Merge branch 'negatives_in_polynomials'
This commit is contained in:
Hugo Sales
commit
899313cf19
174
polimani.pl
174
polimani.pl
@ -26,6 +26,7 @@
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* reversing of a predicate.
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*/
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:- use_module(library(clpfd)).
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%% :- use_module(library(clpr)).
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/*******************************
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@ -38,21 +39,24 @@
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argument) and vice-versa.
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*/
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poly2list(P, L) :-
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polynomial_to_list(P, L).
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polynomial_to_list(P, L),
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!.
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/*
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simpolylist/2 simplifies a polynomial represented as a list into
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another polynomial as a list.
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*/
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simpoly_list(L, S) :-
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simplify_polynomial_list(L, S).
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simplify_polynomial_as_list(L, S),
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!.
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/*
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simpoly/2 simplifies a polynomial represented as an expression
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as another polynomial as an expression.
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*/
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simpoly(P, S) :-
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simplify_polynomial(P, S).
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simplify_polynomial(P, S),
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!.
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/*
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scalepoly/3 multiplies a polynomial represented as an expression by a scalar
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@ -60,7 +64,8 @@ simpoly(P, S) :-
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be ground. The polynomial resulting from the sum is in simplified form.
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*/
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scalepoly(P1, P2, S) :-
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scale_polynomial(P1, P2, S).
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scale_polynomial(P1, P2, S),
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!.
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/*
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addpoly/3 adds two polynomials as expressions resulting in a
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@ -68,7 +73,8 @@ scalepoly(P1, P2, S) :-
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The polynomial resulting from the sum is in simplified form.
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*/
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addpoly(P1, P2, S) :-
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add_polynomial(P1, P2, S).
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add_polynomial(P1, P2, S),
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!.
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/*******************************
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@ -99,12 +105,13 @@ polynomial_variable(X) :-
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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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(
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N #>= 1,
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%% zcompare((<), -1, 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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@ -119,12 +126,12 @@ power(X) :-
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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^_2420,
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%@ _2420 in 0..sup ;
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%@ X = y^_2420,
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%@ _2420 in 0..sup ;
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%@ X = z^_2420,
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%@ _2420 in 0..sup ;
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%@ X = x ;
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%@ X = y ;
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%@ X = z.
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@ -134,14 +141,19 @@ power(X) :-
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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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(nonvar(N),
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number(N));
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(not(compound(N)),
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var(N),
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N in inf..sup).
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%% {N >= -1000, N =< 1000}.
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%% N ::= inf..sup.
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%% (var(N), 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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@ -156,9 +168,31 @@ term(L * R) :-
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%% ?- term(3.2*x).
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%@ true .
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%% ?- term(X).
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%@ X in inf..sup ;
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%@ X = x^_1242,
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%@ _1242 in 1..sup ;
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%@ X = y^_1242,
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%@ _1242 in 1..sup ;
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%@ X = z^_1242,
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%@ _1242 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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%@ X = _1330*_1332,
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%@ _1330 in inf..sup,
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%@ _1332 in inf..sup ;
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%@ X = _1406*x^_1414,
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%@ _1406 in inf..sup,
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%@ _1414 in 1..sup ;
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%@ X = _1406*y^_1414,
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%@ _1406 in inf..sup,
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%@ _1414 in 1..sup ;
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%@ X = _1406*z^_1414,
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%@ _1406 in inf..sup,
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%@ _1414 in 1..sup ;
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%@ X = _1188*x,
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%@ _1188 in inf..sup .
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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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@ -247,6 +281,8 @@ term_to_list(P, [P2]) :-
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%@ X = [1] .
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%% ?- term_to_list(-1, X).
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%@ X = [-1] .
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%% ?- term_to_list(2 * 3, X).
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%@ X = [3, 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, [-1]).
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@ -343,17 +379,8 @@ simplify_polynomial(0, 0) :-
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!.
