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Add better support for negative numbers

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Hugo Sales 2018-11-25 16:47:43 +00:00
parent d298364d0f
commit 962bab21ba
1 changed files with 244 additions and 103 deletions
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polymani.pl
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@ -27,6 +27,11 @@
* reversing of a predicate. * reversing of a predicate.
*/ */
:- use_module(library(clpfd)). :- use_module(library(clpfd)).
/*
* Import Constraint Logic Programming for Reals library, which is somewhat
* similar to clpfd, but for real numbers
*/
:- use_module(library(clpr)).
/******************************* /*******************************
@ -82,130 +87,9 @@ addpoly(P1, P2, S) :-
is_polynomial_valid_in_predicate(P2, "addpoly"), is_polynomial_valid_in_predicate(P2, "addpoly"),
add_polynomial(P1, P2, S), add_polynomial(P1, P2, S),
!. !.
/*******************************
* BACKEND *
*******************************/
%% polynomial_variable_list(-List) is det
%
% List of possible polynomial variables
%
polynomial_variable_list([x, y, z]).
%% polynomial_variable(?X:atom) is semidet
%
% Returns true if X is a polynomial variable, false otherwise.
%
polynomial_variable(X) :-
polynomial_variable_list(V),
member(X, V).
%% Tests: %% Tests:
%% ?- polynomial_variable(x). %% ?- addpoly(3 + x, 3 - x, S).
%@ true . %@ S = 0*x+6. TODO HERE
%% ?- polynomial_variable(a).
%@ false.
%% power(+X:atom) is semidet
%
% Returns true if X is a power term, false otherwise.
%
power(P^N) :-
(
N #>= 1,
polynomial_variable(P)
;
fail
).
power(X) :-
polynomial_variable(X).
%% Tests:
%% ?- power(x).
%@ true .
%% ?- power(a).
%@ false.
%% ?- power(x^1).
%@ true .
%% ?- power(x^3).
%@ true .
%% ?- power(x^(-3)).
%@ false.
%% ?- power(X).
%@ X = x^_2420,
%@ _2420 in 0..sup ;
%@ X = y^_2420,
%@ _2420 in 0..sup ;
%@ X = z^_2420,
%@ _2420 in 0..sup ;
%@ X = x ;
%@ X = y ;
%@ X = z.
%% term(+N:atom) is semidet
%
% Returns true if N is a term, false otherwise.
%
term(N) :-
(
% If N is non 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
).
term(X) :-
power(X).
term(L * R) :-
term(L),
term(R).
%% Tests:
%% ?- term(2*x^3).
%@ true .
%% ?- term(x^(-3)).
%@ false.
%% ?- term(a).
%@ false.
%% ?- term(-1*x).
%@ true .
%% ?- term((-3)*x^2).
%@ true .
%% ?- 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
%% is_polynomial_valid_in_predicate(+T, +F) is det %% is_polynomial_valid_in_predicate(+T, +F) is det
% %
@ -249,6 +133,130 @@ is_polynomial_as_list_valid_in_predicate(L, F) :-
%@ Invalid polynomial in Test: a*4+0*x %@ Invalid polynomial in Test: a*4+0*x
%@ false. %@ false.
/*******************************
* BACKEND *
*******************************/
%% polynomial_variable_list(-List) is det
%
% List of possible polynomial variables
%
polynomial_variable_list([x, y, z]).
%% polynomial_variable(?X:atom) is semidet
%
% Returns true if X is a polynomial variable, false otherwise.
%
polynomial_variable(X) :-
polynomial_variable_list(V),
member(X, V).
%% Tests:
%% ?- polynomial_variable(x).
%@ true .
%% ?- polynomial_variable(a).
%@ false.
%% power(+X:atom) is semidet
%
% Returns true if X is a power term, false otherwise.
%
power(P^N) :-
N #>= 1,
polynomial_variable(P).
power(X) :-
polynomial_variable(X).
%% Tests:
%% ?- power(x).
%@ true .
%% ?- power(a).
%@ false.
%% ?- power(x^1).
%@ true .
%% ?- power(x^3).
%@ true .
%% ?- power(x^(-3)).
%@ false.
%% ?- power(-x).
%@ false.
%% ?- power(X).
%@ X = x^_462546,
%@ _462546 in 1..sup ;
%@ X = y^_462546,
%@ _462546 in 1..sup ;
%@ X = z^_462546,
%@ _462546 in 1..sup ;
%@ X = x ;
%@ X = y ;
%@ X = z.
