%% -*- Mode: Prolog-*- %% vim: set softtabstop=4 shiftwidth=4 tabstop=4 expandtab: /** * * polimani.pl * * Assignment 1 - Polynomial Manipulator * Programming in Logic - DCC-FCUP * * Diogo Peralta Cordeiro * up201705417@fc.up.pt * * Hugo David Cordeiro Sales * up201704178@fc.up.pt * ********************************************* * Follows 'Coding guidelines for Prolog' * * https://doi.org/10.1017/S1471068411000391 * *********************************************/ /* * Import the Constraint Logic Programming over Finite Domains library * Essentially, this library improves the way Prolog deals with integers, * allowing more predicates to be reversible. * For instance, number(N) is always false, which prevents the * reversing of a predicate. */ :- use_module(library(clpfd)). /* * Import Constraint Logic Programming for Reals library, which is somewhat * similar to clpfd, but for real numbers */ :- use_module(library(clpr)). /******************************* * NLP * *******************************/ %% polyplay() is det % % Interactive prompt for the NLP Interface % polyplay :- %% Replace the prompt and save the old one prompt(OldPrompt, '> '), %% Read a line as codes, from the 'user_input' stream read_line_to_codes(user_input, InCodes), %% Restore old prompt prompt(_, OldPrompt), %% Split the input at spaces and ignore \r and \t split_string(InCodes, " ", "\r\t", LS), %% Convert each set of codes into a term or atom, as appropriate maplist(name, LA, LS), ( %% If we read a 'bye', terminate LA == [bye], write("See ya"), nl, ! ; ( %% Parse the input into a tree parse_input(TIn, LA, NC), ( %% If the tree is empty, it means nothing was understood TIn == void, writeln("I didn't understand what you want."), writeln(NC) ; ( %% If there is unconsumed input, it means there was a syntatic error NC \== [], write("Syntax error in token: "), %% Take the head of the list cons(H, _, NC), write(H), nl ; ( %% If the debug_print flag is true, print some extract debug info debug_print(true), write(LA), nl, write(TIn), nl ; %% Otherwise, process the parse tree and execute the commands within process_input(TIn) ) ) ) ; %% Parsing failed writeln("I didn't understand what you want.") ), %% Go back to the beginning polyplay ), !. %% Flag which determines whether to print the parsed input or to process it debug_print(false). %% process_input(+tree) is determines % % Execute the commands from the parse tree % process_input(command(CL, TCR)) :- %% Process first command do_process_input(CL), %% If there's a tree on the right TCR \== void, %% recurse process_input(TCR). process_input(command(CL, void)) :- %% Process only command left do_process_input(CL). %% do_process_input(+tree) is det % % Process a single command from the input % Takes, as the only argument, the tree representing % the work to be done % do_process_input(help_menu) :- writeln("Please allow me to introduce myself"), writeln("I'm a man[ual] of wealth and taste"), writeln("I've been around for a long, long semester"), writeln("Saved many a man's soul and faith"), writeln("Pleased to meet you"), writeln("Hope you guess my name"), writeln("But what's puzzling you"), writeln("Is the nature of my game"), nl, writeln("I'm a Polynomial Manipulator and the following commands are available:"), writeln("=> Show - Allows to print a polynomial mathematically"), writeln("=> Multiply - Allows to make multiplications"), writeln("=> Simplify - Allows to simplify a given polynomial"), writeln("=> Add - Allows to make sums"), writeln("=> bye - Hello darkness, my old friend"), writeln("Use 'tell me about {command}' to learn more about a specific command"), nl, writeln("Furthermore, I'm capable of memorizing polynomials during runtime. To learn more on that, type: tell me about storage"). do_process_input(help(show)) :- writeln("It's almost an echo of what you said, but a mathy one."), writeln("Some example queries:"), writeln(">"). do_process_input(help(multiply)) :- writeln("Multiplies a polynomial represented as an expression by a scalar resulting in a second polynomial. The two first arguments are assumed to be ground. The polynomial resulting from the sum is in simplified form."), writeln("Some example queries:"), writeln(">"). do_process_input(help(simplify)) :- writeln("Simplifies a polynomial represented as an expression as another polynomial as an expression."), writeln("Some example queries:"), writeln(">"). do_process_input(help(add)) :- writeln("Adds two polynomials as expressions resulting in a third one. The two first arguments are assumed to be ground. The polynomial resulting from the sum is in simplified form."), writeln("Some example queries:"), writeln(">"). do_process_input(help(storage)) :- writeln("Polynomials, pressed between the entries of my storage"), writeln("Polynomials, simplified through the ages just like predicates"), writeln("Quiet goal come floating down"), writeln("And settle softly to the ground"), writeln("Like golden atom leaves around my root"), writeln("I touched them and they burst apart with sweet polynomials"), writeln("Sweet