Merged documentation with latest code
This commit is contained in:
Hugo Sales
commit
1c6d63ed1b
363
polimani.pl
363
polimani.pl
@ -2,116 +2,122 @@
|
||||
%% Follows 'Coding guidelines for Prolog' - Theory and Practice of Logic Programming
|
||||
%% https://doi.org/10.1017/S1471068411000391
|
||||
|
||||
polynomial_variables([x, y, z]).
|
||||
polynomial_variable_p(X) :-
|
||||
polynomial_variables(V),
|
||||
member(X, V).
|
||||
polynomial_variable_p(P) :-
|
||||
polynomial_variables(V),
|
||||
member(X, V),
|
||||
%% number(N),
|
||||
P = X^N.
|
||||
%% polynomial_variable_list(-List:atom) is det
|
||||
%
|
||||
% List of possible polynomial variables
|
||||
%
|
||||
|
||||
polynomial_variable_list([x, y, z]).
|
||||
|
||||
%% polynomial_variable(?X:atom) is det
|
||||
%
|
||||
% Returns true if X is a polynomial variable, false otherwise.
|
||||
%
|
||||
polynomial_variable(X) :-
|
||||
polynomial_variable_list(V),
|
||||
member(X, V).
|
||||
polynomial_variable(P) :-
|
||||
polynomial_variable_list(V),
|
||||
member(X, V),
|
||||
P = X^N.
|
||||
%% Tests:
|
||||
%% ?- term_to_list(X, [x^4]).
|
||||
%@ X = x^4 .
|
||||
|
||||
power_p(X) :-
|
||||
polynomial_variable_p(X).
|
||||
power_p(X^N) :-
|
||||
polynomial_variable_p(X), integer(N), N >= 1.
|
||||
|
||||
%% ?- power_p(x^1).
|
||||
%% power(+X:atom) is det
|
||||
%
|
||||
% Returns true if X is a power term, false otherwise.
|
||||
%
|
||||
power(X) :-
|
||||
polynomial_variable(X).
|
||||
power(X^N) :-
|
||||
polynomial_variable(X),
|
||||
integer(N),
|
||||
N >= 1.
|
||||
%% Tests:
|
||||
%% ?- power(x^1).
|
||||
%@ true .
|
||||
%@ true.
|
||||
|
||||
term_p(N) :-
|
||||
|
||||
%% term(+N:atom) is det
|
||||
%
|
||||
% Returns true if N is a term, false otherwise.
|
||||
%
|
||||
term(N) :-
|
||||
number(N).
|
||||
term_p(X) :-
|
||||
power_p(X).
|
||||
term_p(L * R) :-
|
||||
term_p(L),
|
||||
term_p(R), !.
|
||||
|
||||
polynomial_p(M) :-
|
||||
term_p(M).
|
||||
polynomial_p(L + R) :- % Left greedy
|
||||
polynomial_p(L), % Why?
|
||||
term_p(R), !.
|
||||
|
||||
%% ?- polynomial_p(3*x^2+y*z).
|
||||
%@ true.
|
||||
%% ?- polynomial_p(x^100*y*z).
|
||||
%@ true.
|
||||
%% ?- polynomial_p(x+y+z).
|
||||
%@ true.
|
||||
%@ false.
|
||||
%@ false.
|
||||
%% ?- polynomial_p(3*x^2+y*z+x^100*y*z).
|
||||
%@ true.
|
||||
%@ true.
|
||||
%% @ false. WIP
|
||||
|
||||
simplify_term(1 * P, P) :-
|
||||
term_p(P), !.
|
||||
simplify_term(0 * _, 0) :-
|
||||
term(X) :-
|
||||
power(X).
|
||||
term(L * R) :-
|
||||
term(L),
|
||||
term(R),
|
||||
!.
|
||||
simplify_term(T, T2) :-
|
||||
term_to_list(T, L),
|
||||
sort(0, @=<, L, L2),
|
||||
join_like_terms(L2, L3),
|
||||
list_to_term(L3, T2). % Responsible for parenthesis
|
||||
%% sort(0, @>=, L3, L4),
|
||||
%% term_to_list(T2, L4).
|
||||
%% Tests:
|
||||
%% TODO
|
||||
|
||||
%% ?- simplify_term(2*y*z*x^3*x, X).
|
||||
%@ X = 2*(x^4*(y*z)).
|
||||
%@ X = z*(y*(x^4*2)).
|
||||
%% ?- simplify_term(2*y*z*23*x*y*x^3*x, X).
