Merge branch 'master' into add_polynomial
This commit is contained in:
Diogo Cordeiro
GitHub
commit
de103aee27
421
polimani.pl
421
polimani.pl
|
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@ -1,15 +1,81 @@
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%% -*- mode: prolog-*-
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%% vim: set softtabstop=4 shiftwidth=4 tabstop=4 expandtab:
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%% Follows 'Coding guidelines for Prolog' - Theory and Practice of Logic Programming
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%% https://doi.org/10.1017/S1471068411000391
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%% Import the Constraint Logic Programming over Finite Domains lybrary
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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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*
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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 lybrary
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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 argu-
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ment) and vice-versa.
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*/
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poly2list(P, L) :-
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polynomial_to_list(P, L).
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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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simplify_polynomial_list(L, S).
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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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simplify_polynomial(P, S).
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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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scale_polynomial(P1, P2, S).
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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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add_polynomial(P1, P2, S).
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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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@ -84,6 +150,8 @@ term(L * R) :-
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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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@ -178,8 +246,17 @@ term_to_list(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(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(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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@ -203,7 +280,7 @@ simplify_term(Term_In, Term_Out) :-
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Term_Out = Term_In
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);
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exclude(==(1), L2, L3),
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join_like_terms(L3, L4),
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join_similar_parts_of_term(L3, L4),
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sort(0, @>=, L4, L5),
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term_to_list(Term_Out, L5)
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),
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@ -227,112 +304,218 @@ simplify_term(Term_In, Term_Out) :-
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%% ?- simplify_term(x^(-3), X).
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%@ false.
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%% join_like_terms(+List, -List)
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%% join_similar_parts_of_term(+List, -List)
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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_like_terms([P1, P2 | L], [B^N | L2]) :-
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join_similar_parts_of_term([P1, P2 | L], L2) :-
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power(P1),
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power(P2),
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B^N1 = P1,
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B^N2 = P2,
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N is N1 + N2,
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join_like_terms(L, L2).
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join_like_terms([N1, N2 | L], [N | L2]) :-
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join_similar_parts_of_term([B^N | L], L2).
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join_similar_parts_of_term([N1, N2 | L], L2) :-
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number(N1),
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number(N2),
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N is N1 * N2,
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join_like_terms(L, L2).
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join_like_terms([X | L], [X | L2]) :-
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join_like_terms(L, L2).
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join_like_terms([], []).
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join_similar_parts_of_term([N | L], L2).
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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([], []).
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%% Tests:
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%% ?- join_like_terms([2, 3, x^1, x^2], T).
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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_like_terms([2, 3, x^1, x^2, y^1, y^6], T).
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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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% TODO: not everything is a +, there are -
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%
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simplify_polynomial(M, M2) :-
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%% Are we dealing with a valid term?
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%is_term_valid_in_predicate(M, "simplify_polynomial(M, M2)"),
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%% term(M),
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%% If so, simplify it.
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simplify_term(M, M2),
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simplify_polynomial(0, 0) :-
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!.
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simplify_polynomial(P + 0, P) :-
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%% Ensure valid term
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%is_term_valid_in_predicate(P, "simplify_polynomial(P + 0, P)"),
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term(P),
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simplify_polynomial(P, P2) :-
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polynomial_to_list(P, L),
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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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list_to_polynomial(L11, P2),
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!.
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simplify_polynomial(0 + P, P) :-
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%% Ensure valid term
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%is_term_valid_in_predicate(P, "simplify_polynomial(0 + P, P)"),
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term(P),
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!.
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simplify_polynomial(P + M, P2 + M2) :-
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simplify_polynomial(P, P2),
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simplify_term(M, M2).
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simplify_polynomial(P + M, P2 + M3) :-
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monomial_parts(M, _, XExp),
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delete_monomial(P, XExp, M2, P2),
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!,
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add_monomial(M, M2, M3).
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simplify_polynomial(P + M, P2 + M2) :-
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simplify_polynomial(P, P2),
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simplify_term(M, M2).
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%% Tests:
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%% ?- simplify_polynomial(1, X).
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%@ false.
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%@ false.
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%@ Invalid term in simplify_polynomial(M, M2): 1
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%@ false.
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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 + 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*1.