%% term(+N:atom) is semidet
%
% 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}
).
term(X) :-
power(X).
term(-X) :-
power(X).
term(L * R) :-
term(L),
term(R).
%% Tests:
%% ?- term(2*x^3).
%@ true .
%% ?- term(x^(-3)).
%@ false.
%% ?- term(a).
%@ false.
%% ?- term(-1*x).
%@ true .
%% ?- term(-x).
%@ true .
%% ?- term((-3)*x^2).
%@ true .
%% ?- term(3.2*x).
%@ true .
%% ?- term(-x*(-z)).
%@ true .
%% ?- term(X).
%@ {X>=0.0} ;
%@ {X<0.0} ;
%@ X = x^_111514,
%@ _111514 in 1..sup ;
%@ X = y^_111514,
%@ _111514 in 1..sup ;
%@ X = z^_111514,
%@ _111514 in 1..sup ;
%@ X = x ;
%@ X = y ;
%@ X = z ;
%@ X = -x^_111522,
%@ _111522 in 1..sup ;
%@ X = -y^_111522,
%@ _111522 in 1..sup ;
%@ X = -z^_111522,
%@ _111522 in 1..sup ;
%@ X = -x ;
%@ X = -y ;
%@ X = -z ;
%% polynomial(+M:atom) is semidet %% polynomial(+M:atom) is semidet
% %
% Returns true if polynomial, false otherwise. % Returns true if polynomial, false otherwise.
@ -279,6 +287,10 @@ polynomial(L - R) :-
%@ false. %@ false.
%% ?- polynomial(x^(-3)). %% ?- polynomial(x^(-3)).
%@ false. %@ false.
%% ?- polynomial(-x + 3).
%@ true .
%% ?- polynomial(-x - -z).
%@ true .
%% power_to_canon(+T:atom, -T^N:atom) is semidet %% power_to_canon(+T:atom, -T^N:atom) is semidet
% %
@ -291,9 +303,14 @@ power_to_canon(T^N, T^N) :-
N #\= 1. N #\= 1.
power_to_canon(T, T^1) :- power_to_canon(T, T^1) :-
polynomial_variable(T). polynomial_variable(T).
%% power_to_canon(-P, -P2) :-
%% power_to_canon(P, P2).
%% Tests: %% Tests:
%% ?- power_to_canon(x, X). %% ?- power_to_canon(x, X).
%@ X = x^1 . %@ X = x^1 .
%% ?- power_to_canon(-x, X).
%@ false.
%@ X = -1*x^1 .
%% ?- power_to_canon(X, x^1). %% ?- power_to_canon(X, x^1).
%@ X = x . %@ X = x .
%% ?- power_to_canon(X, x^4). %% ?- power_to_canon(X, x^4).
@ -302,6 +319,8 @@ power_to_canon(T, T^1) :-
%@ false. %@ false.
%% ?- power_to_canon(X, x^(-3)). %% ?- power_to_canon(X, x^(-3)).
%@ X = x^ -3 . %@ X = x^ -3 .
%% ?- power_to_canon(X, -1*x^1).
%@ X = -x .
%% term_to_list(?T, ?List) is semidet %% term_to_list(?T, ?List) is semidet
% %
@ -317,16 +336,28 @@ term_to_list(L * P, [P2 | TS]) :-
power(P), power(P),
power_to_canon(P, P2), power_to_canon(P, P2),
term_to_list(L, TS). term_to_list(L, TS).
term_to_list(L * -P, [-P2 | TS]) :-
power(P),
power_to_canon(P, P2),
term_to_list(L, TS).
term_to_list(N, [N]) :- term_to_list(N, [N]) :-
number(N). number(N).
term_to_list(P, [P2]) :- term_to_list(P, [P2]) :-
power(P), power(P),
power_to_canon(P, P2). power_to_canon(P, P2).
term_to_list(-P, [-P2]) :-
power(P),
power_to_canon(P, P2).
%% Tests: %% Tests:
%% ?- term_to_list(1, X). %% ?- term_to_list(1, X).
%@ X = [1] . %@ X = [1] .
%@ X = [1] .
%% ?- term_to_list(-1, X). %% ?- term_to_list(-1, X).
%@ X = [-1] . %@ X = [-1] .
%% ?- term_to_list(x, X).
%@ X = [x^1] .
