Merge branch 'negatives_in_polynomials'

polimani.pl

@@ -26,6 +26,7 @@
  * reversing of a predicate.
  */
 :- use_module(library(clpfd)).
+%% :- use_module(library(clpr)).
 
 
                  /*******************************
@@ -38,21 +39,24 @@
     argument) and vice-versa.
 */
 poly2list(P, L) :-
-    polynomial_to_list(P, L).
+    polynomial_to_list(P, L),
+    !.
 
 /*
     simpolylist/2 simplifies a polynomial represented as a list into
     another polynomial as a list.
 */
 simpoly_list(L, S) :-
-    simplify_polynomial_list(L, S).
+    simplify_polynomial_as_list(L, S),
+    !.
 
 /*
     simpoly/2 simplifies a polynomial represented as an expression
     as another polynomial as an expression.
 */
 simpoly(P, S) :-
-    simplify_polynomial(P, S).
+    simplify_polynomial(P, S),
+    !.
 
 /*
     scalepoly/3 multiplies a polynomial represented as an expression by a scalar
@@ -60,7 +64,8 @@ simpoly(P, S) :-
     be ground. The polynomial resulting from the sum is in simplified form.
 */
 scalepoly(P1, P2, S) :-
-    scale_polynomial(P1, P2, S).
+    scale_polynomial(P1, P2, S),
+    !.
 
 /*
     addpoly/3 adds two polynomials as expressions resulting in a
@@ -68,7 +73,8 @@ scalepoly(P1, P2, S) :-
     The polynomial resulting from the sum is in simplified form.
 */
 addpoly(P1, P2, S) :-
-    add_polynomial(P1, P2, S).
+    add_polynomial(P1, P2, S),
+    !.
 
 
                  /*******************************
@@ -99,12 +105,13 @@ polynomial_variable(X) :-
 %  Returns true if X is a power term, false otherwise.
 %
 power(P^N) :-
-    (
+(
-        zcompare((<), 0, N),
+    N #>= 1,
-        polynomial_variable(P)
+    %% zcompare((<), -1, N),
-    ;
+    polynomial_variable(P)
-        fail
+;
-    ).
+    fail
+).
 power(X) :-
     polynomial_variable(X).
 %% Tests:
@@ -119,12 +126,12 @@ power(X) :-
 %% ?- power(x^(-3)).
 %@ false.
 %% ?- power(X).
-%@ X = x^_7334,
+%@ X = x^_2420,
-%@ _7334 in 1..sup ;
+%@ _2420 in 0..sup ;
-%@ X = y^_7334,
+%@ X = y^_2420,
-%@ _7334 in 1..sup ;
+%@ _2420 in 0..sup ;
-%@ X = z^_7334,
+%@ X = z^_2420,
-%@ _7334 in 1..sup ;
+%@ _2420 in 0..sup ;
 %@ X = x ;
 %@ X = y ;
 %@ X = z.
@@ -134,14 +141,19 @@ power(X) :-
 %  Returns true if N is a term, false otherwise.
 %
 term(N) :-
-    number(N).
+    (nonvar(N),
-%% N in inf..sup.
+     number(N));
+    (not(compound(N)),
+     var(N),
+     N in inf..sup).
+    %% {N >= -1000, N =< 1000}.
+    %% N ::= inf..sup.
+    %% (var(N), N in inf..sup).
 term(X) :-
     power(X).
 term(L * R) :-
     term(L),
     term(R).
-%% append_two_atoms_with_star(L, R, T).
 %% Tests:
 %% ?- term(2*x^3).
 %@ true .
@@ -156,9 +168,31 @@ term(L * R) :-
 %% ?- term(3.2*x).
 %@ true .
 %% ?- term(X).
+%@ X in inf..sup ;
+%@ X = x^_1242,
+%@ _1242 in 1..sup ;
+%@ X = y^_1242,
+%@ _1242 in 1..sup ;
+%@ X = z^_1242,
+%@ _1242 in 1..sup ;
+%@ X = x ;
+%@ X = y ;
+%@ X = z ;
+%@ X = _1330*_1332,
+%@ _1330 in inf..sup,
+%@ _1332 in inf..sup ;
+%@ X = _1406*x^_1414,
+%@ _1406 in inf..sup,
+%@ _1414 in 1..sup ;
+%@ X = _1406*y^_1414,
+%@ _1406 in inf..sup,
+%@ _1414 in 1..sup ;
+%@ X = _1406*z^_1414,
+%@ _1406 in inf..sup,
+%@ _1414 in 1..sup ;
+%@ X = _1188*x,
+%@ _1188 in inf..sup .
 %% Doesn't give all possible terms, because number(N) is not reversible
-%% The ic library seems to be able to help here, but it's not a part of
-%% SwiPL by default
 
 %% is_term_valid_in_predicate(+T, +F) is det
 %
@@ -247,6 +281,8 @@ term_to_list(P, [P2]) :-
 %@ X = [1] .
 %% ?- term_to_list(-1, X).
 %@ X = [-1] .
+%% ?- term_to_list(2 * 3, X).
+%@ X = [3, 2] .
 %% ?- 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, 1] .
 %% ?- term_to_list(X, [-1]).
@@ -343,17 +379,8 @@ simplify_polynomial(0, 0) :-
     !.
 simplify_polynomial(P, P2) :-
     polynomial_to_list(P, L),
-    maplist(term_to_list, L, L2),
+    simplify_polynomial_as_list(L, L2),
-    maplist(sort(0, @>=), L2, L3),
+    polynomial_to_list(P2, L2),
-    sort(0, @>=, L3, L4),
-    maplist(join_similar_parts_of_term, L4, L5),
-    maplist(sort(0, @=<), L5, L6),
-    join_similar_terms(L6, L7),
-    maplist(reverse, L7, L8),
-    maplist(term_to_list, L9, L8),
-    delete(L9, 0, L10),
-    sort(0, @=<, L10, L11),
-    list_to_polynomial(L11, P2),
     !.
 %% Tests:
 %% ?- simplify_polynomial(1, X).
@@ -454,49 +481,53 @@ add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
 %% ?- add_terms([2, x^3], [3, x^3], R).
 %@ R = [5, x^3].
 