polynomials"), nl, writeln("Storage manipulation is better illustrated with examples. Some example queries:"), writeln("Asking me to memorize something:"), writeln(">"), nl, writeln("Asking me to forget something:"), writeln(">"), nl, writeln("Some examples of memory resources usage:"), writeln(">"). do_process_input(help(bye)) :- writeln("There must be some kind of way outta here"), writeln("Said the joker to the thief"), writeln("There's too much confusion"), writeln("I can't get no relief"). do_process_input(show_stored_polynomials) :- %% If the command is 'show_stored_polynomials' %% Store in D the list of all results of %% polynomial_store, which is a dynamic predicate findall(nm(X,Y), polynomial_store(X,Y), D), %% Print the list of stored variables print_all_stored_variables(D). do_process_input(show(store(P), T)) :- %% If the command was to store and show %% Delegate the work of storing do_process_input(store(P, T)), %% Show the variable and the polynomial. Delegate do_process_input(show(P, T)). do_process_input(show(load(P), void)) :- %% Make sure there's a variable P \== void, ( %% Check if the variable is stored polynomial_store(P, T), %% Show the variable and the polynomial. Delegate do_process_input(show(P, T)) ; writeln("Variable not stored") ). do_process_input(show(void, T)) :- %% Make sure there's a tree T \== void, %% Convert it to a flat polynomial polynomial_tree_to_polynomial(T, Pl), writeln(Pl). do_process_input(show(P, T)) :- %% Make sure the arguments are in the right format and not one %% that should be handled by other clauses P \== void, P \== store(_), P \== load(_), T \== void, %% Write out the variable and the normal %% representation of the polynomial write(P), write(" = "), %% Convert the input tree to a flat polynomial, to print polynomial_tree_to_polynomial(T, Pl), writeln(Pl). do_process_input(store_simplified(V,PTNS)) :- polynomial_tree_to_polynomial(PTNS, PNS), simpoly(PNS,P), assertz(polynomial_store(V, P)), write(V), write(" = "), write(P), nl. do_process_input(store(P, T)) :- ( %% If there is a polynomial stored with the same name polynomial_store(P, _), %% Delete all occurences of it retractall(polynomial_store(P, _)) ; %% Otherwise, move forward and don't do anything special true ), !, %% Dynamically add to the end of the predicate, effectively storing it assertz(polynomial_store(P, T)). do_process_input(forget(P)) :- %% Remove all stored predicates with this variable retractall(polynomial_store(P, _)). do_process_input(simplify(PT)) :- %% Convert the polynomial to it's flat representation polynomial_tree_to_polynomial(PT, P), %% Use simpoly from the UI layer to simplify, so it %% gives nice error messages simpoly(P, SP), writeln(SP). do_process_input(store_multiplication(TN, PT, V)) :- polynomial_tree_to_polynomial(TN, N), polynomial_tree_to_polynomial(PT, P), ( not(number(N)), scalepoly(N, P, P2) ; number(N), scalepoly(P, N, P2) ), simpoly(P2, SP), assertz(polynomial_store(V, SP)), write(V), write(" = "), write(SP), nl. do_process_input(multiply(TN, PT)) :- %% To multiply, assume the left is a number %% Flatten both polynomial_tree_to_polynomial(TN, N), polynomial_tree_to_polynomial(PT, P), %% Use function from UI layer ( not(number(N)), scalepoly(N, P, P2) ; number(N), scalepoly(P, N, P2) ), simpoly(P2, SP), writeln(SP). %% print_all_stored_variables % % Prints the stored variables, given the list % print_all_stored_variables([nm(X,T) | TS]) :- %% Print write(X), write(" = "), polynomial_tree_to_polynomial(T, P), writeln(P), %% Recurse on the right print_all_stored_variables(TS). print_all_stored_variables([]). %% polynomial_tree_to_polynomial(+tree, -polynomial) is det % % Flatten a polynomail tree into a simple polynomial % polynomial_tree_to_polynomial(op(Op, TL, TR), P) :- %% If it matched on the version with a node, don't go back !, %% Recurse on the left and right polynomial_tree_to_polynomial(TL, PL), polynomial_tree_to_polynomial(TR, PR), %% Convert the results of the recursion to atoms term_to_atom(PL, TermL), term_to_atom(PR, TermR), %% Concat the parts atom_concat(TermL, Op, Temp), atom_concat(Temp, TermR, PA), %% Convert back to terms term_to_atom(P, PA). polynomial_tree_to_polynomial(load(P), Pl) :- %% If there's a load tag, don't go back !, %% Retrieve the polynomial from the store polynomial_store(P, TP), %% Recurse as if there was a normal tree here polynomial_tree_to_polynomial(TP, Pl). %% If we get here, it means we didn't match any of the previous %% clauses, so the tree is already flat polynomial_tree_to_polynomial(T, T). %% special_word_number(?W:Atom, ?D:Int) is det % % Definition of a Alphabetical and Numerical relation % The third argument refers to different types of precedence: % - f means a single unit digit, which doesn't % combine on the right, but can on the left % - g means a number which doesn't combine left or right % - fy means a number which can optionally combine on the right % - xfy means a number which requires a number on the left and % an optional one on the right % special_word_number(zero, 