%% ?- term_to_list(-x, X).
%@ X = [-x^1] .
%% ?- term_to_list(2 * 3, X). %% ?- term_to_list(2 * 3, X).
%@ X = [3, 2] . %@ X = [3, 2] .
%% ?- term_to_list(1*2*y*z*23*x*y*x^3*x, X). %% ?- term_to_list(1*2*y*z*23*x*y*x^3*x, X).
@ -337,6 +368,9 @@ term_to_list(P, [P2]) :-
%@ X = -1 . %@ X = -1 .
%% ?- term_to_list(X, [x^1, -1]). %% ?- term_to_list(X, [x^1, -1]).
%@ X = -1*x . %@ X = -1*x .
%@ X = -1*x .
%% ?- term_to_list(X, [-x^1]).
%@ X = -x .
%% ?- term_to_list(X, [y^1, x^1]). %% ?- term_to_list(X, [y^1, x^1]).
%@ X = x*y . %@ X = x*y .
%% ?- term_to_list(X, [x^4]). %% ?- term_to_list(X, [x^4]).
@ -393,6 +427,10 @@ simplify_term(Term_In, Term_Out) :-
%@ X = 0. %@ X = 0.
%% ?- simplify_term(6*y*z*7*x*y*x^3*x, X). %% ?- simplify_term(6*y*z*7*x*y*x^3*x, X).
%@ X = 42*x^5*y^2*z. %@ X = 42*x^5*y^2*z.
%% ?- simplify_term(-x, X).
%@ X = -x.
%% ?- simplify_term(-x*y*(-z)*3, X).
%@ X = 3* -x* -z*y.
%% ?- simplify_term(a, X). %% ?- simplify_term(a, X).
%@ false. %@ false.
%% ?- simplify_term(x^(-3), X). %% ?- simplify_term(x^(-3), X).
@ -439,6 +477,8 @@ join_similar_parts_of_term([], []).
%@ T = [6, x^3]. %@ T = [6, x^3].
%% ?- join_similar_parts_of_term([2, 3, x^1, x^2, y^1, y^6], T). %% ?- join_similar_parts_of_term([2, 3, x^1, x^2, y^1, y^6], T).
%@ T = [6, x^3, y^7]. %@ T = [6, x^3, y^7].
%% ?- join_similar_parts_of_term([2, 3, -x^1, -x^2], T).
%@ T = [6, -x^1, -x^2].
%% simplify_polynomial(+P:atom, -P2:atom) is det %% simplify_polynomial(+P:atom, -P2:atom) is det
% %
@ -511,8 +551,12 @@ simplify_polynomial_as_list(L, L11) :-
%% Tests: %% Tests:
%% ?- simplify_polynomial_as_list([x, 1, x^2, x*y, 3*x^2, 4*x], L). %% ?- simplify_polynomial_as_list([x, 1, x^2, x*y, 3*x^2, 4*x], L).
%@ L = [1, 4*x^2, 5*x, x*y] . %@ L = [1, 4*x^2, 5*x, x*y] .
%@ L = [1, 4*x^2, 5*x, x*y] .
%% ?- simplify_polynomial_as_list([1, x^2, x*y, 3*x^2, -4, -1*x], L). %% ?- simplify_polynomial_as_list([1, x^2, x*y, 3*x^2, -4, -1*x], L).
%@ L = [-3, -1*x, 4*x^2, x*y] . %@ L = [-3, -1*x, 4*x^2, x*y] .
%@ L = [-3, -1*x, 4*x^2, x*y] .
%% ?- simplify_polynomial_as_list([0*x], L).
%@ L = [0*x] .
%% join_similar_terms(+P:ListList, -P2:ListList) is det %% join_similar_terms(+P:ListList, -P2:ListList) is det
% %
@ -544,34 +588,130 @@ join_similar_terms([], []).
%% term_to_canon(+T:List, -T2:List) is det %% term_to_canon(+T:List, -T2:List) is det
% %
% Adds a 1 if there's no number in the list. % Adds the coefficient of the term as the first element of the list
% Requires the list to be sorted such that the
% numbers come first.
% For instance with `sort(0, @=<)`.
% %
term_to_canon([T | TS], [1, T | TS]) :- term_to_canon([1], [1]) :-
%% Since the list is sorted, if the first element
%% is not a number, then we need to add the 1
not(number(T)),
%% Give only first result. Red cut
!. !.
term_to_canon([T | TS], [N, T | TS]) :- term_to_canon(L2, [1 | L]) :-
%% Since the list is sorted, if the first element nonvar(L),
%% is not a number, then we need to add the 1 L2 = L,
not(number(T)), !.
