diogo/polynomialmani.pl
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Simplifying polynomials should now work

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Hugo Sales 2018-11-22 15:59:00 +00:00
parent c6640bf7bb
commit e9536674be
1 changed files with 127 additions and 62 deletions
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polimani.pl
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@ -203,7 +203,7 @@ simplify_term(Term_In, Term_Out) :-
Term_Out = Term_In Term_Out = Term_In
); );
exclude(==(1), L2, L3), exclude(==(1), L2, L3),
join_like_terms(L3, L4), join_similar_parts_of_term(L3, L4),
sort(0, @>=, L4, L5), sort(0, @>=, L4, L5),
term_to_list(Term_Out, L5) term_to_list(Term_Out, L5)
), ),
@ -227,29 +227,35 @@ simplify_term(Term_In, Term_Out) :-
%% ?- simplify_term(x^(-3), X). %% ?- simplify_term(x^(-3), X).
%@ false. %@ false.
%% join_like_terms(+List, -List) %% join_similar_parts_of_term(+List, -List)
% %
% Combine powers of the same variable in the given list % Combine powers of the same variable in the given list
% %
join_like_terms([P1, P2 | L], [B^N | L2]) :- join_similar_parts_of_term([P1, P2 | L], L2) :-
power(P1), power(P1),
power(P2), power(P2),
B^N1 = P1, B^N1 = P1,
B^N2 = P2, B^N2 = P2,
N is N1 + N2, N is N1 + N2,
join_like_terms(L, L2). join_similar_parts_of_term([B^N | L], L2).
join_like_terms([N1, N2 | L], [N | L2]) :- join_similar_parts_of_term([N1, N2 | L], L2) :-
number(N1), number(N1),
number(N2), number(N2),
N is N1 * N2, N is N1 * N2,
join_like_terms(L, L2). join_similar_parts_of_term([N | L], L2).
join_like_terms([X | L], [X | L2]) :- join_similar_parts_of_term([X | L], [X | L2]) :-
join_like_terms(L, L2). join_similar_parts_of_term(L, L2).
join_like_terms([], []). join_similar_parts_of_term([], []).
%% Tests: %% Tests:
%% ?- join_like_terms([2, 3, x^1, x^2], T). %% ?- join_similar_parts_of_term([3], T).
%@ T = [3].
%% ?- join_similar_parts_of_term([x^2], T).
%@ T = [x^2].
%% ?- join_similar_parts_of_term([x^1, x^1, x^1, x^1], T).
%@ T = [x^4] .
%% ?- join_similar_parts_of_term([2, 3, x^1, x^2], T).
%@ T = [6, x^3] . %@ T = [6, x^3] .
%% ?- join_like_terms([2, 3, x^1, x^2, y^1, y^6], T). %% ?- join_similar_parts_of_term([2, 3, x^1, x^2, y^1, y^6], T).
%@ T = [6, x^3, y^7] . %@ T = [6, x^3, y^7] .
%% simplify_polynomial(+P:atom, -P2:atom) is det %% simplify_polynomial(+P:atom, -P2:atom) is det
@ -260,38 +266,85 @@ join_like_terms([], []).
simplify_polynomial(M, M2) :- simplify_polynomial(M, M2) :-
%% Are we dealing with a valid term? %% Are we dealing with a valid term?
%is_term_valid_in_predicate(M, "simplify_polynomial(M, M2)"), %is_term_valid_in_predicate(M, "simplify_polynomial(M, M2)"),
%% term(M), term(M),
%% If so, simplify it. %% If so, simplify it.
simplify_term(M, M2), simplify_term(M, M2),
!. !.
simplify_polynomial(P + 0, P) :- simplify_polynomial(P, P2) :-
%% Ensure valid term polynomial_to_list(P, L),
%is_term_valid_in_predicate(P, "simplify_polynomial(P + 0, P)"), transform_list(term_to_list, L, L2),
term(P), transform_list(join_similar_parts_of_term, L2, L3),
transform_list(sort(0, @=<), L3, L4),
join_similar_terms(L4, L5),
transform_list(sort(0, @>=), L5, L6),
transform_list(term_to_list, L7, L6),
polynomial_to_list(P2, L7),
!. !.