-%% simplify_polynomial_list(+L:list, -S:list) is det
+%% simplify_polynomial_as_list(+L1:List,-L3:List) is det
 %
 %  Simplifies a polynomial represented as a list
 %
-simplify_polynomial_list(L, S) :-
+simplify_polynomial_as_list(L, L11) :-
-    polynomial_to_list(P1, L),
+    maplist(term_to_list, L, L2),
-    simplify_polynomial(P1, P2),
+    maplist(sort(0, @>=), L2, L3),
-    polynomial_to_list(P2, S).
+    sort(0, @>=, L3, L4),
+    maplist(join_similar_parts_of_term, L4, L5),
+    maplist(sort(0, @=<), L5, L6),
+    join_similar_terms(L6, L7),
+    maplist(reverse, L7, L8),
+    maplist(term_to_list, L9, L8),
+    delete(L9, 0, L10),
+    sort(0, @=<, L10, L11).
 
-%% polynomial_to_list(+P:polynomial, -L:List)
+%% polynomial_to_list(+P:polynomial, -L:List) is det
 %
 %  Converts a polynomial in a list.
 %
 polynomial_to_list(L - T, [T2 | LS]) :-
     term(T),
     negate_term(T, T2),
-    polynomial_to_list(L, LS).
+    polynomial_to_list(L, LS),
+    !.
 polynomial_to_list(L + T, [T | LS]) :-
     term(T),
-    polynomial_to_list(L, LS).
+    polynomial_to_list(L, LS),
+    !.
 polynomial_to_list(T, [T]) :-
-    term(T).
+    term(T),
+    !.
 %% Tests:
 %% ?- polynomial_to_list(2, S).
-%@ S = [2] .
+%@ S = [2].
 %% ?- polynomial_to_list(x^2, S).
-%@ S = [x^2] .
+%@ S = [x^2].
 %% ?- polynomial_to_list(x^2 + x^2, S).
-%@ S = [x^2, x^2] .
+%@ S = [x^2, x^2].
 %% ?- polynomial_to_list(2*x^2+5+y*2, S).
-%@ S = [y*2, 5, 2*x^2] .
+%@ S = [y*2, 5, 2*x^2].
 %% ?- polynomial_to_list(2*x^2+5-y*2, S).
-%@ S = [-2*y, 5, 2*x^2] .
+%@ S = [-2*y, 5, 2*x^2].
 %% ?- polynomial_to_list(2*x^2-5-y*2, S).
-%@ S = [-2*y, -5, 2*x^2] .
+%@ S = [-2*y, -5, 2*x^2].
-%% ?- polynomial_to_list(P, [2]).
+%% ?- polynomial_to_list(2*x^2+3*x+5*x^17-7*x^21+3*x^3-23*x^4+25*x^5-4.3, S).
-%@ P = 2 .
+%@ S = [-4.3, 25*x^5, -23*x^4, 3*x^3, -7*x^21, 5*x^17, 3*x, 2* ... ^ ...].
-%% ?- polynomial_to_list(P, [x]).
-%@ P = x .
-%% ?- polynomial_to_list(P, [x^2, x, 2.3]).
-%@ Action (h for help) ? abort
-%@ % Execution Aborted
-%@ P = -2.3+x+x^2 .
 
 %% list_to_polynomial(+P:polynomial, -L:List)
 %
@@ -551,36 +582,23 @@ negate_term(T, T2) :-
 %% ?- negate_term(3*x*y^2, R).
 %@ R = -3*x*y^2.
 
-%% append_two_atoms_with_star(+V1, +V2, -R) is det
-%
-%  Returns R = V1 * V2
-%
-append_two_atoms_with_star(V1, V2, R) :-
-    % Convert term V2 into a string V3
-    term_string(V2, V3),
-    % Concat atom V1 with * into a compound V4
-    atom_concat(V1, *, V4),
-    % Concat atom V4 with V3 into a compound S
-    atom_concat(V4, V3, S),
-    % Convert compound S into a term R
-    term_string(R, S).
-%% Tests:
-%  ?- append_two_atoms_with_star(2, x^2, R).
-%@ R = 2*x^2.
-%@ R = 2*x^2.
-%@ R = 2*3.
-
 %% scale_polynomial(+P:polynomial,+C:constant,-S:polynomial) is det
 %
 %  Scales a polynomial with a constant
 %
 scale_polynomial(P, C, S) :-
     polynomial_to_list(P, L),
-    maplist(append_two_atoms_with_star(C), L, L2),
+    maplist(term_to_list, L, L2),
-    list_to_polynomial(L2, S).
+    maplist(cons(C), L2, L3),
+    maplist(term_to_list, L4, L3),
+    simplify_polynomial_as_list(L4, L5),
+    list_to_polynomial(L5, S),
+    !.
 %% Tests:
 %% ?- scale_polynomial(3*x^2, 2, S).
-%@ S = 2*3*x^2.
+%@ S = 6*x^2.
+
+cons(C, L, [C | L]).
 
 %% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det
 %

test.pl

@@ -0,0 +1,2 @@
+:- use_module(library(clpfd)).
+foo(N) :- (nonvar(N), number(N));(var(N), N in inf..sup).