Add better support for negative numbers
This commit is contained in:
Hugo Sales
parent
d298364d0f
commit
962bab21ba
347
polymani.pl
347
polymani.pl
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@ -27,6 +27,11 @@
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* reversing of a predicate.
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*/
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:- use_module(library(clpfd)).
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/*
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* Import Constraint Logic Programming for Reals library, which is somewhat
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* similar to clpfd, but for real numbers
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*/
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:- use_module(library(clpr)).
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/*******************************
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@ -82,6 +87,51 @@ addpoly(P1, P2, S) :-
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is_polynomial_valid_in_predicate(P2, "addpoly"),
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add_polynomial(P1, P2, S),
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!.
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%% Tests:
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%% ?- addpoly(3 + x, 3 - x, S).
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%@ S = 0*x+6. TODO HERE
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%% is_polynomial_valid_in_predicate(+T, +F) is det
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%
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% Returns true if valid polynomial, fails with UI message otherwise.
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% The failure message reports which polynomial is invalid and in which
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% predicate the problem ocurred.
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%
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is_polynomial_valid_in_predicate(P, _) :-
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%% If P is a valid polynomial, return true
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polynomial(P),
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!.
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is_polynomial_valid_in_predicate(P, F) :-
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%% Writes the polynomial and fails otherwise
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write("Invalid polynomial in "),
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write(F),
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write(": "),
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write(P),
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fail.
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%% Tests:
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%% ?- is_polynomial_valid_in_predicate(1, "Test").
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%@ true.
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%% ?- is_polynomial_valid_in_predicate(a*4-0*x, "Test").
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%@ Invalid polynomial in Test: a*4-0*x
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%@ false.
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%% is_polynomial_as_list_valid_in_predicate(+L, +F) is det
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%
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% Returns true if the polynomial represented as list is valid,
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% fails with UI message otherwise.
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% The failure message reports which polynomial is invalid and
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% in which predicate the problem ocurred.
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%
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is_polynomial_as_list_valid_in_predicate(L, F) :-
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%% If L is a valid polynomial, return true
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list_to_polynomial(L, P),
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is_polynomial_valid_in_predicate(P, F).
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%% Tests:
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%% ?- is_polynomial_as_list_valid_in_predicate([1], "Test").
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%@ true.
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%% ?- is_polynomial_as_list_valid_in_predicate([0*x, a*4], "Test").
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%@ Invalid polynomial in Test: a*4+0*x
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%@ false.
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/*******************************
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@ -112,12 +162,8 @@ 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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N #>= 1,
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polynomial_variable(P)
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;
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fail
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).
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N #>= 1,
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polynomial_variable(P).
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power(X) :-
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polynomial_variable(X).
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%% Tests:
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@ -131,13 +177,15 @@ power(X) :-
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%@ true .
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%% ?- power(x^(-3)).
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%@ false.
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%% ?- power(-x).
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%@ false.
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%% ?- power(X).
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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^_462546,
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%@ _462546 in 1..sup ;
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%@ X = y^_462546,
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%@ _462546 in 1..sup ;
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%@ X = z^_462546,
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%@ _462546 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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@ -148,22 +196,25 @@ power(X) :-
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%
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term(N) :-
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(
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% If N is non a free variable
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% If N is not a free variable
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nonvar(N),
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% Assert it as a number
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number(N)
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;
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% If N is a free variable
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not(compound(N)),
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%% not(compound(N)),
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var(N),
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% Assert it must be between negative and positive infinity
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% This uses the CLP(FD) library, which makes this reversible,
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% whereas `number(N)` is always false, since it only succeeds
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% if the argument is bound to a intger or float
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N in inf..sup
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%% N in inf..sup
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{N >= 0; N < 0}
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).
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term(X) :-
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power(X).
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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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@ -176,78 +227,35 @@ term(L * R) :-
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%@ false.
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%% ?- term(-1*x).
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%@ true .
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%% ?- term(-x).
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%@ true .
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%% ?- term((-3)*x^2).
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%@ true .
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%% ?- term(3.2*x).
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%@ true .
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%% ?- term(-x*(-z)).
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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>=0.0} ;
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%@ {X<0.0} ;
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%@ X = x^_111514,
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%@ _111514 in 1..sup ;
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%@ X = y^_111514,
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%@ _111514 in 1..sup ;
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%@ X = z^_111514,
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%@ _111514 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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%% is_polynomial_valid_in_predicate(+T, +F) is det
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%
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% Returns true if valid polynomial, fails with UI message otherwise.
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% The failure message reports which polynomial is invalid and in which
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% predicate the problem ocurred.
