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Merge pull request #3 from diogogithub/negatives_in_polynomials

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Negatives in polynomials
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Diogo Cordeiro 2018-11-22 23:28:43 +00:00 committed by GitHub
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1 changed files with 140 additions and 108 deletions
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polimani.pl
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@ -150,6 +150,8 @@ term(L * R) :-
%@ false.
%% ?- term(a).
%@ false.
%% ?- term(-1*x).
%@ true .
%% ?- term((-3)*x^2).
%@ true .
%% ?- term(3.2*x).
@ -244,8 +246,17 @@ term_to_list(P, [P2]) :-
%% Tests:
%% ?- term_to_list(1, X).
%@ X = [1] .
%% ?- term_to_list(-1, X).
%@ X = [-1] .
%% ?- 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]).
%@ X = -1 .
%% ?- term_to_list(X, [x^1, -1]).
%@ X = -1*x .
%% ?- term_to_list(X, [- 1, x^1]).
%@ false.
%@ X = x* -1 .
%% ?- term_to_list(X, [y^1, x^1]).
%@ X = x*y .
%% ?- term_to_list(X, [x^4]).
@ -327,20 +338,22 @@ join_similar_parts_of_term([], []).
%% simplify_polynomial(+P:atom, -P2:atom) is det
%
% Simplifies a polynomial.
% TODO: not everything is a +, there are -
%
simplify_polynomial(0, 0) :-
!.
simplify_polynomial(P, P2) :-
polynomial_to_list(P, L),
maplist(term_to_list, L, L2),
maplist(join_similar_parts_of_term, L2, L3),
maplist(sort(0, @=<), L3, L4),
join_similar_terms(L4, L5),
transform_list(sort(0, @>=), L5, L6),
transform_list(term_to_list, L7, L6),
delete(L7, 0, L8),
polynomial_to_list(P2, L8),
maplist(sort(0, @>=), L2, L3),
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).
@ -351,19 +364,43 @@ simplify_polynomial(P, P2) :-
%@ X = x.
%% ?- simplify_polynomial(x*x, X).
%@ X = x^2.
%% ?- simplify_polynomial(2 + 2, X).
%@ X = 2*2.
%% ?- simplify_polynomial(x + x, X).
%@ X = 2*x.
%% ?- simplify_polynomial(0 + x*x, X).
%@ X = x^2.
%% ?- simplify_polynomial(x^2*x + 3*x^3, X).
%@ X = 4*x^3.
%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*x, X).
%@ X = 6*x^3.
%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*4 + z, X).
%@ X = 5*x^3+4*x^2+z.
%% ?- simplify_polynomial(x + 1 + x, X).
%@ X = 2*x+1.
%% ?- simplify_polynomial(x + 1 + x + 1 + x + 1 + x, X).
%@ X = 4*x+3*1.
%% join_similar_terms(+P:ListList, -P2:ListList) is det
%
% Joins similar sublists representing terms by using
% `add_terms` to check if they can be merged and perform
% the addition. Requires the list of list be sorted with
% `maplist(sort(0, @>=), L, L2),
% sort(0, @>=, L2, L3)`
% and that the sublists to be sorted with
% `sort(0, @=<)` since that is inherited from `add_terms`
%
join_similar_terms([TL, TR | L], L2) :-
%% Check if terms can be added and add them
add_terms(TL, TR, T2),
%% Recurse, accumulation on the first element
join_similar_terms([T2 | L], L2),
%% Give only first result. Red cut
!.
join_similar_terms([X | L], [X | L2]) :-
%% If a pair of elements can't be added, skip one
%% and recurse
join_similar_terms(L, L2),
%% Give only first result. Red cut
!.
@ -372,46 +409,51 @@ join_similar_terms([], []).
%% ?- join_similar_terms([[2, x^3], [3, x^3], [x^3]], L).
%@ L = [[6, x^3]].
term_to_canon([T], [1, T]) :-
%% term_to_canon(+T:List, -T2:List) is det
%
% Adds a 1 if there's no number in 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]) :-
%% 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(L, L).
%% Tests:
%% ?- term_to_canon([2], T).
%@ T = [2].
%% ?- term_to_canon([x^3], T).
%@ T = [1, x^3].
%% ?- term_to_canon([x^3, z], T).
%@ T = [1, x^3, z].
%% ?- term_to_canon([2, x^3], T).
%@ T = [2, x^3].
%% add_terms(+L:List, +R:List, -Result:List) is det
%
% Adds two terms represented as list by adding
% the coeficients if the power is the same.
% Requires the list of terms to be simplified.
%
add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
term_to_canon([NL | TL], [NL2 | TL2]),
term_to_canon([NR | TR], [NR2 | TR2]),
TL2 == TR2,
number(NL2),
number(NR2),
N2 is NL2 + NR2.
%% Tests
%% ?- add_terms([1], [1], R).
%@ R = [2].
%% ?- add_terms([x], [x], R).
%@ R = [2, x].
%% ?- add_terms([2, x^3], [x^3], R).
%@ R = [3, x^3].
%% ?- add_terms([2, x^3], [3, x^3], R).
%@ R = [5, x^3].
%% transform_list(+Pred, +L, -R) is det
%
% Apply predicate to each of the elements of L, producing R
%
transform_list(_, [], []).
transform_list(Pred, [L | LS], [R | RS]) :-
call(Pred, L, R),
transform_list(Pred, LS, RS),
!.