0, f). special_word_number(a, 1, f). special_word_number(one, 1, f). special_word_number(two, 2, f). special_word_number(three, 3, f). special_word_number(four, 4, f). special_word_number(five, 5, f). special_word_number(six, 6, f). special_word_number(seven, 7, f). special_word_number(eight, 8, f). special_word_number(nine, 9, f). special_word_number(ten, 10, g). special_word_number(eleven, 11, g). special_word_number(twelve, 12, g). special_word_number(thirteen, 13, g). special_word_number(fourteen, 14, g). special_word_number(fifteen, 15, g). special_word_number(sixteen, 16, g). special_word_number(seventeen, 17, g). special_word_number(eighteen, 18, g). special_word_number(nineteen, 19, g). special_word_number(twenty, 20, fy). special_word_number(thirty, 30, fy). special_word_number(forty, 40, fy). special_word_number(fifty, 50, fy). special_word_number(sixty, 60, fy). special_word_number(seventy, 70, fy). special_word_number(eighty, 80, fy). special_word_number(ninety, 90, fy). special_word_number(hundred, 100, xfy). special_word_number(thousand, 1000, xfy). special_word_number(million, 1000000, xfy). %% special_word_number(half, 0.5, xf). %% special_word_number(third, 0.33333, xf). %% special_word_number(quarter, 0.25, xf). %% parse_number_explicit(+precedence, +tree_left, -tree, %% +stream, -not_consumed) is det % % Use the precedence of the last number and the tree % on the left to create the tree on the right, parsing % the input stream. % % You probably want to call this with void in the first % two arguments. They are for internal use % parse_number_explicit(void, void, T, [WN | In], NC) :- %% Entry point %% Convert a word to a number with precedence f, g, or fy special_word_number(WN, N, P), member(P, [f, g, fy]), !, %% Recurse with the previous precedence %% and tree as arguments. The same in the other clauses parse_number_explicit(P, N, T, In, NC). parse_number_explicit(fy, NL, T, [WN | In], NC) :- special_word_number(WN, N, f), !, %% Add them on the left tree and recurse parse_number_explicit(f, op(+, NL, N), T, In, NC). parse_number_explicit(xfy, TL, T, [WN | In], NC) :- TL \= void, special_word_number(WN, N, P), member(P, [f, g, fy]), !, %% Add the parts parse_number_explicit(P, op(+, TL, N), T, In, NC). parse_number_explicit(_, TL, T, [WN | In], NC) :- %% Whatever the precedence on the left special_word_number(WN, N, xfy), %% Enforce there was a left argument TL \= void, !, %% Multiply this and the left parse_number_explicit(xfy, op(*, TL, N), T, In, NC). parse_number_explicit(P, TL, T, [and, WN | In], NC) :- %% And is part of a valid number if there's a valid %% number on the left and right special_word_number(WN, _, _), %% Passthrough parse_number_explicit(P, TL, T, [WN | In], NC), !. parse_number_explicit(_, T, T, [WN | In], [WN | In]) :- %% If there's a tree T \= void, %% And can't consume more words as %% numbers (fail on first), then we're done not(special_word_number(WN, _, _)), !. parse_number_explicit(_, T, T, [], []) :- %% If consumed all innput and there's a %% tree, we're done T \= void, !. %% parse_floating_number(-tree, +stream, -not_consumed) is det % % Parse a floating point number % parse_floating_number(op('.', TL, TR)) --> %% A float is a node with a dot as the operator %% If there's a number on the left parse_number(TL), %% Followed by either point or dot [X], { member(X, [point, dot]), ! }, %% Followed by another number parse_positive_number(TR). parse_floating_number(TN) --> %% Or just a number parse_number(TN). %% parse_positive_number(-tree, +stream, -not_consumed) is det % % Parse an positive integer number % parse_positive_number(N) --> [N], %% CLPFD, a number between 0 and infinity { N in 0..sup, ! }. parse_positive_number(T) --> parse_number_explicit(void, void, T). %% parse_number(-tree, +stream, -not_consumed) is det % % Parse an integer number % parse_number(N) --> [N], %% CLPFD, a number between negative infinity and positive infinity { not(atom(N)), N in inf..sup, ! }. parse_number(op(neg, T)) --> % TODO %% A number can start with negative, to negate it [negative], parse_number_explicit(void, void, T). parse_number(T) --> parse_number_explicit(void, void, T). %% Tests: %% ?- parse_number(T, [two], _). %@ T = 2. %% ?- parse_number(T, [43], _). %@ T = 43. %% ?- parse_number(T, [nineteen, two], _). %@ false. %% ?- parse_number(T, [twenty], _). %@ T = 20. %% ?- parse_number(T, [twenty, point, two], NC). %@ T = op('.', 20, 2), %@ NC = []. %% ?- parse_number(T, [twenty, twenty], _). %@ false. %% ?- parse_number(T, [twenty, one], _). %@ T = op(+, 20, 1). %% ?- parse_number(T, [negative, one, hundred], _). %@ T = op(neg, op(*, 1, 100)) ; %@ false. %% ?- parse_number(T, [three, hundred], _). %@ T = op(*, 3, 100). %% ?- parse_number(T, [twenty, hundred], _). %@ T = op(*, 20, 100). %% ?- parse_number(T, [twenty, one, hundred], _). %@ T = op(*, op(+, 20, 1), 100). %% ?- parse_number(T, [two, hundred, and, one], _). %@ T = op(+, op(*, 2, 100), 1). %% ?- parse_number(T, [twenty, one, hundred, and, twenty, one], _). %@ T = op(+, op(+, op(*, op(+, 20, 1), 100), 20), 1). %% ?