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%
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is_polynomial_valid_in_predicate(P, _) :-
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%% If P is a valid polynomial, return true
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polynomial(P),
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!.
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is_polynomial_valid_in_predicate(P, F) :-
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%% Writes the polynomial and fails otherwise
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write("Invalid polynomial in "),
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write(F),
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write(": "),
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write(P),
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fail.
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%% Tests:
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%% ?- is_polynomial_valid_in_predicate(1, "Test").
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%@ true.
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%% ?- is_polynomial_valid_in_predicate(a*4-0*x, "Test").
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%@ Invalid polynomial in Test: a*4-0*x
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%@ false.
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%% is_polynomial_as_list_valid_in_predicate(+L, +F) is det
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%
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% Returns true if the polynomial represented as list is valid,
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% fails with UI message otherwise.
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% The failure message reports which polynomial is invalid and
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% in which predicate the problem ocurred.
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%
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is_polynomial_as_list_valid_in_predicate(L, F) :-
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%% If L is a valid polynomial, return true
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list_to_polynomial(L, P),
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is_polynomial_valid_in_predicate(P, F).
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%% Tests:
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%% ?- is_polynomial_as_list_valid_in_predicate([1], "Test").
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%@ true.
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%% ?- is_polynomial_as_list_valid_in_predicate([0*x, a*4], "Test").
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%@Invalid polynomial in Test: a*4+0*x
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%@false.
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%@ X = -x^_111522,
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%@ _111522 in 1..sup ;
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%@ X = -y^_111522,
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%@ _111522 in 1..sup ;
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%@ X = -z^_111522,
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%@ _111522 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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%% polynomial(+M:atom) is semidet
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%
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@ -279,6 +287,10 @@ polynomial(L - R) :-
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%@ false.
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%% ?- polynomial(x^(-3)).
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%@ false.
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%% ?- polynomial(-x + 3).
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%@ true .
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%% ?- polynomial(-x - -z).
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%@ true .
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%% power_to_canon(+T:atom, -T^N:atom) is semidet
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%
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@ -291,9 +303,14 @@ power_to_canon(T^N, T^N) :-
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N #\= 1.
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power_to_canon(T, T^1) :-
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polynomial_variable(T).
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%% power_to_canon(-P, -P2) :-
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%% power_to_canon(P, P2).
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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).
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%@ false.
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%@ X = -1*x^1 .
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%% ?- power_to_canon(X, x^1).
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%@ X = x .
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%% ?- power_to_canon(X, x^4).
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@ -302,6 +319,8 @@ power_to_canon(T, T^1) :-
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%@ false.
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%% ?- power_to_canon(X, x^(-3)).
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%@ X = x^ -3 .
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%% ?- power_to_canon(X, -1*x^1).
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%@ X = -x .
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%% term_to_list(?T, ?List) is semidet
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%
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@ -317,16 +336,28 @@ term_to_list(L * P, [P2 | TS]) :-
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power(P),
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power_to_canon(P, P2),
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term_to_list(L, TS).
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term_to_list(L * -P, [-P2 | TS]) :-
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power(P),
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power_to_canon(P, P2),
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term_to_list(L, TS).
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term_to_list(N, [N]) :-
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number(N).
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term_to_list(P, [P2]) :-
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power(P),
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power_to_canon(P, P2).
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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(1, X).
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%@ X = [1] .
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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(x, X).
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%@ X = [x^1] .
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%% ?- term_to_list(-x, X).
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%@ X = [-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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@ -337,6 +368,9 @@ term_to_list(P, [P2]) :-
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%@ X = -1 .
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%% ?- term_to_list(X, [x^1, -1]).
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%@ X = -1*x .
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%@ X = -1*x .
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%% ?- term_to_list(X, [-x^1]).
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%@ X = -x .
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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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@ -393,6 +427,10 @@ simplify_term(Term_In, Term_Out) :-
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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^5*y^2*z.
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%% ?- simplify_term(-x, X).
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%@ X = -x.
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%% ?- simplify_term(-x*y*(-z)*3, X).
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%@ X = 3* -x* -z*y.
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%% ?- simplify_term(a, X).
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%@ false.
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%% ?- simplify_term(x^(-3), X).
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@ -439,6 +477,8 @@ join_similar_parts_of_term([], []).
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%@ T = [6, x^3].
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%% ?- join_similar_parts_of_term([2, 3, x^1, x^2, y^1, y^6], T).
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%@ T = [6, x^3, y^7].
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%% ?- join_similar_parts_of_term([2, 3, -x^1, -x^2], T).
