Extensive documentation writing and testing
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Hugo Sales
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polymani.pl
212
polymani.pl
@ -19,7 +19,8 @@
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* https://doi.org/10.1017/S1471068411000391 *
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*********************************************/
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/* Import the Constraint Logic Programming over Finite Domains library
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/*
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* Import the Constraint Logic Programming over Finite Domains library
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* Essentially, this library improves the way Prolog deals with integers,
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* allowing more predicates to be reversible.
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* For instance, number(N) is always false, which prevents the
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@ -38,6 +39,7 @@
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argument) and vice-versa.
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*/
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poly2list(P, L) :-
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is_term_valid_in_predicate(P, "poly2list"),
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polynomial_to_list(P, L),
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!.
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@ -46,6 +48,7 @@ poly2list(P, L) :-
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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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is_polynomial_list_valid_in_predicate(L, "simpoly_list"), %TODO IMPLEMENT
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simplify_polynomial_as_list(L, S),
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!.
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@ -54,6 +57,7 @@ simpoly_list(L, S) :-
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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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is_term_valid_in_predicate(P, "simpoly"),
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simplify_polynomial(P, S),
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!.
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@ -63,6 +67,8 @@ 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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is_term_valid_in_predicate(P1, "scalepoly"),
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is_term_valid_in_predicate(P2, "scalepoly"),
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scale_polynomial(P1, P2, S),
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!.
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@ -72,6 +78,8 @@ 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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is_term_valid_in_predicate(P1, "addpoly"),
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is_term_valid_in_predicate(P2, "addpoly"),
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add_polynomial(P1, P2, S),
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!.
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@ -86,7 +94,7 @@ addpoly(P1, P2, S) :-
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%
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polynomial_variable_list([x, y, z]).
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%% polynomial_variable(?X:atom) is det
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%% polynomial_variable(?X:atom) is semidet
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%
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% Returns true if X is a polynomial variable, false otherwise.
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%
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@ -135,20 +143,27 @@ power(X) :-
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%@ X = y ;
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%@ X = z.
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%% term(+N:atom) is det
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%% term(+N:atom) is semidet
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%
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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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(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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(
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% If N is non 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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(
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% If N is a free variable
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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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).
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term(X) :-
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power(X).
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term(L * R) :-
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@ -200,28 +215,37 @@ term(L * R) :-
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% The fail message reports which Term is invalid and in which
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% predicate the problem ocurred.
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%
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is_term_valid_in_predicate(T, F) :-
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(
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term(T)
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;
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write("Invalid term in "),
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write(F),
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write(": "),
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write(T),
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fail
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).
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is_term_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_term_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_term_valid_in_predicate(1, "Test").
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%@ true .
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%% ?- is_term_valid_in_predicate(a, "Test").
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%@ true.
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%% ?- is_term_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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%% polynomial(+M:atom) is det
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%% polynomial(+M:atom) is semidet
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%
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% Returns true if polynomial, false otherwise.
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%
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polynomial(M) :-
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%% A polynomial is either a term
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term(M).
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polynomial(L + R) :-
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%% Or a sum of terms
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polynomial(L),
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term(R).
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polynomial(L - R) :-
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%% Or a subtraction of terms
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polynomial(L),
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term(R).
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%% Tests:
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@ -233,17 +257,21 @@ polynomial(L + R) :-
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%@ true .
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%% ?- polynomial(2 + 3*x + 4*x*y^3).
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%@ true .
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%% ?- polynomial(2 - 3*x + 4*x*y^3).
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%@ true .
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%% ?- polynomial(a).
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%@ false.
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%% ?- polynomial(x^(-3)).
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%@ false.
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%% power_to_canon(+T:atom, -T^N:atom) is det
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%% power_to_canon(+T:atom, -T^N:atom) is semidet
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%
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% Returns a canon power term.
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%
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power_to_canon(T^N, T^N) :-
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polynomial_variable(T),
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% CLP(FD) operator to ensure N is different from 1,
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% in a reversible way
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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(X, x^(-3)).
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%@ X = x^ -3 .
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%% term_to_list(?T, ?List) is det
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%% term_to_list(?T, ?List) is semidet
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%
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% Converts a term to a list and vice versa.
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% A term is multiplication of a number or a power
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% and another term
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% Can verify if term and list are compatible.
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%
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term_to_list(L * N, [N | TS]) :-
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@ -285,19 +315,20 @@ term_to_list(P, [P2]) :-
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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(1*2*y*z*23*x*y*(-1), X).
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%@ X = [-1, y^1, x^1, 23, z^1, y^1, 2, 1] .
