Merge branch 'master' into scale_polynomial
This commit is contained in:
Diogo Cordeiro
GitHub
commit
fb49c34ae4
131
polimani.pl
131
polimani.pl
@ -3,11 +3,17 @@
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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_variable_list(-List:atom) is det
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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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@ -17,28 +23,38 @@ polynomial_variable_list([x, y, z]).
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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^_.
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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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%% ?- 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 det
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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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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).
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%@ true .
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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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%@ error.
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%% ?- power(X).
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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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@ -50,10 +66,14 @@ 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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term(R).
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%% Tests:
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%% TODO
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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((-3)*x^2).
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%@ true .
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%% is_term_valid_in_predicate(+T, +F) is det
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%
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@ -72,7 +92,8 @@ is_term_valid_in_predicate(T, F) :-
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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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%% ?- is_term_valid_in_predicate(1, "Chuck Norris").
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%@ true .
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%% polynomial(+M:atom) is det
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%
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@ -84,22 +105,37 @@ 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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%% ?- 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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%% 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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polynomial_variable(T),
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%% N \= 1.
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(
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zcompare(=, 1, N)
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;
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true
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).
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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^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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%@ X = x .
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%% ?- power_to_canon(X, x^4).
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%@ X = x^4 .
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%% term_to_list(?T, ?List) is det
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%
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@ -119,38 +155,44 @@ 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(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(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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%@ false.
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%@ false.
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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(+T:atom, -P) is det
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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(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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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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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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(
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member(0, L2),
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Term_Out = 0
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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(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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%@ 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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%% join_like_terms(+List, -List)
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%
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@ -214,7 +256,10 @@ 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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%% TODO
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%% ?- simplify_polynomial(1, 1).
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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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