- parse_number(T, [twenty, one, hundred, and, twenty, one, foo, bar, blah], NC). %@ T = op(+, op(+, op(*, op(+, 20, 1), 100), 20), 1), %@ NC = [foo, bar, blah]. %% ?- parse_number(T, [twenty, one, hundred, and, bleg, twenty, quux, one, foo, bar], NC). %@ T = op(*, op(+, 20, 1), 100), %@ NC = [and, bleg, twenty, quux, one, foo, bar]. %% ?- parse_number(T, [two, hundred, thousand], _). %@ T = op(*, op(*, 2, 100), 1000). %% ?- parse_number(T, [twenty, one, hundred, thousand], _). %@ T = op(*, op(*, op(+, 20, 1), 100), 1000). %% ?- parse_number(T, [thirty, five, million, five, hundred, thirty, four], _). %@ T = op(+, op(+, op(*, op(+, op(*, op(+, 30, 5), 1000000), 5), 100), 30), 4). %% ?- parse_number(T, [foo, five, million], NC). %@ false. %% nlp_parse_power(?List, ?List) is det % % Parse powers % parse_power(op(^, TB, 2)) --> parse_polynomial_variable(TB), [squared]. parse_power(op(^, TB, 3)) --> parse_polynomial_variable(TB), [cubed]. parse_power(op(^, TB, TN)) --> parse_polynomial_variable(TB), [raised, to], parse_positive_number(TN). parse_power(TB) --> parse_polynomial_variable(TB). %% parse_operation(+Op, +stream, -not_consumed) is det % % Associate an operator with a word % parse_operation(-) --> [minus]. parse_operation(+) --> [plus]. parse_operation(*) --> [times]. %% parse_polynomial_operand(-tree) is det % % Parse a valid operand for either side of an % operation in a polynomial % parse_polynomial_operand(T) --> parse_floating_number(T). parse_polynomial_operand(T) --> parse_power(T). parse_polynomial_operand(load(T)) --> %% Tag the variable, to be loaded later parse_stored_variable(T), { ! }. %% Tests: %% ?- parse_polynomial_operand(T, [two], NC). %@ T = 2, %@ NC = [] ; %@ false. %% Declare polynomial_store as a dynamic predicate with two arguments %% Used to store and retrieve polynomials associated with a variable :- dynamic polynomial_store/2. %% parse_stored_variable(-var) is det % % Parse a valid variable name, for storage % A valid varaible is one that would be valid in Prolog % parse_stored_variable(P) --> [P], { valid_store_variable(P) }. %% Tests: %% ?- parse_stored_variable(P, ['P1'], _). %@ P = 'P1'. %% ?- parse_stored_variable(P, ['x1'], _). %@ false. %% parse_stored_variable(+var) is det % % Check if var is a valid variable name, for storage % A valid varaible is one that would be valid in Prolog % valid_store_variable(P) :- %% Get the list of codes of the atom atom_codes(P, L), %% Extract the first element cons(F, R, L), %% Partially builtin facilities: %% Check if it's a valid start to a Prolog variable code_type(F, prolog_var_start), %% Check that each of the following is a valid %% continuation to a variable name maplist(code_type_swap(prolog_identifier_continue), R). %% code_type_swap - swap arguments of code_type, so %% it can be used with maplist. No lambdas... code_type_swap(X, Y) :- code_type(Y, X). %% parse_polynomial_variable(-base, +stream, -not_consumed) is det % % Parse a polynomial variable % parse_polynomial_variable(B) --> [B], { polynomial_variable(B) }. %% parse_polynomial(-tree, +stream, -not_consumed) is det % % Parse a polynomial. Delegates to explicit variant % parse_polynomial(T) --> %% Ignore "polynomail", if followed by a valid polynomial [polynomial], { ! }, %% Delegate parse_polynomial_explicit(_-_, T). parse_polynomial(T) --> %% Delegate parse_polynomial_explicit(_-_, T), !. %% Tests: %% ?- parse_polynomial(T, [], _). %@ false. %% ?- parse_polynomial(T, [two], _). %@ T = 2, %@ NC = []. %% ?- parse_polynomial(T, [two, times, three], _). %@ T = op(*, 2, 3), %@ NC = []. %% ?- parse_polynomial(T, [two, times, three, plus, four], _). %@ T = op(+, op(*, 2, 3), 4). %% ?- parse_polynomial(T, [two, plus, three, times, four], _). %@ T = op(+, 2, op(*, 3, 4)). %% ?- parse_polynomial(T, [two, plus, three, times, four, plus, six, times, five], _). %@ T = op(+, 2, op(+, op(*, 3, 4), op(*, 6, 5))). %% ?- parse_polynomial(T, [two, times, times, two], NC). %@ T = void, %@ NC = [two, times, times, two]. %% ?- parse_polynomial(T, [two, plus, x, times, four], _). %@ T = op(+, 2, op(*, x, 4)). %% ?- parse_polynomial(T, [two, plus, x, times, four, plus, y, raised, to, five], _). %@ T = op(+, 2, op(+, op(*, x, 4), op(^, y, 5))). %% ?- parse_polynomial(T, [two, plus, two, plus, one, times, y], _). %@ true. %@ T = op(+, op(+, 2, 2), op(*, 1, y)). %% ?