|
||||
%@ X = 46*(x^2*(x^3*(y^2*z))).
|
||||
%@ X = z*(y^2*(x^3*(x^2*46))).
|
||||
%@ X = [2, 23, x^1, x^3, y^1, z^1].
|
||||
%@ X = [46, x^4, y^1, z^1].
|
||||
%% is_term_valid_in_predicate(+T, +F) is det
|
||||
%
|
||||
% Returns true if valid Term, fails with UI message otherwise.
|
||||
% The fail message reports which Term is invalid and in which
|
||||
% predicate the problem ocurred.
|
||||
%
|
||||
is_term_valid_in_predicate(T, F) :-
|
||||
(
|
||||
term(T)
|
||||
;
|
||||
write("Invalid term in "),
|
||||
write(F),
|
||||
write(": "),
|
||||
write(T),
|
||||
fail
|
||||
).
|
||||
%% Tests:
|
||||
%% ?- is_term_valid_in_predicate().
|
||||
|
||||
join_like_terms([P1, P2 | L], [B^N | L2]) :-
|
||||
power_p(P1),
|
||||
power_p(P2),
|
||||
B^N1 = P1,
|
||||
B^N2 = P2,
|
||||
%% B1 == B2, % Wasn't working before..?
|
||||
N is N1 + N2,
|
||||
join_like_terms(L, L2),
|
||||
!.
|
||||
join_like_terms([N1, N2 | L], [N | L2]) :-
|
||||
number(N1),
|
||||
number(N2),
|
||||
N is N1 * N2,
|
||||
join_like_terms(L, L2),
|
||||
!.
|
||||
join_like_terms([X | L], [X | L2]) :-
|
||||
join_like_terms(L, L2).
|
||||
join_like_terms([], []).
|
||||
|
||||
%% ?- join_like_terms([2, 3, x^1, x^2], T).
|
||||
%@ T = [6, x^3].
|
||||
%@ T = [6, x^3].
|
||||
%% ?- join_like_terms([2, 3, x^1, x^2, y^1, y^6], T).
|
||||
%@ T = [6, x^3, y^7].
|
||||
%@ T = [6, x^3, y^7].
|
||||
%% polynomial(+M:atom) is det
|
||||
%
|
||||
% Returns true if polynomial, false otherwise.
|
||||
%
|
||||
polynomial(M) :-
|
||||
term(M).
|
||||
polynomial(L + R) :-
|
||||
polynomial(L),
|
||||
term(R).
|
||||
%% Tests:
|
||||
%% TODO
|
||||
|
||||
%% power_to_canon(+T:atom, -T^N:atom) is det
|
||||
%
|
||||
% Returns a canon power term.
|
||||
%
|
||||
power_to_canon(T^N, T^N) :-
|
||||
polynomial_variable(T).
|
||||
power_to_canon(T, T^1) :-
|
||||
polynomial_variable(T).
|
||||
%% Tests:
|
||||
%% ?- power_to_canon(x, X).
|
||||
%@ X = x^1.
|
||||
%% ?- power_to_canon(X, X^1).
|
||||
%@ X = x .
|
||||
%@ X = x.
|
||||
|
||||
%% term_to_list(?T, ?List) is det
|
||||
%
|
||||
% Converts a term to a list and vice versa.
|
||||
% Can verify if term and list are compatible.
|
||||
%
|
||||
term_to_list(L * N, [N | TS]) :-
|
||||
number(N),
|
||||
term_to_list(L, TS).
|
||||
term_to_list(L * P, [P2 | TS]) :-
|
||||
power_p(P),
|
||||
power(P),
|
||||
power_to_canon(P, P2),
|
||||
term_to_list(L, TS).
|
||||
term_to_list(N, [N]) :-
|
||||
number(N).
|
||||
term_to_list(P, [P2]) :-
|
||||
power_p(P),
|
||||
power(P),
|
||||
power_to_canon(P, P2).
|
||||
|
||||
%% Tests:
|
||||
%% ?- term_to_list(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] .
|
||||
%% ?- term_to_list(X, [y^1, x^1]).
|
||||
@ -122,84 +128,142 @@ term_to_list(P, [P2]) :-
|
||||
%% ?- term_to_list(X, [y^6, z^2, x^4]).
|
||||
%@ X = x^4*z^2*y^6 .
|
||||
|
||||
%% list_to_term([], 1).
|
||||
list_to_term([N], N) :-
|
||||
number(N),
|
||||
!.
|
||||
list_to_term([P], P2) :-
|
||||
power_p(P),
|
||||
power_to_canon(P2, P),
|
||||
!.
