Merge branch 'master' into scale_polynomial

polimani.pl

@@ -3,11 +3,17 @@
 %% Follows 'Coding guidelines for Prolog' - Theory and Practice of Logic Programming
 %% https://doi.org/10.1017/S1471068411000391
 
-%% polynomial_variable_list(-List:atom) is det
+%% Import the Constraint Logic Programming over Finite Domains lybrary
+%% Essentially, this library improves the way Prolog deals with integers,
+%% allowing more predicates to be reversible.
+%% For instance, number(N) is always false, which prevents the
+%% reversing of a predicate.
+:- use_module(library(clpfd)).
+
+%% polynomial_variable_list(-List) is det
 %
 %  List of possible polynomial variables
 %
-
 polynomial_variable_list([x, y, z]).
 
 %% polynomial_variable(?X:atom) is det
@@ -17,28 +23,38 @@ polynomial_variable_list([x, y, z]).
 polynomial_variable(X) :-
     polynomial_variable_list(V),
     member(X, V).
-polynomial_variable(P) :-
-    polynomial_variable_list(V),
-    member(X, V),
-    P = X^_.
 %% Tests:
-%% ?- term_to_list(X, [x^4]).
+%% ?- polynomial_variable(x).
-%@ X = x^4 .
+%@ true .
+%% ?- polynomial_variable(a).
+%@ false.
 
-%% power(+X:atom) is det
+%% power(+X:atom) is semidet
 %
 %  Returns true if X is a power term, false otherwise.
 %
+power(P^N) :-
+(
+    zcompare((<), 0, N), 
+    polynomial_variable(P)
+;
+    fail
+).
 power(X) :-
     polynomial_variable(X).
-power(X^N) :-
-    polynomial_variable(X),
-    integer(N),
-    N >= 1.
 %% Tests:
+%% ?- power(x).
+%@ true .
 %% ?- power(x^1).
 %@ true .
-
+%% ?- power(x^3).
+%@ true .
+%% ?- power(x^(-3)).
+%@ error.
+%% ?- power(X).
+%@ X = x ;
+%@ X = y ;
+%@ X = z.
 
 %% term(+N:atom) is det
 %
@@ -50,10 +66,14 @@ term(X) :-
     power(X).
 term(L * R) :-
     term(L),
-    term(R),
+    term(R).
-    !.
 %% Tests:
-%% TODO
+%% ?- term(2*x^3).
+%@ true .
+%% ?- term(x^(-3)).
+%@ false.
+%% ?- term((-3)*x^2).
+%@ true .
 
 %% is_term_valid_in_predicate(+T, +F) is det
 %
@@ -72,7 +92,8 @@ is_term_valid_in_predicate(T, F) :-
         fail
     ).
 %% Tests:
-%% ?- is_term_valid_in_predicate().
+%% ?- is_term_valid_in_predicate(1, "Chuck Norris").
+%@ true .
 
 %% polynomial(+M:atom) is det
 %
@@ -84,22 +105,37 @@ polynomial(L + R) :-
     polynomial(L),
     term(R).
 %% Tests:
-%% TODO
+%% ?- polynomial(x).
+%@ true .
+%% ?- polynomial(x^3).
+%@ true .
+%% ?- polynomial(3*x^7).
+%@ true .
+%% ?- polynomial(2 + 3*x + 4*x*y^3).
+%@ true .
 
 %% power_to_canon(+T:atom, -T^N:atom) is det
 %
 %  Returns a canon power term.
 %
 power_to_canon(T^N, T^N) :-
-    polynomial_variable(T).
+    polynomial_variable(T),
+    %% N \= 1.
+    (
+	zcompare(=, 1, N)
+    ;
+	true
+    ).
 power_to_canon(T, T^1) :-
     polynomial_variable(T).
 %% Tests:
 %% ?- power_to_canon(x, X).
-%@ X = x^1.
+%@ X = x^1 .
-%% ?- power_to_canon(X, X^1).
+%% ?- power_to_canon(X, x^1).
 %@ X = x .
-%@ X = x.
+%@ X = x .
+%% ?- power_to_canon(X, x^4).
+%@ X = x^4 .
 
 %% term_to_list(?T, ?List) is det
 %
@@ -119,38 +155,44 @@ term_to_list(P, [P2]) :-
     power(P),
     power_to_canon(P, P2).
 %% Tests:
-%% ?- term_to_list(2*y*z*23*x*y*x^3*x, X).
+%% ?- term_to_list(1*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, 1] .
 %% ?- term_to_list(X, [y^1, x^1]).
 %@ X = x*y .
 %% ?- term_to_list(X, [x^4]).
-%@ X = x^4 .
 %@ false.
+%@ false.
+%@ X = x^4 .
 %% ?- term_to_list(X, [y^6, z^2, x^4]).
 %@ X = x^4*z^2*y^6 .
 
-%% simplify_term(+T:atom, -P) is det
+%% simplify_term(+Term_In:term, ?Term_Out:term) is det
 %
 %  Simplifies a term.
 %
-simplify_term(1 * P, P).
+simplify_term(Term_In, Term_Out) :-
-simplify_term(0 * _, 0).
+    term_to_list(Term_In, L),
-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
+    member(0, L2),
-%% sort(0, @>=, L3, L4),
+    Term_Out = 0
-%% term_to_list(T2, L4).
+;
+    exclude(==(1), L2, L3),
+    join_like_terms(L3, L4),
+    sort(0, @>=, L4, L5),
+    term_to_list(Term_Out, L5)
+),
+    % First result is always the most simplified form.
+    !.
 %% Tests:
 %% ?- simplify_term(2*y*z*x^3*x, X).
-%@ X = 2*(x^4*(y*z)).
+%@ X = 2*x^4*y*z.
-%@ X = z*(y*(x^4*2)).
+%% ?- simplify_term(1*y*z*x^3*x, X).
-%% ?- simplify_term(2*y*z*23*x*y*x^3*x, X).
+%@ X = x^4*y*z.
-%@ X = 46*(x^2*(x^3*(y^2*z))).
+%% ?- simplify_term(0*y*z*x^3*x, X).
-%@ X = z*(y^2*(x^3*(x^2*46))).
+%@ X = 0.
-%@ X = [2, 23, x^1, x^3, y^1, z^1].
+%% ?- simplify_term(6*y*z*7*x*y*x^3*x, X).
-%@ X = [46, x^4, y^1, z^1].
+%@ X = 42*x^2*x^3*y^2*z.
 
 %% join_like_terms(+List, -List)
 %
@@ -214,7 +256,10 @@ simplify_polynomial(P + M, P2 + M2) :-
     simplify_polynomial(P, P2),
     simplify_term(M, M2).
 %% Tests:
-%% TODO
+%% ?- simplify_polynomial(1, 1).
+%@ Invalid term in simplify_polynomial(M, M2): 1
+%@ false.
+
 
 %% simplify_polynomial_list(+L1,-L3) is det
 %