445 lines
9.7 KiB
Prolog
445 lines
9.7 KiB
Prolog
%% -*- mode: prolog-*-
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%% vim: set softtabstop=4 shiftwidth=4 tabstop=4 expandtab:
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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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%% Import the Constraint Logic Programming over Finite Domains lybrary
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%% Essentially, this library improves the way Prolog deals with integers,
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%% allowing more predicates to be reversible.
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%% For instance, number(N) is always false, which prevents the
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%% reversing of a predicate.
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:- use_module(library(clpfd)).
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%% polynomial_variable_list(-List) 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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%% Tests:
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%% ?- polynomial_variable(x).
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%@ true .
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%% ?- polynomial_variable(a).
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%@ false.
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%% power(+X:atom) is semidet
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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(P^N) :-
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(
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zcompare((<), 0, N),
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polynomial_variable(P)
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;
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fail
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).
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power(X) :-
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polynomial_variable(X).
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%% Tests:
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%% ?- power(x).
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%@ true .
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%% ?- power(a).
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%@ false.
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%% ?- power(x^1).
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%@ true .
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%% ?- power(x^3).
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%@ true .
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%% ?- power(x^(-3)).
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%@ false.
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%% ?- power(X).
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%@ X = x^_7334,
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%@ _7334 in 1..sup ;
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%@ X = y^_7334,
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%@ _7334 in 1..sup ;
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%@ X = z^_7334,
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%@ _7334 in 1..sup ;
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%@ X = x ;
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%@ X = y ;
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%@ X = z.
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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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%% N in inf..sup.
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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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%% append_two_atoms_with_star(L, R, T).
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%% Tests:
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%% ?- term(2*x^3).
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%@ true .
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%% ?- term(x^(-3)).
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%@ false.
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%% ?- term(a).
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%@ false.
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%% ?- term((-3)*x^2).
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%@ true .
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%% ?- term(3.2*x).
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%@ true .
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%% ?- term(X).
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%% Doesn't give all possible terms, because number(N) is not reversible
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%% The ic library seems to be able to help here, but it's not a part of
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%% SwiPL by default
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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(1, "Test").
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%@ true .
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%% ?- is_term_valid_in_predicate(a, "Test").
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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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%% ?- polynomial(x).
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%@ true .
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%% ?- polynomial(x^3).
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%@ true .
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%% ?- polynomial(3*x^7).
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%@ true .
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%% ?- polynomial(2 + 3*x + 4*x*y^3).
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%@ true .
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%% ?- polynomial(a).
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%@ false.
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%% ?- polynomial(x^(-3)).
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%@ false.
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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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N #\= 1.
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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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%% ?- power_to_canon(X, x^4).
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%@ X = x^4 .
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%% ?- power_to_canon(X, a^1).
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%@ false.
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%% ?- power_to_canon(X, x^(-3)).
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%@ X = x^ -3 .
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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),
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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),
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power_to_canon(P, P2).
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%% Tests:
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%% ?- term_to_list(1, X).
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%@ X = [1] .
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%% ?- term_to_list(1*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, 1] .
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%% ?- term_to_list(X, [y^1, x^1]).
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%@ X = x*y .
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%% ?- term_to_list(X, [x^4]).
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%@ X = x^4 .
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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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%% simplify_term(+Term_In:term, ?Term_Out:term) is det
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%
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% Simplifies a term.
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%
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simplify_term(Term_In, Term_Out) :-
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term_to_list(Term_In, L),
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sort(0, @=<, L, L2),
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(
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member(0, L2),
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Term_Out = 0
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;
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(
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length(L2, 1),
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Term_Out = Term_In
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);
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exclude(==(1), L2, L3),
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join_like_terms(L3, L4),
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sort(0, @>=, L4, L5),
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term_to_list(Term_Out, L5)
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),
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% First result is always the most simplified form.
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!.
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%% Tests:
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%% ?- simplify_term(1, X).
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%@ X = 1.
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%% ?- simplify_term(x, X).
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%@ X = x.
