3, x^1, x^2, y^1, y^6], T).
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%@ T = [6, x^3, y^7] .
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%% simplify_polynomial(+P:atom, -P2:atom) is det
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@ -260,38 +266,85 @@ join_like_terms([], []).
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simplify_polynomial(M, M2) :-
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%% Are we dealing with a valid term?
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%is_term_valid_in_predicate(M, "simplify_polynomial(M, M2)"),
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%% term(M),
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term(M),
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%% If so, simplify it.
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simplify_term(M, M2),
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!.
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simplify_polynomial(P + 0, P) :-
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%% Ensure valid term
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%is_term_valid_in_predicate(P, "simplify_polynomial(P + 0, P)"),
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term(P),
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simplify_polynomial(P, P2) :-
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polynomial_to_list(P, L),
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transform_list(term_to_list, L, L2),
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transform_list(join_similar_parts_of_term, L2, L3),
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transform_list(sort(0, @=<), L3, L4),
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join_similar_terms(L4, L5),
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transform_list(sort(0, @>=), L5, L6),
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transform_list(term_to_list, L7, L6),
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polynomial_to_list(P2, L7),
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!.
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simplify_polynomial(0 + P, P) :-
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%% Ensure valid term
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%is_term_valid_in_predicate(P, "simplify_polynomial(0 + P, P)"),
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term(P),
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!.
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simplify_polynomial(P + M, P2 + M2) :-
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simplify_polynomial(P, P2),
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simplify_term(M, M2).
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simplify_polynomial(P + M, P2 + M3) :-
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monomial_parts(M, _, XExp),
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delete_monomial(P, XExp, M2, P2),
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!,
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add_monomial(M, M2, M3).
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simplify_polynomial(P + M, P2 + M2) :-
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simplify_polynomial(P, P2),
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simplify_term(M, M2).
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%% Tests:
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%% ?- simplify_polynomial(1, X).
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%@ false.
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%@ false.
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%@ Invalid term in simplify_polynomial(M, M2): 1
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%@ false.
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%@ X = 1.
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%% ?- simplify_polynomial(x, X).
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%@ X = x.
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%% ?- simplify_polynomial(x*x, X).
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%@ X = x^2.
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%% ?- simplify_polynomial(x^2*x + 3*x^3, X).
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%@ X = 4*x^3.
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%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*x, X).
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%@ X = 6*x^3.
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join_similar_terms([TL, TR | L], L2) :-
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add_terms(TL, TR, T2),
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join_similar_terms([T2 | L], L2),
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%% Give only first result. Red cut
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!.
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join_similar_terms([X | L], [X | L2]) :-
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join_similar_terms(L, L2),
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%% Give only first result. Red cut
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!.
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join_similar_terms([], []).
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%% Tests:
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%% ?- join_similar_terms([[2, x^3], [3, x^3], [x^3]], L).
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%@ L = [[6, x^3]].
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term_to_canon([T], [1, T]) :-
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%% Give only first result. Red cut
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!.
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term_to_canon(L, L).
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%% Tests:
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%% ?- term_to_canon([x^3], T).
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%@ T = [1, x^3].
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%% ?- term_to_canon([2, x^3], T).
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%@ T = [2, x^3].
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add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
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term_to_canon([NL | TL], [NL2 | TL2]),
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term_to_canon([NR | TR], [NR2 | TR2]),
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TL2 == TR2,
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number(NL2),
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number(NR2),
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N2 is NL2 + NR2.
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%% Tests
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%% ?- add_terms([2, x^3], [x^3], R).
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%@ R = [3, x^3].
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%% ?- add_terms([2, x^3], [3, x^3], R).
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%@ R = [5, x^3].
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%% transform_list(+Pred, +L, -R) is det
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%
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% Apply predicate to each of the elements of L, producing R
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%
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transform_list(_, [], []).
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transform_list(Pred, [L | LS], [R | RS]) :-
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call(Pred, L, R),
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transform_list(Pred, LS, RS),
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!.
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%% Tests:
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%% ?- transform_list(term_to_list, [x, 2], L).
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%@ L = [[x^1], [2]].
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%% ?- transform_list(term_to_list, [x, x, 2], L).
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%@ L = [[x^1], [x^1], [2]].
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%% ?- transform_list(term_to_list, L, [[x^1], [x^1], [2]]).
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%@ L = [x, x, 2].
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%% simplify_polynomial_list(+L1,-L3) is det
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%
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@ -312,36 +365,48 @@ simplify_polynomial_list([L1|L2],L3) :-
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% Converts a polynomial in a list.
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% TODO: not everything is a +, there are -
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%
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polynomial_to_list(T1 + T2, L) :-
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polynomial_to_list(T1, L1),
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L = [T2|L1],
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polynomial_to_list(L + T, [T | LS]) :-
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term(T),
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polynomial_to_list(L, LS).
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% The others computations are semantically meaningless
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!.
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polynomial_to_list(P, L) :-
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L = [P].
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%% !.
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polynomial_to_list(T, [T]) :-
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term(T).
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%% Tests:
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%%?- polynomial_to_list(2, S).
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%@ S = [2] .
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%%?- polynomial_to_list(x^2, S).
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%@ S = [x^2] .
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%%?- polynomial_to_list(x^2 + x^2, S).
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%@ S = [x^2, x^2] .
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%%?- polynomial_to_list(2*x^2+5+y*2, S).
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%@S = [y*2, 5, 2*x^2].
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%@ S = [y*2, 5, 2*x^2] .
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%%?- polynomial_to_list(P, [2]).
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%@ P = 2 .
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%%?- polynomial_to_list(P, [x]).
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%@ P = x .
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%%?- polynomial_to_list(P, [x^2, x, -2.3]).
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%@ P = -2.3+x+x^2 .
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%% list_to_polynomial(+P:polynomial, -L:List)
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%
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% Converts a list in a polynomial.
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% TODO: not everything is a +, there are -
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%
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list_to_polynomial([T1|T2], P) :-
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list_to_polynomial(T2, L1),
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(
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not(L1 = []),
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P = L1+T1
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;
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P = T1
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),
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% The others computations are semantically meaningless
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!.
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list_to_polynomial(T, P) :-
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P = T.
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%% Tests:
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%% TODO
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%% %% list_to_polynomial(+P:polynomial, -L:List)
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%% %
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%% % Converts a list in a polynomial.
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%% % TODO: not everything is a +, there are -
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%% %
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%% list_to_polynomial([T1|T2], P) :-
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%% list_to_polynomial(T2, L1),
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%% (
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%% not(L1 = []),
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%% P = L1+T1
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%% ;
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%% P = T1
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%% ),
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%% % The others computations are semantically meaningless
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%% !.
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%% list_to_polynomial(T, P) :-
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%% P = T.
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%% %% Tests:
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%% %% TODO
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%% append_two_atoms_with_star(+V1, +V2, -R) is det
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%
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