Simplifying polynomials should now work
This commit is contained in:
Hugo Sales
parent
c6640bf7bb
commit
e9536674be
189
polimani.pl
189
polimani.pl
|
|
@ -203,7 +203,7 @@ simplify_term(Term_In, Term_Out) :-
|
|||
Term_Out = Term_In
|
||||
);
|
||||
exclude(==(1), L2, L3),
|
||||
join_like_terms(L3, L4),
|
||||
join_similar_parts_of_term(L3, L4),
|
||||
sort(0, @>=, L4, L5),
|
||||
term_to_list(Term_Out, L5)
|
||||
),
|
||||
|
|
@ -227,29 +227,35 @@ simplify_term(Term_In, Term_Out) :-
|
|||
%% ?- simplify_term(x^(-3), X).
|
||||
%@ false.
|
||||
|
||||
%% join_like_terms(+List, -List)
|
||||
%% join_similar_parts_of_term(+List, -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(P2),
|
||||
B^N1 = P1,
|
||||
B^N2 = P2,
|
||||
N is N1 + N2,
|
||||
join_like_terms(L, L2).
|
||||
join_like_terms([N1, N2 | L], [N | L2]) :-
|
||||
join_similar_parts_of_term([B^N | L], L2).
|
||||
join_similar_parts_of_term([N1, N2 | L], L2) :-
|
||||
number(N1),
|
||||
number(N2),
|
||||
N is N1 * N2,
|
||||
join_like_terms(L, L2).
|
||||
join_like_terms([X | L], [X | L2]) :-
|
||||
join_like_terms(L, L2).
|
||||
join_like_terms([], []).
|
||||
join_similar_parts_of_term([N | L], L2).
|
||||
join_similar_parts_of_term([X | L], [X | L2]) :-
|
||||
join_similar_parts_of_term(L, L2).
|
||||
join_similar_parts_of_term([], []).
|
||||
%% 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] .
|
||||
%% ?- 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] .
|
||||
|
||||
%% simplify_polynomial(+P:atom, -P2:atom) is det
|
||||
|
|
@ -260,38 +266,85 @@ join_like_terms([], []).
|
|||
simplify_polynomial(M, M2) :-
|
||||
%% Are we dealing with a valid term?
|
||||
%is_term_valid_in_predicate(M, "simplify_polynomial(M, M2)"),
|
||||
%% term(M),
|
||||
term(M),
|
||||
%% If so, simplify it.
|
||||
simplify_term(M, M2),
|
||||
!.
|
||||
simplify_polynomial(P + 0, P) :-
|
||||
%% Ensure valid term
|
||||
%is_term_valid_in_predicate(P, "simplify_polynomial(P + 0, P)"),
|
||||
term(P),
|
||||
simplify_polynomial(P, P2) :-
|
||||
polynomial_to_list(P, L),
|
||||
transform_list(term_to_list, L, L2),
|
||||
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:
|
||||
%% ?- simplify_polynomial(1, X).
|
||||
%@ false.
|
||||
%@ false.
|
||||
%@ Invalid term in simplify_polynomial(M, M2): 1
|
||||
%@ false.
|
||||
%@ X = 1.
|
||||
%% ?- simplify_polynomial(x, X).
|
||||
%@ X = x.
|
||||
%% ?- 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
|
||||
%
|
||||
|
|
@ -312,36 +365,48 @@ simplify_polynomial_list([L1|L2],L3) :-
|
|||
% Converts a polynomial in a list.
|
||||
% TODO: not everything is a +, there are -
|
||||
%
|
||||
polynomial_to_list(T1 + T2, L) :-
|
||||
polynomial_to_list(T1, L1),
|
||||
L = [T2|L1],
|
||||
polynomial_to_list(L + T, [T | LS]) :-
|
||||
term(T),
|
||||
polynomial_to_list(L, LS).
|
||||
% The others computations are semantically meaningless
|
||||
!.
|
||||
polynomial_to_list(P, L) :-
|
||||
L = [P].
|
||||
%% !.
|
||||
polynomial_to_list(T, [T]) :-
|
||||
term(T).
|
||||
%% 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).
|
||||
%@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)
|
||||
%
|
||||
% 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
|
||||
%% %% 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
|
||||
|
||||
%% append_two_atoms_with_star(+V1, +V2, -R) is det
|
||||
%
|
||||
|
|
|
|||
Reference in New Issue