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polimani.pl

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+%% 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).
+
+power_p(X) :-
+    polynomial_variable_p(X), !.
+power_p(X^N) :-
+    polynomial_variable_p(X), integer(N), N > 1, !.
+
+coefficient_p(K) :-
+    number(K).
+
+%% monomial_p(X) :-
+%%     polynomial_variable_p(X), !.
+monomial_p(N) :-
+    number(N), !.
+monomial_p(X) :-
+    power_p(X), !.
+monomial_p(K * X) :-
+    coefficient_p(K),
+    power_p(X), !.
+
+polynomial_p(M) :-
+    monomial_p(M), !.
+polynomial_p(P + M) :-
+    monomial_p(M),
+    polynomial_p(P), !.
+
+simplify_monomial(1 * P, P) :-
+    power_p(P), !.
+simplify_monomial(0 * _, 0) :-
+    !.
+simplify_monomial(M, M).
+
+simplify_polynomial(M, M2) :-
+    monomial_p(M), simplify_monomial(M, M2), !.
+simplify_polynomial(P + 0, P) :-
+    monomial_p(P), !.
+simplify_polynomial(0 + P, P) :-
+    monomial_p(P), !.
+simplify_polynomial(P + M, P2 + M2) :-
+    simplify_polynomial(P, P2), simplify_monomial(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_monomial(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) :-
+    monomial_p(M),
+    monomial_parts(M, _, X), !.
+delete_monomial(M + M2, X, M, M2) :-
+    monomial_p(M2), monomial_p(M),
+    monomial_parts(M, _, X), !.
+delete_monomial(P + M, X, M, P) :-
+    monomial_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? .