- parse_polynomial(T, [polynomial, 2, plus, 3, plus, 4, y], NC). %@ T = op(+, op(+, 2, 3), op(*, 4, y)), %@ NC = []. %% parse_polynomial_explicit(+tree-at, -tree) is det % % Explicitly parse a polynomial. You probably don't want % to call this directly. The first argument is a difference % structure of the tree on the left; the second of the pair % represents where to put the rest of the tree, in % subsequent passes % % Call with _-_ on the first argument, outputs the % tree on the right % parse_polynomial_explicit(void-_, T) --> %% Entry point. If the three on the left is void %% Parse an operand and an op parse_polynomial_operand(TL), parse_operation(Op), %% If consumed an op, double down and don't go back !, %% Recurse with the tree on the left populated with %% what we found and a reference to the place to %% place the next tree parse_polynomial_explicit(op(Op, TL, TRP)-TRP, T). parse_polynomial_explicit(TLP-TL, T) --> %% Parse an operand on the left and place it in the tree %% on the left, through the difference structure, parse_polynomial_operand(TL), %% parse either a minus or a plus { member(COp, [-, +]) }, parse_operation(COp), !, %% Recurse on the right with add; position the sub tree on the right parse_polynomial_explicit(op(COp, TLP, TRP)-TRP, T). parse_polynomial_explicit(TLP-T, TLP) --> %% Parse an operand on the left, placing the result of the %% recusion on the TLP, through the difference structure and return that parse_polynomial_operand(TL), %% If we find a times, parse_operation(*), !, %% Place the operand on the left, the following on the %% right and get a T to place in the tree on the left from above parse_polynomial_explicit(op(*, TL, TRP)-TRP, T). parse_polynomial_explicit(TLP-T, TLP) --> %% Same as above, but without an operator, parse_polynomial_operand(TL), %% Assume times parse_polynomial_explicit(op(*, TL, TRP)-TRP, T), !. parse_polynomial_explicit(TLP-TL, TLP) --> { TLP \= void }, %% Base case. Parse a last operand parse_polynomial_operand(TL), !, { TL \= void }. parse_polynomial_explicit(void-_, T) --> %% Base case. Parse a single operand parse_polynomial_operand(T), !, { T \= void }. %% parse_command(-tree, +stream, -not_consumed) is semidet % % Parse each individual command % parse_command(help_menu) --> [help]. parse_command(help(C)) --> [tell, me, about, C]. parse_command(show_stored_polynomials) --> [show, stored, polynomials]. parse_command(forget(P)) --> [forget], parse_stored_variable(P). parse_command(show(store(P), T)) --> [show], parse_polynomial(T), [as], parse_stored_variable(P). parse_command(show(P, void)) --> [show], parse_stored_variable(P). parse_command(show(void, T)) --> [show], parse_polynomial(T), { nonvar(T) }. parse_command(store(P, T)) --> [let], parse_stored_variable(P), [be], parse_polynomial(T). parse_command(store(P, T)) --> [store], parse_polynomial(T), [as], parse_stored_variable(P). parse_command(store_simplified(V, P)) --> [simplify], parse_polynomial(P), [as], [V]. parse_command(simplify(T)) --> [simplify], parse_polynomial(T). parse_command(store_multiplication(TN, TP, V)) --> [multiply], parse_polynomial(TN), [by], parse_polynomial(TP), [as], [V]. parse_command(multiply(TN, TP)) --> [multiply], parse_polynomial(TN), [by], parse_polynomial(TP). parse_command(op(-, TN, TP)) --> [sub], parse_polynomial(TN), [X], { member(X, [to, from, with]) }, parse_polynomial(TP). parse_command(op(+, TN, TP)) --> [add], parse_polynomial(TN), [X], { member(X, [to, with]) }, parse_polynomial(TP). %% Tests: %% ?- parse_command(T, [show, 3], NC). %@ T = show(void, 3), %@ NC = [] . %% ?- parse_command(T, [add, 3, plus, x, to, 4, plus, x], NC). %@ false. %@ T = op(+, op(+, 3, x), op(+, 4, x)), %@ NC = [] ; %@ false. %% parse_input(-tree) is det % % Parse each command and string it into a list % parse_input(command(TCL, TCR)) --> %% Result is a struct with a command on the left %% and a struct of commands on the right %% parse a single command parse_command(TCL), %% separator [and], !, %% Recurse parse_input(TCR). parse_input(command(TC, void)) --> %% If there's no separator, we're done recursing %% parse a single command parse_command(TC). %% ?- parse_input(CT, [show, 3], _). %@ CT = command(show(void, 3), void). /******************************* * UI * *******************************/ /* poly2list/2 transforms a list representing a polynomial (second argument) into a polynomial represented as an expression (first argument) and vice-versa. */ poly2list(P, L) :- is_polynomial_valid_in_predicate(P, "poly2list"), polynomial_to_list(P, L), !. /* simpolylist/2 simplifies a polynomial represented as a list into another polynomial as a list. */ simpoly_list(L, S) :- is_polynomial_as_list_valid_in_predicate(L, "simpoly_list"), simplify_polynomial_as_list(L, S), !. /* simpoly/2 simplifies a polynomial represented as an expression as another polynomial as an expression. */ simpoly(P, S) :- is_polynomial_valid_in_predicate(P, "simpoly"), simplify_polynomial(P, S), !. %% Tests: %% ?- simpoly(2+2+1*y, S). %@ S = y+4. /* scalepoly/3 multiplies a polynomial represented as an expression by a scalar resulting in a second polynomial. The two first arguments are assumed to be ground. The polynomial resulting from the sum is in simplified form. */ scalepoly(P1, C, S) :- is_polynomial_valid_in_predicate(P1, "scalepoly"), is_number_valid_in_predicate(C, "scalepoly"), scale_polynomial(P1, C, S), !. %% Tests: %% ?- scalepoly(3*x*z+2*z, 4, S). %@ S = 12*x*z+8*z. %% ?- scalepoly(3*x*z+2*z, 2, S). %@ S = 6*x*z+4*z. /* addpoly/3 adds two polynomials as expressions resulting in a third one. The two first arguments are assumed to be ground. The polynomial resulting from the sum is in simplified form. */ addpoly(P1, P2, S) :- is_polynomial_valid_in_predicate(P1, "addpoly"), is_polynomial_valid_in_predicate(P2, "addpoly"), add_polynomial(P1, P2, S), !. %% Tests: %% ?