|
||||
list_to_term([N | LS], N * R) :-
|
||||
number(N),
|
||||
list_to_term(LS, R),
|
||||
!.
|
||||
list_to_term([P | LS], P2 * R) :-
|
||||
power_p(P),
|
||||
power_to_canon(P2, P),
|
||||
list_to_term(LS, R),
|
||||
!.
|
||||
%% simplify_term(+T:atom, -P) is det
|
||||
%
|
||||
% Simplifies a term.
|
||||
%
|
||||
simplify_term(1 * P, P).
|
||||
simplify_term(0 * _, 0).
|
||||
simplify_term(T, T2) :-
|
||||
term_to_list(T, L),
|
||||
sort(0, @=<, L, L2),
|
||||
join_like_terms(L2, L3),
|
||||
list_to_term(L3, T2). % Responsible for parenthesis
|
||||
%% sort(0, @>=, L3, L4),
|
||||
%% term_to_list(T2, L4).
|
||||
%% Tests:
|
||||
%% ?- simplify_term(2*y*z*x^3*x, X).
|
||||
%@ X = 2*(x^4*(y*z)).
|
||||
%@ X = z*(y*(x^4*2)).
|
||||
%% ?- simplify_term(2*y*z*23*x*y*x^3*x, X).
|
||||
%@ X = 46*(x^2*(x^3*(y^2*z))).
|
||||
%@ X = z*(y^2*(x^3*(x^2*46))).
|
||||
%@ X = [2, 23, x^1, x^3, y^1, z^1].
|
||||
%@ X = [46, x^4, y^1, z^1].
|
||||
|
||||
%% ?- list_to_term([x^1], X).
|
||||
%@ X = x.
|
||||
%% ?- list_to_term([x^1, y^2, z^3], X).
|
||||
%@ X = x*(y^2*z^3).
|
||||
%@ X = x*y^2.
|
||||
%% ?- list_to_term([x^1, y^3, 5], X).
|
||||
%@ X = x*(y^3*5).
|
||||
%@ X = x*(y^3*(5*1)) .
|
||||
|
||||
power_to_canon(T^N, T^N) :-
|
||||
polynomial_variable_p(T).
|
||||
power_to_canon(T, T^1) :-
|
||||
polynomial_variable_p(T).
|
||||
|
||||
%% ?- power_to_canon(x, X).
|
||||
%@ X = x^1.
|
||||
%% ?- power_to_canon(X, X^1).
|
||||
%@ X = x .
|
||||
%@ X = x.
|
||||
%% join_like_terms(+List, -List)
|
||||
%
|
||||
% Combine powers of the same variable in the given list
|
||||
%
|
||||
join_like_terms([P1, P2 | L], [B^N | L2]) :-
|
||||
power(P1),
|
||||
power(P2),
|
||||
B^N1 = P1,
|
||||
B^N2 = P2,
|
||||
%% B1 == B2, % Wasn't working before..?
|
||||
N is N1 + N2,
|
||||
join_like_terms(L, L2).
|
||||
join_like_terms([N1, N2 | L], [N | L2]) :-
|
||||
number(N1),
|
||||
number(N2),
|
||||
N is N1 * N2,
|
||||
join_like_terms(L, L2).
|
||||
join_like_terms([X | L], [X | L2]) :-
|
||||
join_like_terms(L, L2).
|
||||
join_like_terms([], []).
|
||||
%% Tests:
|
||||
%% ?- join_like_terms([2, 3, x^1, x^2], T).
|
||||
%@ T = [6, x^3].
|
||||
%@ T = [6, x^3].
|
||||
%% ?- join_like_terms([2, 3, x^1, x^2, y^1, y^6], T).
|
||||
%@ T = [6, x^3, y^7].
|
||||
%@ T = [6, x^3, y^7].
|
||||
|
||||
%% simplify_polynomial(+P:atom, -P2:atom) is det
|
||||
%
|
||||
% Simplifies a polynomial.
|
||||
%
|
||||
simplify_polynomial(M, M2) :-
|
||||
term_p(M), simplify_term(M, M2), !.
|
||||
%% Are we dealing with a valid term?
|
||||
is_term_valid_in_predicate(M, "simplify_polynomial(M, M2)"),
|
||||
%% If so, simplify it.
|
||||
simplify_term(M, M2),
|
||||
!.
|
||||
simplify_polynomial(P + 0, P) :-
|
||||
term_p(P), !.