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%% ?- term_to_list(X, [-1]).
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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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%% ?- term_to_list(X, [- 1, x^1]).
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%@ false.
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%@ X = x* -1 .
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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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%@ X = x^4 .
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%% ?- term_to_list(X, [y^6, z^2, x^4]).
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%@ X = x^4*z^2*y^6 .
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%% ?- term_to_list(X, [y^6, z^2, x^4, -2]).
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%@ X = -2*x^4*z^2*y^6 .
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%% simplify_term(+Term_In:term, ?Term_Out:term) is det
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%
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@ -305,18 +336,27 @@ term_to_list(P, [P2]) :-
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%
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simplify_term(Term_In, Term_Out) :-
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term_to_list(Term_In, L),
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%% Sort the list of numbers and power to group them,
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%% simplifying the job of `join_similar_parts_of_term`
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sort(0, @=<, L, L2),
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(
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%% If there's a 0 in the list, then the whole term is 0
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member(0, L2),
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Term_Out = 0
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;
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%% Otherwise
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(
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%% If there's only one element, then the term was already simplified
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%% This is done so that the `exclude` following doesn't remove all ones
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length(L2, 1),
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Term_Out = Term_In
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;
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%% Remove all remaining ones
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exclude(==(1), L2, L3),
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join_similar_parts_of_term(L3, L4),
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sort(0, @>=, L4, L5),
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%% Reverse the list, since the following call gives the result in the
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%% reverse order otherwise
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reverse(L4, L5),
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term_to_list(Term_Out, L5)
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)
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),
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@ -334,30 +374,41 @@ simplify_term(Term_In, Term_Out) :-
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%% ?- simplify_term(0*y*z*x^3*x, X).
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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^2*x^3*y^2*z.
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%@ X = 42*x^5*y^2*z.
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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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%@ false.
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%% join_similar_parts_of_term(+List, -List)
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%% join_similar_parts_of_term(+List, -List) is det
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%
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% Combine powers of the same variable in the given list
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%
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join_similar_parts_of_term([P1, P2 | L], L2) :-
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%% If both symbols are powers
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power(P1),
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power(P2),
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%% Decompose them into their parts
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B^N1 = P1,
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B^N2 = P2,
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%% Sum the exponent
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N is N1 + N2,
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join_similar_parts_of_term([B^N | L], L2).
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join_similar_parts_of_term([B^N | L], L2),
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% First result is always the most simplified form.
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!.
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join_similar_parts_of_term([N1, N2 | L], L2) :-
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%% If they are both numbers
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number(N1),
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number(N2),
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%% Multiply them
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N is N1 * N2,
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join_similar_parts_of_term([N | L], L2).
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join_similar_parts_of_term([N | L], L2),
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% First result is always the most simplified form.
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!.
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join_similar_parts_of_term([X | L], [X | L2]) :-
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join_similar_parts_of_term(L, L2).
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join_similar_parts_of_term(L, L2),
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% First result is always the most simplified form.
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!.
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join_similar_parts_of_term([], []).
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%% Tests:
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%% ?- join_similar_parts_of_term([3], T).
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@ -365,22 +416,25 @@ join_similar_parts_of_term([], []).
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%% ?- join_similar_parts_of_term([x^2], T).
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%@ T = [x^2].
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%% ?- join_similar_parts_of_term([x^1, x^1, x^1, x^1], T).
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%@ T = [x^4] .
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%@ T = [x^4].
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%% ?- join_similar_parts_of_term([2, 3, x^1, x^2], T).
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%@ T = [6, x^3] .
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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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%@ T = [6, x^3, y^7].
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%% simplify_polynomial(+P:atom, -P2:atom) is det
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%
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% Simplifies a polynomial.
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%
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simplify_polynomial(0, 0) :-
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% 0 is already fully simplified and is an
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% exception to the following algorithm
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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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simplify_polynomial_as_list(L, L2),
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list_to_polynomial(L2, P2),
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%% The first result is the most simplified one
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!.
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%% Tests:
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%% ?- simplify_polynomial(1, X).
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@ -403,11 +457,45 @@ simplify_polynomial(P, P2) :-
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%@ X = 6*x^3.
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%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*4 + z, X).
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%@ X = 5*x^3+4*x^2+z.
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%% ?- simplify_polynomial(x^2*x + 3*x^3 - x^3 - x*x*4 + z, X).
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%@ X = 3*x^3-4*x^2+z.
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%% ?- simplify_polynomial(x + 1 + x, X).
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%@ X = 2*x+1.
