polynomialmani.pl/polimani.pl

%% -*- mode: prolog-*-
%% Follows 'Coding guidelines for Prolog' - Theory and Practice of Logic Programming
%% https://doi.org/10.1017/S1471068411000391

polynomial_variables([x, y, z]).
polynomial_variable_p(X) :-
    polynomial_variables(V),
    member(X, V).
polynomial_variable_p(P) :-
    polynomial_variables(V),
    member(X, V),
    %% number(N),
    P is X^N.

power_p(X) :-
    polynomial_variable_p(X).
power_p(X^N) :-
    polynomial_variable_p(X), integer(N), N >= 1.

%% ?- power_p(x^1).
%@ true..

term_p(N) :-
    number(N).
term_p(X) :-
    power_p(X).
term_p(L * R) :-
    term_p(L),
    term_p(R), !.

polynomial_p(M) :-
    term_p(M).
polynomial_p(L + R) :- 		% Left greedy
    polynomial_p(L),		% Why?
    term_p(R), !.

%% ?- polynomial_p(3*x^2+y*z).
%@ true.
%% ?- polynomial_p(x^100*y*z).
%@ true.
%% ?- polynomial_p(x+y+z).
%@ true.
%@ false.
%@ false.
%% ?- polynomial_p(3*x^2+y*z+x^100*y*z).
%@ true.
%@ true.
%% @ false. WIP

simplify_term(1 * P, P) :-
    term_p(P), !.
simplify_term(0 * _, 0) :-
    !.
simplify_term(T, T2) :-
    term_to_list(T, L),
    sort(0, @=<, L, L2),
    join_like_terms(L2, L3),
    list_to_term(L3, T2). 	% Responsible for parenthesis
    %% sort(0, @>=, L3, L4),
    %% term_to_list(T2, L4).

%% ?- simplify_term(2*y*z*x^3*x, X).
%@ X = 2*(x^4*(y*z)).
%@ X = z*(y*(x^4*2)).
%% ?- simplify_term(2*y*z*23*x*y*x^3*x, X).
%@ X = 46*(x^2*(x^3*(y^2*z))).
%@ X = z*(y^2*(x^3*(x^2*46))).
%@ X = [2, 23, x^1, x^3, y^1, z^1].
%@ X = [46, x^4, y^1, z^1].

join_like_terms([P1, P2 | L], [B^N | L2]) :-
    power_p(P1),
    power_p(P2),
    B^N1 = P1,
    B^N2 = P2,
    %% B1 == B2,   % Wasn't working before..?
    N is N1 + N2,
    join_like_terms(L, L2),
    !.
join_like_terms([N1, N2 | L], [N | 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_like_terms([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).
%@ T = [6, x^3, y^7].
%@ T = [6, x^3, y^7].


term_to_list(L * N, [N | TS]) :-
    number(N),
    term_to_list(L, TS).
term_to_list(L * P, [P2 | TS]) :-
    power_p(P),
    power_to_canon(P, P2),
    term_to_list(L, TS).
term_to_list(N, [N]) :-
    number(N).
term_to_list(P, [P2]) :-
    power_p(P),
    power_to_canon(P, P2).

%% ?- term_to_list(2*y*z*23*x*y*x^3*x, X).
%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2] .
%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2]
%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2] .
%@ X = [x, x^3, y, x, 23, z, y, 2] .
%@ X = [x, x^3, y, x, 23, z, y, 2] .
%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2] .
%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2].
%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2].
%% ?- term_to_list(X, [y^1, x^1]).
%@ X = x*y .
%@ X = x*y .
%@ X = x*y .
%@ X = x*y .
%@ X = x*y .
%@ X = x*y .
%@ X = x*y .
%@ false.
%% ?- term_to_list(X, [x^4]).
%@ false.
%@ false.
%@ false.
%@ false.
%@ false.

%@ false.

%% list_to_term([], 1).
list_to_term([N], N) :-
    number(N),
    !.
list_to_term([P], P2) :-
    power_p(P),
    power_to_canon(P2, P),
    !.
list_to_term([N | LS], N * R) :-
    number(N),
    list_to_term(LS, R),
    !.
list_to_term([P | LS], P2 * R) :-
    power_p(P),
    power_to_canon(P2, P),
    list_to_term(LS, R),
    !.

%% ?- list_to_term([x^1], X).
%@ X = x.
%% ?- list_to_term([x^1, y^2, z^3], X).
%@ X = x*(y^2*z^3).
%@ X = x*y^2.
%% ?- list_to_term([x^1, y^3, 5], X).
%@ X = x*(y^3*5).
%@ X = x*(y^3*(5*1)) .

power_to_canon(T^N, T^N) :-
    polynomial_variable_p(T).
power_to_canon(T, T^1) :-
    polynomial_variable_p(T).

%% ?- power_to_canon(x, X).
%@ X = x^1.
%% ?- power_to_canon(X, X^1).
%@ X = x .
%@ X = x.

simplify_polynomial(M, M2) :-
    term_p(M), simplify_term(M, M2), !.
simplify_polynomial(P + 0, P) :-
    term_p(P), !.
simplify_polynomial(0 + P, P) :-
    term_p(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).

%% ?- simplify_polynomial(1*x+(-1)*x, P).

monomial_parts(X, 1, X)     :-
    power_p(X), !.
monomial_parts(X^N, 1, X^N) :-
    power_p(X^N), !.
monomial_parts(K * M, K, M) :-
    coeficient_p(K), !.
monomial_parts(K, K, indep) :-
    coeficient_p(K), !.


delete_monomial(M, X, M, 0) :-
    term_p(M),
    monomial_parts(M, _, X), !.
delete_monomial(M + M2, X, M, M2) :-
    term_p(M2), term_p(M),
    monomial_parts(M, _, X), !.
delete_monomial(P + M, X, M, P) :-
    term_p(M), monomial_parts(M, _, X), !.
delete_monomial(P + M2, X, M, P2 + M2) :-
    delete_monomial(P, X, M, P2).

add_monomial(K1, K2, K3) :-
    number(K1), number(K2), !,
    K3 is K1 + K2.
add_monomial(M1, M2, M3) :-
    monomial_parts(M1, K1, XExp),
    monomial_parts(M2, K2, XExp),
    K3 is K1 + K2,
    p_aux_add_monomial(K3, XExp, M3).

p_aux_add_monomial(K, indep, K) :-
    !.
p_aux_add_monomial(0, _, 0) :-
    !.
p_aux_add_monomial(1, XExp, XExp) :-
    !.
p_aux_add_monomial(K, XExp, K * XExp).

closure_simplify_polynomial(P, P) :-
    simplify_polynomial(P, P2),
    P==P2, !.
closure_simplify_polynomial(P, P3) :-
    simplify_polynomial(P, P2),
    closure_simplify_polynomial(P2, P3), !.

%% ?- simplify_polynomial(1*x+(-1)*x, P).
%@ P = x+ -1*x .
%@ P = x+ -1*x
%@ Unknown action: q (h for help)
%@ Action?
%@ Unknown action: q (h for help)
%@ Action? .