simplify_polynomial(0 + P, P) :-
%% Ensure valid term
%is_term_valid_in_predicate(P, "simplify_polynomial(0 + P, P)"),
term(P),
!.
simplify_polynomial(P + M, P2 + M2) :-
simplify_polynomial(P, P2),
simplify_term(M, M2).
simplify_polynomial(P + M, P2 + M3) :-
monomial_parts(M, _, XExp),
delete_monomial(P, XExp, M2, P2),
!,
add_monomial(M, M2, M3).
simplify_polynomial(P + M, P2 + M2) :-
simplify_polynomial(P, P2),
simplify_term(M, M2).
%% Tests: %% Tests:
%% ?- simplify_polynomial(1, X). %% ?- simplify_polynomial(1, X).
%@ false. %@ X = 1.
%@ false. %% ?- simplify_polynomial(x, X).
%@ Invalid term in simplify_polynomial(M, M2): 1 %@ X = x.
%@ false. %% ?- simplify_polynomial(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.
join_similar_terms([TL, TR | L], L2) :-
add_terms(TL, TR, T2),
join_similar_terms([T2 | L], L2),
%% Give only first result. Red cut
!.
join_similar_terms([X | L], [X | L2]) :-
join_similar_terms(L, L2),
%% Give only first result. Red cut
!.
join_similar_terms([], []).
%% Tests:
%% ?- join_similar_terms([[2, x^3], [3, x^3], [x^3]], L).
%@ L = [[6, x^3]].
term_to_canon([T], [1, T]) :-
%% Give only first result. Red cut
!.
term_to_canon(L, L).
%% Tests:
%% ?- term_to_canon([x^3], T).
%@ T = [1, x^3].
%% ?- term_to_canon([2, x^3], T).
%@ T = [2, x^3].
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([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 %% simplify_polynomial_list(+L1,-L3) is det
% %
@ -312,36 +365,48 @@ simplify_polynomial_list([L1|L2],L3) :-
% Converts a polynomial in a list. % Converts a polynomial in a list.
% TODO: not everything is a +, there are - % TODO: not everything is a +, there are -
% %
polynomial_to_list(T1 + T2, L) :- polynomial_to_list(L + T, [T | LS]) :-
polynomial_to_list(T1, L1), term(T),
L = [T2|L1], polynomial_to_list(L, LS).
% The others computations are semantically meaningless % The others computations are semantically meaningless
!. %% !.
polynomial_to_list(P, L) :- polynomial_to_list(T, [T]) :-
L = [P]. term(T).
%% Tests: %% Tests:
%%?- polynomial_to_list(2, S).
%@ S = [2] .
%%?- polynomial_to_list(x^2, S).
%@ S = [x^2] .
%%?- 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]. %@ S = [y*2, 5, 2*x^2] .
%%?- polynomial_to_list(P, [2]).
%@ P = 2 .
%%?- polynomial_to_list(P, [x]).
%@ P = x .
%%?- polynomial_to_list(P, [x^2, x, -2.3]).
%@ P = -2.3+x+x^2 .
%% list_to_polynomial(+P:polynomial, -L:List) %% %% list_to_polynomial(+P:polynomial, -L:List)
% %% %
% Converts a list in a polynomial. %% % Converts a list in a polynomial.
% TODO: not everything is a +, there are - %% % TODO: not everything is a +, there are -
% %% %
list_to_polynomial([T1|T2], P) :- %% list_to_polynomial([T1|T2], P) :-
list_to_polynomial(T2, L1), %% list_to_polynomial(T2, L1),
( %% (
not(L1 = []), %% not(L1 = []),
P = L1+T1 %% P = L1+T1
; %% ;
P = T1 %% P = T1
), %% ),
% The others computations are semantically meaningless %% % The others computations are semantically meaningless
!. %% !.
list_to_polynomial(T, P) :- %% list_to_polynomial(T, P) :-
P = T. %% P = T.
%% Tests: %% %% Tests:
%% TODO %% %% TODO
%% append_two_atoms_with_star(+V1, +V2, -R) is det %% append_two_atoms_with_star(+V1, +V2, -R) is det
% %