- addpoly(3 + x, 3 - x, S). %@ S = 6. %% is_polynomial_valid_in_predicate(+T, +F) is det % % Returns true if valid polynomial, fails with UI message otherwise. % The failure message reports which polynomial is invalid and in which % predicate the problem ocurred. % is_polynomial_valid_in_predicate(P, _) :- %% If P is a valid polynomial, return true polynomial(P), !. is_polynomial_valid_in_predicate(P, F) :- %% Otherwise, write the polynomial and fails write("Invalid polynomial in "), write(F), write(": "), write(P), fail. %% Tests: %% ?- is_polynomial_valid_in_predicate(1-x, "Test"). %@ true. %% ?- is_polynomial_valid_in_predicate(a*4-0*x, "Test"). %@ Invalid polynomial in Test: a*4-0*x %@ false. %% is_polynomial_as_list_valid_in_predicate(+L, +F) is det % % Returns true if the polynomial represented as list is valid, % fails with UI message otherwise. % The failure message reports which polynomial is invalid and % in which predicate the problem ocurred. % is_polynomial_as_list_valid_in_predicate(L, F) :- %% If L is a valid polynomial, return true list_to_polynomial(L, P), is_polynomial_valid_in_predicate(P, F). %% Tests: %% ?- is_polynomial_as_list_valid_in_predicate([1], "Test"). %@ true. %% ?- is_polynomial_as_list_valid_in_predicate([0*x, a*4], "Test"). %@ Invalid polynomial in Test: a*4+0*x %@ false. %% is_number_valid_in_predicate(+C:number, +F:string) is det % % Validates that C is a number or prints F and it then it % is_number_valid_in_predicate(C, _) :- number(C), !. is_number_valid_in_predicate(C, F) :- %% Writes the argument and fails write("Invalid number in "), write(F), write(": "), write(C), fail. /******************************* * BACKEND * *******************************/ %% polynomial_variable_list(-List) is det % % List of possible polynomial variables % polynomial_variable_list([x, y, z]). %% polynomial_variable(?X:atom) is semidet % % Returns true if X is a polynomial variable, false otherwise. % polynomial_variable(X) :- polynomial_variable_list(V), member(X, V). %% Tests: %% ?- polynomial_variable(x). %@ true . %% ?- polynomial_variable(a). %@ false. %% power(+X:atom) is semidet % % Returns true if X is a power term, false otherwise. % power(P^N) :- %% CLPFD comparison. Reversible N #>= 1, polynomial_variable(P). power(X) :- polynomial_variable(X). %% Tests: %% ?- power(x). %@ true . %% ?- power(a). %@ false. %% ?- power(x^1). %@ true . %% ?- power(x^3). %@ true . %% ?- power(x^(-3)). %@ false. %% ?- power(-x). %@ false. %% ?- power(X). %@ X = x^_462546, %@ _462546 in 1..sup ; %@ X = y^_462546, %@ _462546 in 1..sup ; %@ X = z^_462546, %@ _462546 in 1..sup ; %@ X = x ; %@ X = y ; %@ X = z. %% term(+N:atom) is semidet % % Returns true if N is a term, false otherwise. % term(N) :- % If N is not a free variable nonvar(N), % Assert it as a number number(N). term(N) :- % If N is a free variable and not compound not(compound(N)), var(N), % Assert it must be between negative and positive infinity % This uses the CLPR library, which makes this reversible, % whereas `number(N)` is always false, since it only succeeds % if the argument is bound (to a integer or float) {N >= 0; N < 0}. term(X) :- power(X). term(-X) :- power(X). term(L * In) :- term(L), term(In). %% Tests: %% ?- term(2*x^3). %@ true . %% ?- term(x^(-3)). %@ false. %% ?- term(a). %@ false. %% ?- term(-1*x). %@ true . %% ?- term(-x). %@ true . %% ?- term((-3)*x^2). %@ true . %% ?- term(3.2*x). %@ true . %% ?- term(-x*(-z)). %@ true . %% ?- term(X). %@ {X>=0.0} ; %@ {X<0.0} ; %@ X = x^_111514, %@ _111514 in 1..sup ; %@ X = y^_111514, %@ _111514 in 1..sup ; %@ X = z^_111514, %@ _111514 in 1..sup ; %@ X = x ; %@ X = y ; %@ X = z ; %@ X = -x^_111522, %@ _111522 in 1..sup ; %@ X = -y^_111522, %@ _111522 in 1..sup ; %@ X = -z^_111522, %@ _111522 in 1..sup ; %@ X = -x ; %@ X = -y ; %@ X = -z ; %% polynomial(+M:atom) is semidet % % Returns true if polynomial, false otherwise. % polynomial(M) :- %% A polynomial is either a term term(M). polynomial(L + In) :- %% Or a sum of terms polynomial(L), term(In). polynomial(L - In) :- %% Or a subtraction of terms polynomial(L), term(In). %% Tests: %% ?- polynomial(x). %@ true . %% ?- polynomial(x^3). %@ true . %% ?- polynomial(3*x^7). %@ true . %% ?- polynomial(2+3*x+4*x*y^3). %@ true . %% ?- polynomial(2 - 3*x + 4*x*y^3). %@ true . %% ?- polynomial(a). %@ false. %% ?- polynomial(x^(-3)). %@ false. %% ?- polynomial(-x + 3). %@ true . %% ?- polynomial(-x - -z). %@ true . %% power_to_canon(+T:atom, -T^N:atom) is semidet % % Returns a canon power term. % power_to_canon(T^N, T^N) :- polynomial_variable(T), % CLP(FD) operator to ensure N is different from 1, % in a reversible way N #\= 1. power_to_canon(T, T^1) :- polynomial_variable(T). %% Tests: %% ?- power_to_canon(x, X). %@ X = x^1 . %% ?- power_to_canon(-x, X). %@ false. %@ X = -1*x^1 . %% ?- power_to_canon(X, x^1). %@ X = x . %% ?- power_to_canon(X, x^4). %@ X = x^4 . %% ?