736 lines
19 KiB
Prolog
736 lines
19 KiB
Prolog
%% -*- mode: prolog-*-
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%% vim: set softtabstop=4 shiftwidth=4 tabstop=4 expandtab:
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/**
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*
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* polimani.pl
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*
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* Assignment 1 - Polynomial Manipulator
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* Programming in Logic - DCC-FCUP
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*
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* Diogo Peralta Cordeiro
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* up201705417@fc.up.pt
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*
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* Hugo David Cordeiro Sales
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* up201704178@fc.up.pt
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*
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*********************************************
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* Follows 'Coding guidelines for Prolog' *
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* https://doi.org/10.1017/S1471068411000391 *
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*********************************************/
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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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* reversing of a predicate.
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*/
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:- use_module(library(clpfd)).
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/*******************************
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* USER INTERFACE *
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*******************************/
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/*
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poly2list/2 transforms a list representing a polynomial (second
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argument) into a polynomial represented as an expression (first
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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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/*
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simpolylist/2 simplifies a polynomial represented as a list into
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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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/*
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simpoly/2 simplifies a polynomial represented as an expression
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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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/*
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scalepoly/3 multiplies a polynomial represented as an expression by a scalar
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resulting in a second polynomial. The two first arguments are assumed to
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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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/*
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addpoly/3 adds two polynomials as expressions resulting in a
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third one. The two first arguments are assumed to be ground.
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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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/*******************************
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* BACKEND *
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*******************************/
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%% polynomial_variable_list(-List) is det
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%
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% List of possible polynomial variables
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%
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polynomial_variable_list([x, y, z]).
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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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polynomial_variable(X) :-
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polynomial_variable_list(V),
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member(X, V).
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%% Tests:
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%% ?- polynomial_variable(x).
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%@ true .
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%% ?- polynomial_variable(a).
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%@ false.
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%% power(+X:atom) is semidet
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%
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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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power(X) :-
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polynomial_variable(X).
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%% Tests:
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%% ?- power(x).
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%@ true .
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%% ?- power(a).
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%@ false.
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%% ?- power(x^1).
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%@ true .
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%% ?- power(x^3).
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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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%@ 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 ;
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%@ X = y ;
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%@ X = z.
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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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(
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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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% 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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term(L),
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term(R).
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%% Tests:
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%% ?- term(2*x^3).
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%@ true .
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%% ?- term(x^(-3)).
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%@ false.
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%% ?- term(a).
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%@ false.
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%% ?- term(-1*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).
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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 = 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_term_valid_in_predicate(+T, +F) is det
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%
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% Returns true if valid Term, fails with UI message otherwise.
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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(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*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 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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%% ?- polynomial(x).
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%@ true .
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%% ?- polynomial(x^3).
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%@ true .
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%% ?- polynomial(3*x^7).
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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 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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%% 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^1).
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%@ X = x .
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%% ?- power_to_canon(X, x^4).
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%@ X = x^4 .
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%% ?- power_to_canon(X, a^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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%% 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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number(N),
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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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%% Tests:
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%% ?- term_to_list(1, X).
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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(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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%@ 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, [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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% Simplifies a given term.
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% This function can also be be used to verify if
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% a term is simplified.
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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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%% 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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% First result is always the most simplified form.
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!.
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%% Tests:
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%% ?- simplify_term(1, X).
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%@ X = 1.
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%% ?- simplify_term(x, X).
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%@ X = x.
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%% ?- simplify_term(2*y*z*x^3*x, X).
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%@ X = 2*x^4*y*z.
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%% ?- simplify_term(1*y*z*x^3*x, X).
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%@ X = x^4*y*z.
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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^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) 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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% 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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% 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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% 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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%@ T = [3].
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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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%% ?- join_similar_parts_of_term([2, 3, x^1, x^2], T).
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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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%% 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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%@ X = 1.
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%% ?- simplify_polynomial(0, X).
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%@ X = 0.
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%% ?- simplify_polynomial(x, X).
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%@ X = x.
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%% ?- simplify_polynomial(x*x, X).
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%@ X = x^2.
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%% ?- simplify_polynomial(2 + 2, X).
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%@ X = 2*2.
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%% ?- simplify_polynomial(x + x, X).
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%@ X = 2*x.
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%% ?- simplify_polynomial(0 + x*x, X).
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%@ X = x^2.
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%% ?- simplify_polynomial(x^2*x + 3*x^3, X).
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%@ X = 4*x^3.
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%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*x, X).
