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Hugo Sales
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polimani.pl
363
polimani.pl
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@ -2,116 +2,122 @@
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%% Follows 'Coding guidelines for Prolog' - Theory and Practice of Logic Programming
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%% https://doi.org/10.1017/S1471068411000391
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polynomial_variables([x, y, z]).
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polynomial_variable_p(X) :-
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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 = X^N.
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%% polynomial_variable_list(-List:atom) is det
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%
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% List of possible polynomial variables
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%
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polynomial_variable_list([x, y, z]).
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%% polynomial_variable(?X:atom) is det
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%
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% Returns true if X is a polynomial variable, false otherwise.
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%
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polynomial_variable(X) :-
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polynomial_variable_list(V),
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member(X, V).
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polynomial_variable(P) :-
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polynomial_variable_list(V),
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member(X, V),
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P = X^N.
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%% Tests:
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%% ?- term_to_list(X, [x^4]).
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%@ X = x^4 .
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power_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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%% ?- power_p(x^1).
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%% power(+X:atom) is det
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%
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% Returns true if X is a power term, false otherwise.
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%
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power(X) :-
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polynomial_variable(X).
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power(X^N) :-
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polynomial_variable(X),
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integer(N),
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N >= 1.
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%% Tests:
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%% ?- power(x^1).
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%@ true .
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%@ true.
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term_p(N) :-
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%% term(+N:atom) is det
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%
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% Returns true if N is a term, false otherwise.
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%
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term(N) :-
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number(N).
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term_p(X) :-
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power_p(X).
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term_p(L * R) :-
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term_p(L),
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term_p(R), !.
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polynomial_p(M) :-
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term_p(M).
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polynomial_p(L + R) :- % Left greedy
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polynomial_p(L), % Why?
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term_p(R), !.
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%% ?- polynomial_p(3*x^2+y*z).
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%@ true.
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%% ?- polynomial_p(x^100*y*z).
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%@ true.
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%% ?- polynomial_p(x+y+z).
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%@ true.
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%@ false.
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%@ false.
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%% ?- polynomial_p(3*x^2+y*z+x^100*y*z).
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%@ true.
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%@ true.
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%% @ false. WIP
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simplify_term(1 * P, P) :-
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term_p(P), !.
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simplify_term(0 * _, 0) :-
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term(X) :-
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power(X).
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term(L * R) :-
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term(L),
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term(R),
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!.
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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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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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%% Tests:
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%% TODO
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%% ?- simplify_term(2*y*z*x^3*x, X).
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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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%% is_term_valid_in_predicate(+T, +F) is det
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%
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% Returns true if valid Term, fails with UI message otherwise.
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% The fail message reports which Term is invalid and in which
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% predicate the problem ocurred.
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%
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is_term_valid_in_predicate(T, F) :-
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(
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term(T)
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;
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write("Invalid term in "),
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write(F),
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write(": "),
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write(T),
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fail
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).
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%% Tests:
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%% ?- is_term_valid_in_predicate().
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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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number(N2),
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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([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^7].
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%% polynomial(+M:atom) is det
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%
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% Returns true if polynomial, false otherwise.
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%
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polynomial(M) :-
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term(M).
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polynomial(L + R) :-
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polynomial(L),
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term(R).
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%% Tests:
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%% TODO
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%% power_to_canon(+T:atom, -T^N:atom) is det
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%
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% Returns a canon power term.
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%
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power_to_canon(T^N, T^N) :-
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polynomial_variable(T).
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power_to_canon(T, T^1) :-
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polynomial_variable(T).
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%% Tests:
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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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%% term_to_list(?T, ?List) is det
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%
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% Converts a term to a list and vice versa.
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% Can verify if term and list are compatible.
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%
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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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term_to_list(L * P, [P2 | TS]) :-
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power_p(P),
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power(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(P),
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power_to_canon(P, P2).
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%% Tests:
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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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%% ?- term_to_list(X, [y^1, x^1]).