%% Tests:
%% ?- transform_list(term_to_list, [x, 2], L).
%@ L = [[x^1], [2]].
%% ?- transform_list(term_to_list, [x, x, 2], L).
%@ L = [[x^1], [x^1], [2]].
%% ?- transform_list(term_to_list, L, [[x^1], [x^1], [2]]).
%@ L = [x, x, 2].
%% simplify_polynomial_list(+L:list, -S:list) is det
%
% Simplifies a polynomial represented as a list
@ -424,31 +466,91 @@ simplify_polynomial_list(L, S) :-
%% polynomial_to_list(+P:polynomial, -L:List)
%
% Converts a polynomial in a list.
% TODO: not everything is a +, there are -
%
polynomial_to_list(L - T, [T2 | LS]) :-
term(T),
negate_term(T, T2),
polynomial_to_list(L, LS).
polynomial_to_list(L + T, [T | LS]) :-
term(T),
polynomial_to_list(L, LS).
% The others computations are semantically meaningless
%% !.
polynomial_to_list(T, [T]) :-
term(T).
%% Tests:
%%?- polynomial_to_list(2, S).
%% ?- polynomial_to_list(2, S).
%@ S = [2] .
%%?- polynomial_to_list(x^2, S).
%% ?- polynomial_to_list(x^2, S).
%@ S = [x^2] .
%%?- polynomial_to_list(x^2 + x^2, S).
%% ?- polynomial_to_list(x^2 + x^2, S).
%@ S = [x^2, x^2] .
%%?- polynomial_to_list(2*x^2+5+y*2, S).
%% ?- polynomial_to_list(2*x^2+5+y*2, S).
%@ S = [y*2, 5, 2*x^2] .
%%?- polynomial_to_list(P, [2]).
%% ?- polynomial_to_list(2*x^2+5-y*2, S).
%@ 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]).
%@ P = 2 .
%%?- polynomial_to_list(P, [x]).
%% ?- polynomial_to_list(P, [x]).
%@ P = x .
%%?- polynomial_to_list(P, [x^2, x, -2.3]).
%% ?- 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)
%
% Converts a list in a polynomial.
%
list_to_polynomial([T1|T2], P) :-
list_to_polynomial(T2, L1),
(
not(L1 = []),
(
term_string(T1, S1),
string_chars(S1, [First|_]),
First = -,
term_string(L1, S2),
string_concat(S2,S1,S3),
term_string(P, S3)
;
P = L1+T1
)
;
P = T1
),
% The others computations are semantically meaningless
!.
list_to_polynomial(T, P) :-
P = T.
%% Tests:
%% TODO
%% negate_term(T, T2) is det
%
% Negate the coeficient of a term and return the negated term
%
negate_term(T, T2) :-
term_to_list(T, L),
sort(0, @=<, L, L2),
term_to_canon(L2, L3),
[N | R] = L3,
%% (-)/1 is an operator, needs to be evaluated, otherwise
%% it gives a symbolic result, which messes with further processing
N2 is -N,
reverse([N2 | R], L4),
term_to_list(T2, L4),
!.
%% Tests:
%% ?- negate_term(1, R).
%@ R = -1.
%% ?- negate_term(x, R).
%@ R = -1*x.
%% ?- negate_term(x^2, R).
%@ R = -1*x^2.
%% ?- 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
@ -481,73 +583,3 @@ scale_polynomial(P, C, S) :-
%% Tests:
%% ?- scale_polynomial(3*x^2, 2, S).
%@ S = 2*3*x^2.
/* CENAS DO PROF: */
%% monomial_parts(X, Y, Z)
%
% TODO Maybe remove
% Separate monomial into it's parts. Given K*X^N, gives K and N
%
monomial_parts(X, 1, X) :-
power(X),
!.
monomial_parts(X^N, 1, X^N) :-
power(X^N),
!.
monomial_parts(K * M, K, M) :-
number(K),
!.
monomial_parts(K, K, indep) :-
number(K),
!.
delete_monomial(M, X, M, 0) :-
term(M),
monomial_parts(M, _, X),
!.
delete_monomial(M + M2, X, M, M2) :-
term(M2),
term(M),
monomial_parts(M, _, X),
!.
delete_monomial(P + M, X, M, P) :-
term(M),
monomial_parts(M, _, X),
!.
delete_monomial(P + M2, X, M, P2 + M2) :-
delete_monomial(P, X, M, P2).
add_monomial(K1, K2, K3) :-
number(K1),
number(K2), !,
K3 is K1 + K2.
add_monomial(M1, M2, M3) :-
monomial_parts(M1, K1, XExp),
monomial_parts(M2, K2, XExp),
K3 is K1 + K2,
p_aux_add_monomial(K3, XExp, M3).
p_aux_add_monomial(K, indep, K) :-
!.
p_aux_add_monomial(0, _, 0) :-
!.
p_aux_add_monomial(1, XExp, XExp) :-
!.
p_aux_add_monomial(K, XExp, K * XExp).
closure_simplify_polynomial(P, P) :-
simplify_polynomial(P, P2),
P==P2,
!.
closure_simplify_polynomial(P, P3) :-
simplify_polynomial(P, P2),
closure_simplify_polynomial(P2, P3),
!.