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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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%% ?- simplify_term(1*y*z*x^3*x, X).
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%@ X = x^4*y*z.
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%% ?- simplify_term(0*y*z*x^3*x, X).
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%@ X = 0.
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%% ?- simplify_term(6*y*z*7*x*y*x^3*x, X).
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%@ X = 42*x^2*x^3*y^2*z.
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%% ?- simplify_term(a, X).
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%@ false.
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%% ?- simplify_term(x^(-3), X).
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%@ false.
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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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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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%% ?- 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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%% simplify_polynomial(+P:atom, -P2:atom) is det
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%
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% Simplifies a polynomial.
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% TODO: not everything is a +, there are -
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%
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simplify_polynomial(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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%% term(M),
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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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%% Ensure valid term
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%is_term_valid_in_predicate(P, "simplify_polynomial(P + 0, P)"),
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term(P),
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!.
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simplify_polynomial(0 + 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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term(P),
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!.
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simplify_polynomial(P + M, P2 + 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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!,
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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),
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simplify_term(M, M2).
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%% Tests:
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%% ?- simplify_polynomial(1, X).
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%@ false.
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%@ false.
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%@ Invalid term in simplify_polynomial(M, M2): 1
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%@ false.
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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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%% polynomial_to_list(+P:polynomial, -L:List)
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%
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% Converts a polynomial in a list.
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% TODO: not everything is a +, there are -
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%
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polynomial_to_list(T1 + T2, L) :-
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polynomial_to_list(T1, L1),
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L = [T2|L1],
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% The others computations are semantically meaningless
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!.
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polynomial_to_list(P, L) :-
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L = [P].
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%% Tests:
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%%?- polynomial_to_list(2*x^2+5+y*2, S).
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%@S = [y*2, 5, 2*x^2].
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%% list_to_polynomial(+P:polynomial, -L:List)
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%
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% Converts a list in a polynomial.
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% TODO: not everything is a +, there are -
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%
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list_to_polynomial([T1|T2], P) :-
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list_to_polynomial(T2, L1),
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(
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not(L1 = []),
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P = L1+T1
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;
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P = T1
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),
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% The others computations are semantically meaningless
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!.
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list_to_polynomial(T, P) :-
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P = T.
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%% Tests:
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%% TODO
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%% append_two_atoms_with_star(+V1, +V2, -R) is det
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%
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% Returns R = V1 * V2
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%
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append_two_atoms_with_star(V1, V2, R) :-
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% Convert term V2 into a string V3
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term_string(V2, V3),
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% Concat atom V1 with * into a compound V4
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atom_concat(V1, *, V4),
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% Concat atom V4 with V3 into a compound S
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atom_concat(V4, V3, S),
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% Convert compound S into a term R
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term_string(R, S).
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%% Tests:
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% ?- append_two_atoms_with_star(2, x^2, R).
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%@ R = 2*x^2.
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%@ R = 2*x^2.
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%@ R = 2*3.
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%% scale_polynomial(+P:polynomial,+C:constant,-S:polynomial) is det
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%
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% Scales a polynomial with a constant
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%
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scale_polynomial(P, C, S) :-
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polynomial_to_list(P, L),
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maplist(append_two_atoms_with_star(C), L, L2),
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list_to_polynomial(L2, S).
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%simplify_polynomial(S1, S).
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%% Tests:
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%% ?- scale_polynomial(3*x^2, 2, S).
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%@ S = 2*3*x^2.
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%@ S = 2*(3*x^2).
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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(X),
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!.
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monomial_parts(X^N, 1, 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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number(K),
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!.
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monomial_parts(K, K, indep) :-
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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(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(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(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),
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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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monomial_parts(M2, K2, XExp),
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K3 is K1 + K2,
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p_aux_add_monomial(K3, XExp, M3).
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p_aux_add_monomial(K, indep, K) :-
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!.
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p_aux_add_monomial(0, _, 0) :-
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!.
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p_aux_add_monomial(1, XExp, XExp) :-
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!.
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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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!.
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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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!.
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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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