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%% simplify_polynomial_list(+L1,-L3) is det
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%% join_similar_terms(+P:ListList, -P2:ListList) is det
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%
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% Simplifies a list of polynomials
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% Joins similar sublists representing terms by using
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% `add_terms` to check if they can be merged and perform
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% the addition. Requires the list of list be sorted with
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% `maplist(sort(0, @>=), L, L2),
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% sort(0, @>=, L2, L3)`
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% and that the sublists to be sorted with
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% `sort(0, @=<)` since that is inherited from `add_terms`
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%
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simplify_polynomial_list([L1], L3) :-
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simplify_polynomial(L1, L2),
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L3 = [L2].
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simplify_polynomial_list([L1|L2],L3) :-
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simplify_polynomial(L1, P1),
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simplify_polynomial_list(L2, P2),
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L3 = [P1|P2],
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% There is nothing further to compute at this point
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join_similar_terms([TL, TR | L], L2) :-
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%% Check if terms can be added and add them
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add_terms(TL, TR, T2),
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%% Recurse, accumulation on the first element
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join_similar_terms([T2 | L], L2),
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%% Give only first result. Red cut
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!.
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join_similar_terms([X | L], [X | L2]) :-
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%% If a pair of elements can't be added, skip one
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%% and recurse
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join_similar_terms(L, L2),
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%% Give only first result. Red cut
|
||||
!.
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join_similar_terms([], []).
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%% Tests:
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%% ?- join_similar_terms([[2, x^3], [3, x^3], [x^3]], L).
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%@ L = [[6, x^3]].
|
||||
|
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%% term_to_canon(+T:List, -T2:List) is det
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||||
%
|
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% 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).
|
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%% 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,
|
||||
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].
|
||||
|
||||
%% simplify_polynomial_list(+L:list, -S:list) is det
|
||||
%
|
||||
% Simplifies a polynomial represented as a list
|
||||
%
|
||||
simplify_polynomial_list(L, S) :-
|
||||
polynomial_to_list(P1, L),
|
||||
simplify_polynomial(P1, P2),
|
||||
polynomial_to_list(P2, S).
|
||||
|
||||
%% polynomial_to_list(+P:polynomial, -L:List)
|
||||
%
|
||||
% Converts a polynomial in a list.
|
||||
% TODO: not everything is a +, there are -
|
||||
%
|
||||
polynomial_to_list(T1 + T2, L) :-
|
||||
polynomial_to_list(T1, L1),
|
||||
L = [T2|L1],
|
||||
% The others computations are semantically meaningless
|
||||
!.
|
||||
polynomial_to_list(P, L) :-
|
||||
L = [P].
|
||||
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*x^2+5+y*2, S).
|
||||
%@S = [y*2, 5, 2*x^2].
|
||||
%% ?- 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(P, [2]).
|
||||
%@ P = 2 .
|
||||
%% ?- polynomial_to_list(P, [x]).
|
||||
%@ P = x .
|
||||
%% ?- 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.
|
||||
% TODO: not everything is a +, there are -
|
||||
%
|
||||
list_to_polynomial([T1|T2], P) :-
|
||||
list_to_polynomial(T2, L1),
|
||||
(
|
||||
not(L1 = []),
|
||||
P = L1+T1
|
||||
(
|
||||
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
|
||||
),
|
||||
|
|
@ -343,6 +526,31 @@ list_to_polynomial(T, P) :-
|
|||
%% 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
|
||||
|
|
@ -370,11 +578,9 @@ scale_polynomial(P, C, S) :-
|
|||
polynomial_to_list(P, L),
|
||||
maplist(append_two_atoms_with_star(C), L, L2),
|
||||
list_to_polynomial(L2, S).
|
||||
%simplify_polynomial(S1, S).
|
||||
%% Tests:
|
||||
%% ?- scale_polynomial(3*x^2, 2, S).
|
||||
%@ S = 2*3*x^2.
|
||||
%@ S = 2*(3*x^2).
|
||||
|
||||
%% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det
|
||||
%
|
||||
|
|
@ -389,70 +595,3 @@ add_polynomial(P1, P2, S) :-
|
|||
simplify_polynomial(P, S).
|
||||
%% Tests:
|
||||
%
|
||||
|
||||
%% 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),
|
||||
!.
|
||||
|
||||
list_to_term([N | NS], N * L) :-
|
||||
number(N),
|
||||
term_to_list(L, NS).
|
||||
|
||||
|
|
|
|||
Reference in New Issue