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@ -122,84 +128,142 @@ term_to_list(P, [P2]) :-
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%% ?- term_to_list(X, [y^6, z^2, x^4]).
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%@ X = x^4*z^2*y^6 .
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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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%% simplify_term(+T:atom, -P) is det
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%
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% Simplifies a term.
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%
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simplify_term(1 * P, P).
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simplify_term(0 * _, 0).
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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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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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%% Tests:
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%% ?- simplify_term(2*y*z*x^3*x, X).
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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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%% ?- 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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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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%% join_like_terms(+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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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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%% 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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join_like_terms([N1, N2 | L], [N | 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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%% Tests:
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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^7].
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%% simplify_polynomial(+P:atom, -P2:atom) is det
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%
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% Simplifies a polynomial.
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%
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simplify_polynomial(M, M2) :-
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term_p(M), simplify_term(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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%% 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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term_p(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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!.
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simplify_polynomial(0 + P, P) :-
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term_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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!.
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simplify_polynomial(P + M, P2 + M2) :-
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simplify_polynomial(P, P2), simplify_term(M, 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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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), simplify_term(M, 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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%% TODO
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%% ?- simplify_polynomial(1*x+(-1)*x, P).
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%% simplify_polynomial_list(+L1,-L3) is det
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%
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% Simplifies a list of polynomials
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%
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simplify_polynomial_list([L1], L3) :-
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simplify_polynomial(L1, L2),
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L3 = [L2].
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simplify_polynomial_list([L1|L2],L3) :-
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simplify_polynomial(L1, P1),
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simplify_polynomial_list(L2, P2),
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L3 = [P1|P2],
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% There is nothing further to compute at this point
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!.
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%% monomial_parts(X, Y, Z)
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%
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% TODO Maybe remove
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% Separate monomial into it's parts. Given K*X^N, gives K and N
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%
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monomial_parts(X, 1, X) :-
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power_p(X), !.
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power(X),
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!.
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monomial_parts(X^N, 1, X^N) :-
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power_p(X^N), !.
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power(X^N),
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!.
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monomial_parts(K * M, K, M) :-
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coeficient_p(K), !.
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number(K),
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!.
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monomial_parts(K, K, indep) :-
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coeficient_p(K), !.
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number(K),
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!.
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delete_monomial(M, X, M, 0) :-
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term_p(M),
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monomial_parts(M, _, X), !.
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term(M),
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monomial_parts(M, _, X),
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!.
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delete_monomial(M + M2, X, M, M2) :-
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term_p(M2), term_p(M),
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monomial_parts(M, _, X), !.
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term(M2),
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term(M),
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monomial_parts(M, _, X),
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!.
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delete_monomial(P + M, X, M, P) :-
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term_p(M), monomial_parts(M, _, X), !.
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term(M),
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monomial_parts(M, _, X),
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!.
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delete_monomial(P + M2, X, M, P2 + M2) :-
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delete_monomial(P, X, M, P2).
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add_monomial(K1, K2, K3) :-
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number(K1), number(K2), !,
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number(K1),
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number(K2), !,
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K3 is K1 + K2.
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add_monomial(M1, M2, M3) :-
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monomial_parts(M1, K1, XExp),
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@ -217,15 +281,14 @@ p_aux_add_monomial(K, XExp, K * XExp).
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closure_simplify_polynomial(P, P) :-
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simplify_polynomial(P, P2),
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P==P2, !.
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P==P2,
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!.
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closure_simplify_polynomial(P, P3) :-
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simplify_polynomial(P, P2),
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closure_simplify_polynomial(P2, P3), !.
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closure_simplify_polynomial(P2, P3),
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!.
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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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%% ?- simplify_polynomial(1*x+(-1)*x, P).
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%@ P = x+ -1*x .
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%@ P = x+ -1*x
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%@ Unknown action: q (h for help)
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%@ Action?
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%@ Unknown action: q (h for help)
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%@ Action? .
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Reference in New Issue