- power_to_canon(X, a^1). %@ false. %% ?- power_to_canon(X, x^(-3)). %@ X = x^ -3 . %% ?- power_to_canon(X, -1*x^1). %@ X = -x . %% term_to_list(?T, ?List) is semidet % % Converts a term to a list of its monomials and vice versa. % Can verify if term and monomials list are compatible. % term_to_list(L * N, [N | TS]) :- number(N), term_to_list(L, TS). term_to_list(L * P, [P2 | TS]) :- power(P), power_to_canon(P, P2), term_to_list(L, TS). term_to_list(L * -P, [-P2 | TS]) :- power(P), power_to_canon(P, P2), term_to_list(L, TS). term_to_list(N, [N]) :- number(N). term_to_list(P, [P2]) :- power(P), power_to_canon(P, P2). term_to_list(-P, [-P2]) :- power(P), power_to_canon(P, P2). %% Tests: %% ?- term_to_list(1, X). %@ X = [1] . %% ?- term_to_list(-1, X). %@ X = [-1] . %% ?- term_to_list(x, X). %@ X = [x^1] . %% ?- term_to_list(-x, X). %@ X = [-x^1] . %% ?- term_to_list(2 * 3, X). %@ X = [3, 2] . %% ?- term_to_list(1*2*y*z*23*x*y*x^3*x, X). %@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2, 1] . %% ?- term_to_list(1*2*y*z*23*x*y*(-1), X). %@ X = [-1, y^1, x^1, 23, z^1, y^1, 2, 1] . %% ?- term_to_list(X, [-1]). %@ X = -1 . %% ?- term_to_list(X, [x^1, -1]). %@ X = -1*x . %% ?- term_to_list(X, [-x^1]). %@ X = -x . %% ?- term_to_list(X, [y^1, x^1]). %@ X = x*y . %% ?- term_to_list(X, [x^4]). %@ X = x^4 . %% ?- term_to_list(X, [y^6, z^2, x^4]). %@ X = x^4*z^2*y^6 . %% ?- term_to_list(X, [y^6, z^2, x^4, -2]). %@ X = -2*x^4*z^2*y^6 . %% ?- term_to_list(X, [x^1, 0]). %@ X = 0*x . %% ?- term_to_list(X, [y^1, -2]). %@ X = -2*y . %% simplify_term(+Term_In:term, ?Term_Out:term) is det % % Simplifies a given term. % This function can also be be used to verify if % a term is simplified. % simplify_term(Term_In, Term_Out) :- term_to_list(Term_In, L), %% Sort the list of numbers and power to group them, %% simplifying the job of `join_similar_parts_of_term` sort(0, @=<, L, L2), ( %% If there's a 0 in the list, then the whole term is 0 member(0, L2), Term_Out = 0 ; %% Otherwise ( %% If there's only one element, then the term was already simplified %% This is done so that the `exclude` following doesn't remove all ones length(L2, 1), Term_Out = Term_In ; %% Remove all remaining ones exclude(==(1), L2, L3), join_similar_parts_of_term(L3, L4), %% Reverse the list, since the following call gives the result in the %% reverse order otherwise reverse(L4, L5), term_to_list(Term_Out, L5) ) ), % First result is always the most simplified form. !. %% Tests: %% ?- simplify_term(1, X). %@ X = 1. %% ?- simplify_term(x, X). %@ X = x. %% ?- simplify_term(2*y*z*x^3*x, X). %@ X = 2*x^4*y*z. %% ?- simplify_term(1*y*z*x^3*x, X). %@ X = x^4*y*z. %% ?- simplify_term(0*y*z*x^3*x, X). %@ X = 0. %% ?- simplify_term(6*y*z*7*x*y*x^3*x, X). %@ X = 42*x^5*y^2*z. %% ?- simplify_term(-x, X). %@ X = -x. %% ?- simplify_term(-x*y*(-z)*3, X). %@ X = 3* -x* -z*y. %% ?- simplify_term(a, X). %@ false. %% ?- simplify_term(x^(-3), X). %@ false. %% join_similar_parts_of_term(+List, -List) is det % % Combine powers of the same variable in the given list. % Requires that the list be sorted. % join_similar_parts_of_term([P1, P2 | L], L2) :- %% If both symbols are powers power(P1), power(P2), %% Decompose them into their parts B^N1 = P1, B^N2 = P2, %% Sum the exponent N is N1 + N2, join_similar_parts_of_term([B^N | L], L2), % First result is always the most simplified form. !. join_similar_parts_of_term([N1, N2 | L], L2) :- %% If they are both numbers number(N1), number(N2), %% Multiply them N is N1 * N2, join_similar_parts_of_term([N | L], L2), % First result is always the most simplified form. !. join_similar_parts_of_term([X | L], [X | L2]) :- %% Otherwise consume one element and recurse join_similar_parts_of_term(L, L2), % First result is always the most simplified form. !. join_similar_parts_of_term([], []). %% Tests: %% ?- join_similar_parts_of_term([3], T). %@ T = [3]. %% ?- join_similar_parts_of_term([x^2], T). %@ T = [x^2]. %% ?- join_similar_parts_of_term([x^1, x^1, x^1, x^1], T). %@ T = [x^4]. %% ?- join_similar_parts_of_term([2, 3, x^1, x^2], T). %@ T = [6, x^3]. %% ?- join_similar_parts_of_term([2, 3, x^1, x^2, y^1, y^6], T). %@ T = [6, x^3, y^7]. %% ?- join_similar_parts_of_term([2, 3, -x^1, -x^2], T). %@ T = [6, -x^1, -x^2]. %% simplify_polynomial(+P:atom, -P2:atom) is det % % Simplifies a polynomial. % simplify_polynomial(0, 0) :- % 0 is already fully simplified. This is an % exception to the following algorithm !. simplify_polynomial(P, P2) :- polynomial_to_list(P, L), simplify_polynomial_as_list(L, L2), list_to_polynomial(L2, P2), %% The first result is the most simplified one !. %% Tests: %% ?- simplify_polynomial(1, X). %@ X = 1. %% ?- simplify_polynomial(0, X). %@ X = 0. %% ?- simplify_polynomial(x, X). %@ X = x. %% ?- simplify_polynomial(x*x, X). %@ X = x^2. %% ?- simplify_polynomial(2 + 2, X). %@ X = 2*2. %% ?- simplify_polynomial(x + x, X). %@ X = 2*x. %% ?- simplify_polynomial(0 + x*x, X). %@ X = x^2. %% ?