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%@ T = [6, -x^1, -x^2].
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%% simplify_polynomial(+P:atom, -P2:atom) is det
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%
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@ -511,8 +551,12 @@ simplify_polynomial_as_list(L, L11) :-
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%% Tests:
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%% ?- simplify_polynomial_as_list([x, 1, x^2, x*y, 3*x^2, 4*x], L).
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%@ L = [1, 4*x^2, 5*x, x*y] .
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%@ L = [1, 4*x^2, 5*x, x*y] .
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%% ?- simplify_polynomial_as_list([1, x^2, x*y, 3*x^2, -4, -1*x], L).
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%@ L = [-3, -1*x, 4*x^2, x*y] .
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%@ L = [-3, -1*x, 4*x^2, x*y] .
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%% ?- simplify_polynomial_as_list([0*x], L).
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%@ L = [0*x] .
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%% join_similar_terms(+P:ListList, -P2:ListList) is det
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%
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@ -544,34 +588,130 @@ join_similar_terms([], []).
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%% term_to_canon(+T:List, -T2:List) is det
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%
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% Adds a 1 if there's no number in the list.
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% Requires the list to be sorted such that the
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% numbers come first.
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% For instance with `sort(0, @=<)`.
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% Adds the coefficient of the term as the first element of the list
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%
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term_to_canon([T | TS], [1, T | TS]) :-
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%% Since the list is sorted, if the first element
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%% is not a number, then we need to add the 1
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not(number(T)),
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%% Give only first result. Red cut
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term_to_canon([1], [1]) :-
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!.
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term_to_canon([T | TS], [N, T | TS]) :-
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%% Since the list is sorted, if the first element
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%% is not a number, then we need to add the 1
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not(number(T)),
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N is -1,
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%% Give only first result. Red cut
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term_to_canon(L2, [1 | L]) :-
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nonvar(L),
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L2 = L,
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!.
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term_to_canon([-1], [-1]) :-
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!.
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term_to_canon([-P | L2], [-1, P | L]) :-
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nonvar(L),
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L2 = L,
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!.
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term_to_canon([N2 | L], [N | L]) :-
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number(N),
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N2 = N,
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!.
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term_to_canon(L, [N | L2]) :-
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%% N == 1 -> L = L2
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%% ;
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term_to_canon_with_coefficient(N, L, L2),
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!.
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term_to_canon(L, L).
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%% Tests:
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%% ?- term_to_canon([2], T).
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%@ T = [2].
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%% ?- term_to_canon([-x], T).
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%@ T = [-1, x].
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%% ?- term_to_canon([-x^3], T).
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%@ T = [-1, x^3].
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%% ?- term_to_canon([x^1], T).
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%@ T = [1, x^1].
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%% ?- term_to_canon([x^3], T).
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%@ T = [1, x^3].
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%% ?- term_to_canon([x^3, z], T).
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%@ T = [1, x^3, z].
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%% ?- term_to_canon([2, x^3], T).
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%@ T = [2, x^3].
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%% ?- term_to_canon([2, -x^3], T).
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%@ T = [-2, x^3].
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%% ?- term_to_canon([2, -x^3, -z], T).
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%@ T = [2, x^3, z].
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%% ?- term_to_canon(L, [-1]).
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%@ L = [-1].
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%% ?- term_to_canon(L, [1]).
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%@ L = [1].
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%% ?- term_to_canon(L, [-2]).
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%@ L = [-2].
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%% ?- term_to_canon(L, [-2, x]).
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%@ L = [-2, x].
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%% ?- term_to_canon(L, [1, x]).
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%@ L = [x].
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%% ?- term_to_canon(L, [-1, x]).
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%@ L = [-x].
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%% ?- term_to_canon(L, [1, x, z, y]).
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%@ L = [x, z, y].
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%% ?- term_to_canon(L, [-1, x, z, y]).
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%@ L = [-x, z, y].