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%% ?- simplify_polynomial(x + 1 + x + 1 + x + 1 + x, X).
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%@ X = 4*x+3.
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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_as_list(L, L11) :-
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%% Convert each term to a list
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maplist(term_to_list, L, L2),
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%% Sort each sublist; done so the next
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%% sort gives the correct results
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maplist(sort(0, @>=), L2, L3),
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%% Sort the outer list
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sort(0, @>=, L3, L4),
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%% For each of the parts of the terms, join them
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maplist(join_similar_parts_of_term, L4, L5),
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%% Sort each of the sublists
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%% Done so the next call simplifies has less work
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maplist(sort(0, @=<), L5, L6),
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join_similar_terms(L6, L7),
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%% Reverse each sublist, because the next call
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%% reverses the result
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maplist(reverse, L7, L8),
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maplist(term_to_list, L9, L8),
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%% Delete any 0 from the list
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delete(L9, 0, L10),
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%% Sort list converting back gives the result in the correct order
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sort(0, @=<, L10, 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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%% ?- 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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%% join_similar_terms(+P:ListList, -P2:ListList) is det
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%
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% Joins similar sublists representing terms by using
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@ -449,6 +537,13 @@ term_to_canon([T | TS], [1, T | TS]) :-
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not(number(T)),
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%% Give only first result. Red cut
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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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!.
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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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@ -467,9 +562,13 @@ term_to_canon(L, L).
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% Requires the list of terms to be simplified.
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%
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add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
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%% Convert each term to a canon form. This ensures they
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%% have a number in front, so it can be added
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term_to_canon([NL | TL], [NL2 | TL2]),
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term_to_canon([NR | TR], [NR2 | TR2]),
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%% If they rest of the term is the same
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TL2 == TR2,
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%% Add the coeficients
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N2 is NL2 + NR2.
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%% Tests
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%% ?- add_terms([1], [1], R).
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@ -481,22 +580,6 @@ 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_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_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) is det
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%
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% Converts a polynomial in a list.
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@ -529,7 +612,7 @@ polynomial_to_list(T, [T]) :-
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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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|
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%% list_to_polynomial(+P:polynomial, -L:List)
|
||||
%% list_to_polynomial(+P:polynomial, -L:List) is det
|
||||
%
|
||||
% Converts a list in a polynomial.
|
||||
%
|
||||
@ -555,7 +638,8 @@ list_to_polynomial([T1|T2], P) :-
|
||||
list_to_polynomial(T, P) :-
|
||||
P = T.
|
||||
%% Tests:
|
||||
%% TODO
|
||||
%% ?- list_to_polynomial([1, x, x^2], P).
|
||||
%@ P = x^2+x+1.
|
||||
|
||||
%% negate_term(T, T2) is det
|
||||
%
|
||||
@ -563,12 +647,16 @@ list_to_polynomial(T, P) :-
|
||||
%
|
||||
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,
|
||||
%% (-)/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_list(T2, L4),
|
||||
!.
|
||||
@ -584,13 +672,17 @@ negate_term(T, T2) :-
|
||||
|
||||
%% scale_polynomial(+P:polynomial,+C:constant,-S:polynomial) is det
|
||||
%
|
||||
% Scales a polynomial with a constant
|
||||
% Multiplies a polynomial by a scalar
|
||||
%
|
||||
scale_polynomial(P, C, S) :-
|
||||
polynomial_to_list(P, L),
|
||||
%% Convert each term to a list
|
||||
maplist(term_to_list, L, L2),
|
||||
%% Append C to the start of each sublist
|
||||
maplist(cons(C), L2, L3),
|
||||
%% Convert back
|
||||
maplist(term_to_list, L4, L3),
|
||||
%% Simplify the resulting polynomial
|
||||
simplify_polynomial_as_list(L4, L5),
|
||||
list_to_polynomial(L5, S),
|
||||
!.
|
||||
@ -609,10 +701,14 @@ cons(C, L, [C | L]).
|
||||
% S = P1 + P2
|
||||
%
|
||||
add_polynomial(P1, P2, S) :-
|
||||
%% Convert both polynomials to lists
|
||||
polynomial_to_list(P1, L1),
|
||||
polynomial_to_list(P2, L2),
|
||||
%% Join them
|
||||
append(L1, L2, L3),
|
||||
%% Simplify the resulting polynomial
|
||||
simplify_polynomial_as_list(L3, L4),
|
||||
%% Convert back
|
||||
list_to_polynomial(L4, S),
|
||||
!.
|
||||
%% Tests:
|
||||
|
||||
Reference in New Issue
Block a user