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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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|
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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),
|
|
%% Reverse each sublist, because the next call
|
|
%% reverses the result
|
|
maplist(reverse, L7, L8),
|
|
maplist(term_to_list, L9, L8),
|
|
%% Delete any 0 from the list
|
|
delete(L9, 0, L10),
|
|
%% Sort list converting back gives the result in the correct order
|
|
sort(0, @=<, L10, L11).
|
|
%% Tests:
|
|
%% ?- 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] .
|
|
%% ?- 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] .
|
|
|
|
%% 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
|
|
!.
|
|
join_similar_terms([], []).
|
|
%% Tests:
|
|
%% ?- join_similar_terms([[2, x^3], [3, x^3], [x^3]], L).
|
|
%@ L = [[6, x^3]].
|
|
|
|
%% 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([T | TS], [N, 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)),
|
|
N is -1,
|
|
%% 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]) :-
|
|
%% Convert each term to a canon form. This ensures they
|
|
%% have a number in front, so it can be added
|
|
term_to_canon([NL | TL], [NL2 | TL2]),
|
|
term_to_canon([NR | TR], [NR2 | TR2]),
|
|
%% If they rest of the term is the same
|
|
TL2 == TR2,
|
|
%% Add the coeficients
|
|
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].
|
|
|
|
%% polynomial_to_list(+P:polynomial, -L:List) is det
|
|
%
|
|
% Converts a polynomial in a list.
|
|
%
|
|
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),
|
|
!.
|
|
polynomial_to_list(T, [T]) :-
|
|
term(T),
|
|
!.
|
|
%% Tests:
|
|
%% ?- polynomial_to_list(2, S).
|
|
%@ S = [2].
|
|
%% ?- polynomial_to_list(x^2, S).
|
|
%@ S = [x^2].
|
|
%% ?- polynomial_to_list(x^2 + x^2, S).
|
|
%@ S = [x^2, x^2].
|
|
%% ?- polynomial_to_list(2*x^2+5+y*2, S).
|
|
%@ S = [y*2, 5, 2*x^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(2*x^2+3*x+5*x^17-7*x^21+3*x^3-23*x^4+25*x^5-4.3, S).
|
|
%@ S = [-4.3, 25*x^5, -23*x^4, 3*x^3, -7*x^21, 5*x^17, 3*x, 2* ... ^ ...].
|
|
|
|
%% list_to_polynomial(+L:List, -P:Polynomial) is det
|
|
%
|
|
% Converts a list in a polynomial.
|
|
% An empty list will return false.
|
|
%
|
|
list_to_polynomial([T1|T2], P) :-
|
|
% Start recursive calls until we are in the
|
|
% end of the list. We know that the `-` will
|
|
% always be at the left of a term.
|
|
list_to_polynomial(T2, L1),
|
|
(
|
|
% If this is a negative term
|
|
term_string(T1, S1),
|
|
string_chars(S1, [First|_]),
|
|
First = -,
|
|
% Concat them
|
|
term_string(L1, S2),
|
|
string_concat(S2,S1,S3),
|
|
term_string(P, S3)
|
|
;
|
|
% Otherwise sum them
|
|
P = L1+T1
|
|
),
|
|
% The others computations are semantically meaningless
|
|
!.
|
|
list_to_polynomial([T], T).
|
|
%% Tests:
|
|
%% ?- list_to_polynomial([1, x, x^2], P).
|
|
%@ P = x^2+x+1.
|
|
%% ?- list_to_polynomial([-1, -x, -x^2], P).
|
|
%@ P = -x^2-x-1.
|
|
%% ?- list_to_polynomial([1, -x, x^2], P).
|
|
%@ P = x^2-x+1.
|
|
%% ?- list_to_polynomial([x^2, x, 1], P).
|
|
%@ P = 1+x+x^2.
|
|
%% ?- list_to_polynomial([a,-e], P).
|
|
%@ P = -e+a.
|
|
%% ?- list_to_polynomial([], P).
|
|
%@ false.
|
|
%% ?- list_to_polynomial([a], P).
|
|
%@ P = a.
|
|
|
|
%% 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 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),
|
|
!.
|
|
%% 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.
|
|
|
|
%% scale_polynomial(+P:Polynomial,+C:Constant,-S:Polynomial) is det
|
|
%
|
|
% 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),
|
|
!.
|
|
%% Tests:
|
|
%% ?- scale_polynomial(3*x^2, 2, S).
|
|
%@ S = 6*x^2.
|
|
|
|
%% cons(+C:atom, +L:List, -L2:List) is det
|
|
%
|
|
% Add an atom C to the head of a list L.
|
|
%
|
|
cons(C, L, [C | L]).
|
|
%% Tests:
|
|
%% It just trivially works.
|
|
|
|
%% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det
|
|
%
|
|
% 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:
|
|
%% ?- add_polynomial(2, 2, S).
|
|
%@ S = 4.
|
|
%% ?- add_polynomial(x, x, S).
|
|
%@ S = 2*x.
|
|
%% ?- add_polynomial(2*x+5*z, 2*z+6*x, S).
|
|
%@ S = 8*x+7*z.
|