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%% term_to_canon_with_coefficient(-N:number, +L:List, -L2:List) is semidet
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%
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% Calculates the coefficient of the term and removes negations of powers,
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% accumulating the results in N
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%
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||||
term_to_canon_with_coefficient(N, [N2 | TS], TS2) :-
|
||||
number(N2),
|
||||
%% {N2 >= 0; N2 < 0},
|
||||
term_to_canon_with_coefficient(N3, TS, TS2),
|
||||
N is N2 * N3,
|
||||
!.
|
||||
term_to_canon_with_coefficient(N, [P | TS], [P2 | TS2]) :-
|
||||
sign_of_power(P, N2 * P2),
|
||||
term_to_canon_with_coefficient(N3, TS, TS2),
|
||||
N is N2 * N3,
|
||||
!.
|
||||
term_to_canon_with_coefficient(N, [], []) :-
|
||||
nonvar(N);
|
||||
N = 1.
|
||||
%% Tests:
|
||||
%% ?- term_to_canon_with_coefficient(N, [x], L).
|
||||
%@ N = 1,
|
||||
%@ L = [x].
|
||||
%% ?- term_to_canon_with_coefficient(N, [x, x^2, 2], L).
|
||||
%@ N = 2,
|
||||
%@ L = [x^1, x^2].
|
||||
%% ?- term_to_canon_with_coefficient(N, [x, x^2, 2, 4, z], L).
|
||||
%@ N = 8,
|
||||
%@ L = [x, x^2, z].
|
||||
%% ?- term_to_canon_with_coefficient(N, [x, x^2, 2, 4, -z], L).
|
||||
%@ N = -8,
|
||||
%@ L = [x, x^2, z].
|
||||
%% ?- term_to_canon_with_coefficient(N, [x, -x^2, 2, 4, -z], L).
|
||||
%@ N = 8,
|
||||
%@ L = [x, x^2, z].
|
||||
%% ?- term_to_canon_with_coefficient(N, L, [x]).
|
||||
%@ N = 1,
|
||||
%@ L = [x].
|
||||
%% ?- term_to_canon_with_coefficient(N, L, [1]).
|
||||
%@ N = 1,
|
||||
%@ L = [1].
|
||||
%% ?- term_to_canon_with_coefficient(N, L, [2]).
|
||||
%@ N = 1,
|
||||
%@ L = [2].
|
||||
|
||||
%% sign_of_power(P:power, P:term) is det
|
||||
%
|
||||
% If there isn't a leading minus, multiplies the power by 1,
|
||||
% otherwise by a -1. This way it prefers the positive version.
|
||||
% Not idempotent
|
||||
%
|
||||
sign_of_power(P, 1*P) :-
|
||||
%% If P can't unify with a minus followed by an unnamed variable
|
||||
P \= -_,
|
||||
!.
|
||||
sign_of_power(-P, -1*P).
|
||||
%% Tests:
|
||||
%% ?- sign_of_power(x, X).
|
||||
%@ X = 1*x.
|
||||
%% ?- sign_of_power(-x, X).
|
||||
%@ X = -1*x.
|
||||
%% ?- sign_of_power(X, 1*x).
|
||||
%@ X = x.
|
||||
%% ?- sign_of_power(X, -1*x).
|
||||
%@ X = -x.
|
||||
|
||||
%% add_terms(+L:List, +R:List, -Result:List) is det
|
||||
%
|
||||
|
|
@ -678,28 +818,29 @@ list_to_polynomial([T], T).
|
|||
%
|
||||
negate_term(T, T2) :-
|
||||
term_to_list(T, L),
|
||||
%% Sort the list, so the coeficient is the first element
|
||||
sort(0, @=<, L, L2),
|
||||
%% Ensure there is a coeficient
|
||||
term_to_canon(L2, L3),
|
||||
[N | R] = L3,
|
||||
term_to_canon(L, L2),
|
||||
[N | R] = L2,
|
||||
%% (-)/1 is an operator, needs to be evaluated, otherwise
|
||||
%% it gives a symbolic result, which messes with further processing
|
||||
N2 is -N,
|
||||
%% Reverse the order of the list, because converting
|
||||
%% implicitly reverses it
|
||||
reverse([N2 | R], L4),
|
||||
term_to_canon(L3, [N2 | R]),
|
||||
reverse(L3, L4),
|
||||
term_to_list(T2, L4),
|
||||
!.
|
||||
%% Tests:
|
||||
%% ?- negate_term(1, R).
|
||||
%@ R = -1.
|
||||
%% ?- negate_term(x, R).
|
||||
%@ R = -1*x.
|
||||
%@ R = -x.
|
||||
%% ?- negate_term(-x, R).
|
||||
%@ R = x.
|
||||
%% ?- negate_term(x^2, R).
|
||||
%@ R = -1*x^2.
|
||||
%@ R = -x^2.
|
||||
%% ?- negate_term(3*x*y^2, R).
|
||||
%@ R = -3*x*y^2.
|
||||
%@ R = -3*y^2*x.
|
||||
|
||||
%% scale_polynomial(+P:Polynomial,+C:Constant,-S:Polynomial) is det
|
||||
%
|
||||
|
|
|
|||
Reference in New Issue