Cleaned up some documentation and tests

polymani.pl

@@ -80,6 +80,7 @@ scalepoly(P1, C, S) :-
 %% ?- scalepoly(3*x*z+2*z, 4, S).
 %@ S = 12*x*z+8*z.
 %% ?- scalepoly(3*x*z+2*z, 2, S).
+%@ S = 6*x*z+4*z.
 
 /*
     addpoly/3 adds two polynomials as expressions resulting in a
@@ -113,7 +114,7 @@ is_polynomial_valid_in_predicate(P, F) :-
     write(P),
     fail.
 %% Tests:
-%% ?- is_polynomial_valid_in_predicate(1, "Test").
+%% ?- is_polynomial_valid_in_predicate(1-x, "Test").
 %@ true.
 %% ?- is_polynomial_valid_in_predicate(a*4-0*x, "Test").
 %@ Invalid polynomial in Test: a*4-0*x
@@ -180,6 +181,7 @@ polynomial_variable(X) :-
 %  Returns true if X is a power term, false otherwise.
 %
 power(P^N) :-
+    %% CLPFD comparassion. Reversible
     N #>= 1,
     polynomial_variable(P).
 power(X) :-
@@ -213,22 +215,19 @@ power(X) :-
 %  Returns true if N is a term, false otherwise.
 %
 term(N) :-
-    (
-        % If N is not a free variable
-        nonvar(N),
-        % Assert it as a number
-        number(N)
-    ;
-        % If N is a free variable
-        %% not(compound(N)),
-        var(N),
-        % Assert it must be between negative and positive infinity
-        % This uses the CLP(FD) library, which makes this reversible,
-        % whereas `number(N)` is always false, since it only succeeds
-        % if the argument is bound to a intger or float
-        %% N in inf..sup
-	{N >= 0; N < 0}
-    ).
+    % If N is not a free variable
+    nonvar(N),
+    % Assert it as a number
+    number(N).
+term(N) :-
+    % If N is a free variable and not compound
+    not(compound(N)),
+    var(N),
+    % Assert it must be between negative and positive infinity
+    % This uses the CLPR library, which makes this reversible,
+    % whereas `number(N)` is always false, since it only succeeds
+    % if the argument is bound (to a integer or float)
+    {N >= 0; N < 0}.
 term(X) :-
     power(X).
 term(-X) :-
@@ -321,8 +320,6 @@ power_to_canon(T^N, T^N) :-
     N #\= 1.
 power_to_canon(T, T^1) :-
     polynomial_variable(T).
-%% power_to_canon(-P, -P2) :-
-%%     power_to_canon(P, P2).
 %% Tests:
 %% ?- power_to_canon(x, X).
 %@ X = x^1 .
@@ -397,6 +394,8 @@ term_to_list(-P, [-P2]) :-
 %@ X = -2*x^4*z^2*y^6 .
 %% ?- term_to_list(X, [x^1, 0]).
 %@ X = 0*x .
+%% ?- term_to_list(X, [y^1, -2]).
+%@ X = -2*y .
 
 %% simplify_term(+Term_In:term, ?Term_Out:term) is det
 %
@@ -457,6 +456,7 @@ simplify_term(Term_In, Term_Out) :-
 %% join_similar_parts_of_term(+List, -List) is det
 %
 %  Combine powers of the same variable in the given list.
+%  Requires that the list be sorted
 %
 join_similar_parts_of_term([P1, P2 | L], L2) :-
     %% If both symbols are powers
@@ -480,6 +480,7 @@ join_similar_parts_of_term([N1, N2 | L], L2) :-
     % First result is always the most simplified form.
     !.
 join_similar_parts_of_term([X | L], [X | L2]) :-
+    %% Otherwise consume one element and recurse
     join_similar_parts_of_term(L, L2),
     % First result is always the most simplified form.
     !.
@@ -503,7 +504,7 @@ join_similar_parts_of_term([], []).
 %  Simplifies a polynomial.
 %
 simplify_polynomial(0, 0) :-
-    % 0 is already fully simplified and is an
+    % 0 is already fully simplified. This is an
     % exception to the following algorithm
     !.
 simplify_polynomial(P, P2) :-
@@ -616,6 +617,7 @@ join_similar_terms([], []).
 %
 %  Adds the coefficient of the term as the first element of the list
 %
+%% Special cases to make this predicate reversible
 term_to_canon([1], [1]) :-
     !.
 term_to_canon(L2, [1 | L]) :-
@@ -632,9 +634,8 @@ term_to_canon([N2 | L], [N | L]) :-
     number(N),
     N2 = N,
     !.
+%% Normal case
 term_to_canon(L, [N | L2]) :-
-    %% N == 1 -> L = L2
-    %% ;
     term_to_canon_with_coefficient(N, L, L2),
     !.
 %% Tests:
@@ -742,6 +743,7 @@ sign_of_power(-P, -1*P).
 %
 %  Adds two terms represented as list by adding
 %  the coeficients if the power is the same.
+%  Returns false if they can't be added
 %  Requires the list of terms to be simplified.
 %
 add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
@@ -762,6 +764,8 @@ add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
 %@ R = [3, x^3].
 %% ?- add_terms([2, x^3], [3, x^3], R).
 %@ R = [5, x^3].
+%% ?- add_terms([2, x^3], [3, x^2], R).
+%@ false.
 
 %% polynomial_to_list(+P:polynomial, -L:List) is det
 %
@@ -792,8 +796,6 @@ polynomial_to_list(T, [T]) :-
 %@ S = [-2*y, 5, 2*x^2].
 %% ?- polynomial_to_list(2*x^2-5-y*2, S).
 %@ S = [-2*y, -5, 2*x^2].
-%% ?- polynomial_to_list(P, [-2*y, -5, 2*x^2]).
-%@ ERROR: Unhandled exception: type_error(_527068=_527074*_527076,2,'a real number',_527074*_527076)
 
 %% list_to_polynomial(+L:List, -P:Polynomial) is det
 %
@@ -849,9 +851,10 @@ negate_term(T, T2) :-
     %% (-)/1 is an operator, needs to be evaluated, otherwise
     %% it gives a symbolic result, which messes with further processing
     N2 is -N,
+    %% Convert the term back from canonic form
+    term_to_canon(L3, [N2 | R]),
     %% Reverse the order of the list, because converting
     %% implicitly reverses it
-    term_to_canon(L3, [N2 | R]),
     reverse(L3, L4),
     term_to_list(T2, L4),
     !.
@@ -896,7 +899,8 @@ scale_polynomial(P, C, S) :-
 %
 cons(C, L, [C | L]).
 %% Tests:
-%% No need for tests as it is trivially correct.
+%% ?- cons(C, L, L2).
+%@ L2 = [C|L].
 
 %% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det
 %