N is -1, term_to_canon([-1], [-1]) :-
%% Give only first result. Red cut !.
term_to_canon([-P | L2], [-1, P | L]) :-
nonvar(L),
L2 = L,
!.
term_to_canon([N2 | L], [N | L]) :-
number(N),
N2 = N,
!.
term_to_canon(L, [N | L2]) :-
%% N == 1 -> L = L2
%% ;
term_to_canon_with_coefficient(N, L, L2),
!. !.
term_to_canon(L, L).
%% Tests: %% Tests:
%% ?- term_to_canon([2], T). %% ?- term_to_canon([2], T).
%@ T = [2]. %@ T = [2].
%% ?- term_to_canon([-x], T).
%@ T = [-1, x].
%% ?- term_to_canon([-x^3], T).
%@ T = [-1, x^3].
%% ?- term_to_canon([x^1], T).
%@ T = [1, x^1].
%% ?- term_to_canon([x^3], T). %% ?- term_to_canon([x^3], T).
%@ T = [1, x^3]. %@ T = [1, x^3].
%% ?- term_to_canon([x^3, z], T). %% ?- term_to_canon([x^3, z], T).
%@ T = [1, x^3, z]. %@ T = [1, x^3, z].
%% ?- term_to_canon([2, x^3], T). %% ?- term_to_canon([2, x^3], T).
%@ T = [2, x^3]. %@ T = [2, x^3].
%% ?- term_to_canon([2, -x^3], T).
%@ T = [-2, x^3].
%% ?- term_to_canon([2, -x^3, -z], T).
%@ T = [2, x^3, z].
%% ?- term_to_canon(L, [-1]).
%@ L = [-1].
%% ?- term_to_canon(L, [1]).
%@ L = [1].
%% ?- term_to_canon(L, [-2]).
%@ L = [-2].
%% ?- term_to_canon(L, [-2, x]).
%@ L = [-2, x].
%% ?- term_to_canon(L, [1, x]).
%@ L = [x].
%% ?- term_to_canon(L, [-1, x]).
%@ L = [-x].
%% ?- term_to_canon(L, [1, x, z, y]).
%@ L = [x, z, y].
%% ?- term_to_canon(L, [-1, x, z, y]).
%@ L = [-x, z, y].
%% term_to_canon_with_coefficient(-N:number, +L:List, -L2:List) is semidet
%
% Calculates the coefficient of the term and removes negations of powers,
% accumulating the results in N
%
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 %% add_terms(+L:List, +R:List, -Result:List) is det
% %
@ -678,28 +818,29 @@ list_to_polynomial([T], T).
% %
negate_term(T, T2) :- negate_term(T, T2) :-
term_to_list(T, L), term_to_list(T, L),
%% Sort the list, so the coeficient is the first element
sort(0, @=<, L, L2),
%% Ensure there is a coeficient %% Ensure there is a coeficient
term_to_canon(L2, L3), term_to_canon(L, L2),
[N | R] = L3, [N | R] = L2,
%% (-)/1 is an operator, needs to be evaluated, otherwise %% (-)/1 is an operator, needs to be evaluated, otherwise
%% it gives a symbolic result, which messes with further processing %% it gives a symbolic result, which messes with further processing
N2 is -N, N2 is -N,
%% Reverse the order of the list, because converting %% Reverse the order of the list, because converting
%% implicitly reverses it %% implicitly reverses it
reverse([N2 | R], L4), term_to_canon(L3, [N2 | R]),
reverse(L3, L4),
term_to_list(T2, L4), term_to_list(T2, L4),
!. !.
%% Tests: %% Tests:
%% ?- negate_term(1, R). %% ?- negate_term(1, R).
%@ R = -1. %@ R = -1.
%% ?- negate_term(x, R). %% ?- negate_term(x, R).
%@ R = -1*x. %@ R = -x.
%% ?- negate_term(-x, R).
%@ R = x.
%% ?- negate_term(x^2, R). %% ?- negate_term(x^2, R).
%@ R = -1*x^2. %@ R = -x^2.
%% ?- negate_term(3*x*y^2, R). %% ?- 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 %% scale_polynomial(+P:Polynomial,+C:Constant,-S:Polynomial) is det
% %