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Hugo Sales
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137
polimani.pl
137
polimani.pl
@ -4,12 +4,21 @@
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polynomial_variables([x, y, z]).
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polynomial_variable_p(X) :-
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polynomial_variables(V), member(X, V).
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polynomial_variables(V),
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member(X, V).
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polynomial_variable_p(P) :-
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polynomial_variables(V),
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member(X, V),
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%% number(N),
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P is X^N.
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power_p(X) :-
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polynomial_variable_p(X), !.
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polynomial_variable_p(X).
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power_p(X^N) :-
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polynomial_variable_p(X), integer(N), N > 1, !.
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polynomial_variable_p(X), integer(N), N >= 1.
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%% ?- power_p(x^1).
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%@ true..
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term_p(N) :-
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number(N).
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@ -46,26 +55,27 @@ simplify_term(T, T2) :-
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term_to_list(T, L),
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sort(0, @=<, L, L2),
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join_like_terms(L2, L3),
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sort(0, @>=, L3, L4),
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term_to_list(T2, L4).
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list_to_term(L3, T2). % Responsible for parenthesis
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%% sort(0, @>=, L3, L4),
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%% term_to_list(T2, L4).
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%% ?- simplify_term(2*y*z*x^3*x, X).
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%@ X = [z^1, y^1, x^4, 2].
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%@ false.
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%@ X = [2, x^4, y^1, z^1].
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%@ X = [2, x^1, x^3, y^1, z^1].
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%@ X = 2*(x^4*(y*z)).
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%@ X = z*(y*(x^4*2)).
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%% ?- simplify_term(2*y*z*23*x*y*x^3*x, X).
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%@ X = 46*(x^2*(x^3*(y^2*z))).
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%@ X = z*(y^2*(x^3*(x^2*46))).
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%@ X = [2, 23, x^1, x^3, y^1, z^1].
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%@ X = [46, x^4, y^1, z^1].
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join_like_terms([T1, T2 | L], [B1^N | L2]) :-
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not(number(T1)),
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not(number(T2)),
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B1^N1 = T1,
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B2^N2 = T2,
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B1 == B2,
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join_like_terms(L, L2),
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join_like_terms([P1, P2 | L], [B^N | L2]) :-
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power_p(P1),
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power_p(P2),
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B^N1 = P1,
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B^N2 = P2,
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%% B1 == B2, % Wasn't working before..?
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N is N1 + N2,
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join_like_terms(L, L2),
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!.
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join_like_terms([N1, N2 | L], [N | L2]) :-
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number(N1),
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@ -76,47 +86,92 @@ join_like_terms([N1, N2 | L], [N | 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_like_terms([2, 3, x^1, x^2], T).
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%@ T = [6, x^3].
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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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%@ T = [6, x^3, y^7].
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%@ T = [6, x^3, y].
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%@ T = [6, x^3, y^7].
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term_to_list(L * N, [N | TS]) :-
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number(N),
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term_to_list(L, TS),
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!.
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term_to_list(L * T, [T2 | TS]) :-
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power_p(T),
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power_to_canon(T, T2),
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term_to_list(L, TS),
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!.
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term_to_list(T, [T]).
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list_to_term([N | NS], N * L) :-
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number(N),
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term_to_list(L, NS).
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term_to_list(L, TS).
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term_to_list(L * P, [P2 | TS]) :-
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power_p(P),
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power_to_canon(P, P2),
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term_to_list(L, TS).
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term_to_list(N, [N]) :-
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number(N).
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term_to_list(P, [P2]) :-
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power_p(P),
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power_to_canon(P, P2).
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%% ?- term_to_list(2*y*z*23*x*y*x^3*x, X).
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%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2] .
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%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2]
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%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2] .
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%@ X = [x, x^3, y, x, 23, z, y, 2] .
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%@ X = [x, x^3, y, x, 23, z, y, 2] .
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%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2] .
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%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2].
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%% ?- term_to_list(X, [2, x^1, y^1]).
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%@ X = y^1*x*2.
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%@ X = y^1*x*2.
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%@ X = y^1*x*2.
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%@ X = y*x*2.
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%@ X = x*2.
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%@ X = 2.
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%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2].
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%% ?- term_to_list(X, [y^1, x^1]).
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%@ X = x*y .
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%@ X = x*y .
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%@ X = x*y .
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%@ X = x*y .
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%@ X = x*y .
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%@ X = x*y .
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%@ X = x*y .
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%@ false.
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%% ?- term_to_list(X, [x^4]).
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%@ false.
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%@ false.
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%@ false.
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%@ false.
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%@ false.
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%@ X = x*2.
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power_to_canon(T, T^1) :-
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polynomial_variable_p(T),
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%@ false.
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%% list_to_term([], 1).
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list_to_term([N], N) :-
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number(N),
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!.
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list_to_term([P], P2) :-
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power_p(P),
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power_to_canon(P2, P),
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!.
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list_to_term([N | LS], N * R) :-
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number(N),
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list_to_term(LS, R),
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!.
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list_to_term([P | LS], P2 * R) :-
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power_p(P),
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power_to_canon(P2, P),
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list_to_term(LS, R),
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!.
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%% ?- list_to_term([x^1], X).
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%@ X = x.
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%% ?- list_to_term([x^1, y^2, z^3], X).
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%@ X = x*(y^2*z^3).
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%@ X = x*y^2.
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%% ?- list_to_term([x^1, y^3, 5], X).
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%@ X = x*(y^3*5).
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%@ X = x*(y^3*(5*1)) .
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power_to_canon(T^N, T^N) :-
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polynomial_variable_p(T),
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!.
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polynomial_variable_p(T).
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power_to_canon(T, T^1) :-
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polynomial_variable_p(T).
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%% ?- power_to_canon(x, X).
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%@ X = x^1.
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%% ?- power_to_canon(X, X^1).
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%@ X = x .
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%@ X = x.
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simplify_polynomial(M, M2) :-
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term_p(M), simplify_term(M, M2), !.
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