|
||||
%% Ensure valid term
|
||||
is_term_valid_in_predicate(P, "simplify_polynomial(P + 0, P)"),
|
||||
!.
|
||||
simplify_polynomial(0 + P, P) :-
|
||||
term_p(P), !.
|
||||
%% Ensure valid term
|
||||
is_term_valid_in_predicate(P, "simplify_polynomial(0 + P, P)"),
|
||||
!.
|
||||
simplify_polynomial(P + M, P2 + M2) :-
|
||||
simplify_polynomial(P, P2), simplify_term(M, M2).
|
||||
simplify_polynomial(P, P2),
|
||||
simplify_term(M, M2).
|
||||
simplify_polynomial(P + M, P2 + M3) :-
|
||||
monomial_parts(M, _, XExp),
|
||||
delete_monomial(P, XExp, M2, P2), !,
|
||||
delete_monomial(P, XExp, M2, P2),
|
||||
!,
|
||||
add_monomial(M, M2, M3).
|
||||
simplify_polynomial(P + M, P2 + M2) :-
|
||||
simplify_polynomial(P, P2), simplify_term(M, M2).
|
||||
simplify_polynomial(P, P2),
|
||||
simplify_term(M, M2).
|
||||
%% Tests:
|
||||
%% TODO
|
||||
|
||||
%% ?- simplify_polynomial(1*x+(-1)*x, P).
|
||||
%% simplify_polynomial_list(+L1,-L3) is det
|
||||
%
|
||||
% Simplifies a list of polynomials
|
||||
%
|
||||
|
||||
simplify_polynomial_list([L1], L3) :-
|
||||
simplify_polynomial(L1, L2),
|
||||
L3 = [L2].
|
||||
simplify_polynomial_list([L1|L2],L3) :-
|
||||
simplify_polynomial(L1, P1),
|
||||
simplify_polynomial_list(L2, P2),
|
||||
L3 = [P1|P2],
|
||||
% There is nothing further to compute at this point
|
||||
!.
|
||||
|
||||
%% 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_p(X), !.
|
||||
power(X),
|
||||
!.
|
||||
monomial_parts(X^N, 1, X^N) :-
|
||||
power_p(X^N), !.
|
||||
power(X^N),
|
||||
!.
|
||||
monomial_parts(K * M, K, M) :-
|
||||
coeficient_p(K), !.
|
||||
number(K),
|
||||
!.
|
||||
monomial_parts(K, K, indep) :-
|
||||
coeficient_p(K), !.
|
||||
number(K),
|
||||
!.
|
||||
|
||||
|
||||
delete_monomial(M, X, M, 0) :-
|
||||
term_p(M),
|
||||
monomial_parts(M, _, X), !.
|
||||
term(M),
|
||||
monomial_parts(M, _, X),
|
||||
!.
|
||||
delete_monomial(M + M2, X, M, M2) :-
|
||||
term_p(M2), term_p(M),
|
||||
monomial_parts(M, _, X), !.
|
||||
term(M2),
|
||||
term(M),
|
||||
monomial_parts(M, _, X),
|
||||
!.
|
||||
delete_monomial(P + M, X, M, P) :-
|
||||
term_p(M), monomial_parts(M, _, X), !.
|
||||
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), !,
|
||||
number(K1),
|
||||
number(K2), !,
|
||||
K3 is K1 + K2.
|
||||
add_monomial(M1, M2, M3) :-
|
||||
monomial_parts(M1, K1, XExp),
|
||||
@ -217,15 +281,14 @@ p_aux_add_monomial(K, XExp, K * XExp).
|
||||
|
||||
closure_simplify_polynomial(P, P) :-
|
||||
simplify_polynomial(P, P2),
|
||||
P==P2, !.
|
||||
P==P2,
|
||||
!.
|
||||
closure_simplify_polynomial(P, P3) :-
|
||||
simplify_polynomial(P, P2),
|
||||
closure_simplify_polynomial(P2, P3), !.
|
||||
closure_simplify_polynomial(P2, P3),
|
||||
!.
|
||||
|
||||
list_to_term([N | NS], N * L) :-
|
||||
number(N),
|
||||
term_to_list(L, NS).
|
||||
|
||||
%% ?- simplify_polynomial(1*x+(-1)*x, P).
|
||||
%@ P = x+ -1*x .
|
||||
%@ P = x+ -1*x
|
||||
%@ Unknown action: q (h for help)
|
||||
%@ Action?
|
||||
%@ Unknown action: q (h for help)
|
||||
%@ Action? .
|
||||
|
||||
Reference in New Issue
Block a user