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simplify_polynomial(P, P2) :-
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polynomial_to_list(P, L),
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maplist(term_to_list, L, L2),
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maplist(sort(0, @>=), L2, L3),
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sort(0, @>=, L3, L4),
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maplist(join_similar_parts_of_term, L4, L5),
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maplist(sort(0, @=<), L5, L6),
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join_similar_terms(L6, L7),
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maplist(reverse, L7, L8),
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maplist(term_to_list, L9, L8),
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delete(L9, 0, L10),
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sort(0, @=<, L10, L11),
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list_to_polynomial(L11, P2),
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simplify_polynomial_as_list(L, L2),
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polynomial_to_list(P2, L2),
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!.
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%% Tests:
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%% ?- simplify_polynomial(1, X).
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@ -454,49 +481,53 @@ add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
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%% ?- add_terms([2, x^3], [3, x^3], R).
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%@ R = [5, x^3].
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%% simplify_polynomial_list(+L:list, -S:list) is det
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%% simplify_polynomial_as_list(+L1:List,-L3:List) is det
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%
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% Simplifies a polynomial represented as a list
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%
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simplify_polynomial_list(L, S) :-
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polynomial_to_list(P1, L),
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simplify_polynomial(P1, P2),
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polynomial_to_list(P2, S).
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simplify_polynomial_as_list(L, L11) :-
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maplist(term_to_list, L, L2),
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maplist(sort(0, @>=), L2, L3),
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sort(0, @>=, L3, L4),
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maplist(join_similar_parts_of_term, L4, L5),
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maplist(sort(0, @=<), L5, L6),
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join_similar_terms(L6, L7),
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maplist(reverse, L7, L8),
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maplist(term_to_list, L9, L8),
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delete(L9, 0, L10),
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sort(0, @=<, L10, L11).
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%% polynomial_to_list(+P:polynomial, -L:List)
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%% polynomial_to_list(+P:polynomial, -L:List) is det
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%
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% Converts a polynomial in a list.
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%
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polynomial_to_list(L - T, [T2 | LS]) :-
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term(T),
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negate_term(T, T2),
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polynomial_to_list(L, LS).
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polynomial_to_list(L, LS),
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!.
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polynomial_to_list(L + T, [T | LS]) :-
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term(T),
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polynomial_to_list(L, LS).
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polynomial_to_list(L, LS),
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!.
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polynomial_to_list(T, [T]) :-
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term(T).
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term(T),
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!.
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%% Tests:
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%% ?- polynomial_to_list(2, S).
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%@ S = [2] .
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%@ S = [2].
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%% ?- polynomial_to_list(x^2, S).
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%@ S = [x^2] .
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%@ S = [x^2].
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%% ?- polynomial_to_list(x^2 + x^2, S).
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%@ S = [x^2, x^2] .
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%@ S = [x^2, x^2].
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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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%@ S = [y*2, 5, 2*x^2].
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%% ?- polynomial_to_list(2*x^2+5-y*2, S).
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%@ S = [-2*y, 5, 2*x^2] .
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%@ S = [-2*y, 5, 2*x^2].
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%% ?- polynomial_to_list(2*x^2-5-y*2, S).
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%@ S = [-2*y, -5, 2*x^2] .
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%% ?- polynomial_to_list(P, [2]).
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%@ P = 2 .
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%% ?- polynomial_to_list(P, [x]).
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%@ P = x .
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%% ?- polynomial_to_list(P, [x^2, x, 2.3]).
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%@ Action (h for help) ? abort
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%@ % Execution Aborted
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%@ P = -2.3+x+x^2 .
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%@ S = [-2*y, -5, 2*x^2].
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%% ?- 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).
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%@ S = [-4.3, 25*x^5, -23*x^4, 3*x^3, -7*x^21, 5*x^17, 3*x, 2* ... ^ ...].
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%% list_to_polynomial(+P:polynomial, -L:List)
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%
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@ -551,36 +582,23 @@ negate_term(T, T2) :-
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%% ?- negate_term(3*x*y^2, R).
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%@ R = -3*x*y^2.
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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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maplist(term_to_list, L, L2),
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maplist(cons(C), L2, L3),
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maplist(term_to_list, L4, L3),
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simplify_polynomial_as_list(L4, L5),
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list_to_polynomial(L5, S),
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!.
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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 = 6*x^2.
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cons(C, L, [C | L]).
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%% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det
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%
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