- simplify_polynomial(x^2*x + 3*x^3, X). %@ X = 4*x^3. %% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*x, X). %@ X = 6*x^3. %% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*4 + z, X). %@ X = 5*x^3+4*x^2+z. %% ?- simplify_polynomial(x^2*x + 3*x^3 - x^3 - x*x*4 + z, X). %@ X = 3*x^3-4*x^2+z. %% ?- simplify_polynomial(x + 1 + x, X). %@ X = 2*x+1. %% ?- simplify_polynomial(x + 1 + x + 1 + x + 1 + x, X). %@ X = 4*x+3. %% simplify_polynomial_as_list(+L1:List,-L3:List) is det % % Simplifies a polynomial represented as a list. % simplify_polynomial_as_list(L, L14) :- %% Convert each term to a list maplist(term_to_list, L, L2), %% Sort each sublist so that the next %% sort gives the correct results maplist(sort(0, @>=), L2, L3), %% Sort the outer list sort(0, @>=, L3, L4), %% For each of the parts of the terms, join them maplist(join_similar_parts_of_term, L4, L5), %% Sort each of the sublists %% Done so the next call simplifies has less work maplist(sort(0, @=<), L5, L6), join_similar_terms(L6, L7), %% Exclude any sublist that includes a 0 (such as the %% equivalent to the term 0*x) exclude(member(0), L7, L8), %% Reverse each sublist, because the next call %% reverses the result maplist(reverse, L8, L9), maplist(term_to_list, L10, L9), %% Delete any 0 from the list delete(L10, 0, L11), %% Sort list converting back gives the result in the correct order sort(0, @=<, L11, L12), ( %% If the list is empty, the result is a list with 0 L12 = [], L13 = [0] ; %% Otherwise, this is the result L13 = L12 ), %% Further make sure all terms are simplified maplist(simplify_term, L13, L14). %% 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] . %% ?- simplify_polynomial_as_list([1, 1*x], L). %@ L = [1, x] . %% ?- simplify_polynomial_as_list([0*x, 0], L). %@ L = [0] . %% join_similar_terms(+P:List, -P2:List) 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 the coefficient of the term as the first element of the list % %% Special cases to make this predicate reversible term_to_canon([1], [1]) :- !. term_to_canon(L2, [1 | L]) :- nonvar(L), L2 = L, !. term_to_canon([-1], [-1]) :- !. term_to_canon([-P | L2], [-1, P | L]) :- nonvar(L), L2 = L, !. term_to_canon([N2 | L], [N | L]) :- number(N), N2 = N, !. %% Normal case term_to_canon(L, [N | L2]) :- term_to_canon_with_coefficient(N, L, L2), !. %% Tests: %% ?- term_to_canon([2], T). %@ T = [2]. %% ?- term_to_canon([-x], T). %@ T = [-1, x]. %% ?- term_to_canon([-x^3], T). %@ T = [-1, x^3]. %% ?- term_to_canon([x^1], T). %@ T = [1, x^1]. %% ?- 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]. %% ?- term_to_canon([2, -x^3], T). %@ T = [-2, x^3]. %% ?- term_to_canon([2, -x^3, -z], T). %@ T = [2, x^3, z]. %% ?- term_to_canon(L, [-1]). %@ L = [-1]. %% ?- term_to_canon(L, [1]). %@ L = [1]. %% ?- term_to_canon(L, [-2]). %@ L = [-2]. %% ?- term_to_canon(L, [-2, x]). %@ L = [-2, x]. %% ?- term_to_canon(L, [1, x]). %@ L = [x]. %% ?- term_to_canon(L, [-1, x]). %@ L = [-x]. %% ?- term_to_canon(L, [1, x, z, y]). %@ L = [x, z, y]. %% ?- term_to_canon(L, [-1, x, z, y]). %@ L = [-x, z, y]. %% term_to_canon_with_coefficient(-N:number, +L:List, -L2:List) is semidet % % Calculates the coefficient of the term and removes negations of powers, % accumulating the results in N % term_to_canon_with_coefficient(N, [N2 | TS], TS2) :- number(N2), term_to_canon_with_coefficient(N3, TS, TS2), N is N2 * N3, !. term_to_canon_with_coefficient(N, [P | TS], [P2 | TS2]) :- sign_of_power(P, N2 * P2), term_to_canon_with_coefficient(N3, TS, TS2), N is N2 * N3, !. term_to_canon_with_coefficient(N, [], []) :- nonvar(N); N = 1. %% Tests: %% ?- term_to_canon_with_coefficient(N, [x], L). %@ N = 1, %@ L = [x]. %% ?- term_to_canon_with_coefficient(N, [x, x^2, 2], L). %@ N = 2, %@ L = [x^1, x^2]. %% ?- term_to_canon_with_coefficient(N, [x, x^2, 2, 4, z], L). %@ N = 8, %@ L = [x, x^2, z]. %% ?- term_to_canon_with_coefficient(N, [x, x^2, 2, 4, -z], L). %@ N = -8, %@ L = [x, x^2, z]. %% ?- term_to_canon_with_coefficient(N, [x, -x^2, 2, 4, -z], L). %@ N = 8, %@ L = [x, x^2, z]. %% ?- term_to_canon_with_coefficient(N, L, [x]). %@ N = 1, %@ L = [x]. %% ?- term_to_canon_with_coefficient(N, L, [1]). %@ N = 1, %@ L = [1]. %% ?- term_to_canon_with_coefficient(N, L, [2]). %@ N = 1, %@ L = [2]. %% sign_of_power(P:power, P:term) is det % % If there isn't a leading minus, multiplies the power by 1, % otherwise by a -1. This way it prefers the positive version. % Not idempotent % sign_of_power(P, 1*P) :- %% If P can't unify with a minus followed by an unnamed variable P \= -_, !. sign_of_power(-P, -1*P). %% Tests: %% ?- sign_of_power(x, X). %@ X = 1*x. %% ?- sign_of_power(-x, X). %@ X = -1*x. %% ?- sign_of_power(X, 1*x). %@ X = x. %% ?- sign_of_power(X, -1*x). %@ X = -x. %% add_terms(+L:List, +In:List, -Result:List) is det % % Adds two terms represented as list by adding % the coeficients if the power is the same. % Returns false if they can't be added % 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 the rest of the term is the same TL2 == TR2, %% Add the coeficients N2 is NL2 + NR2. %% Tests %% ?- add_terms([1], [1], In). %@ In = [2]. %% ?- add_terms([x], [x], In). %@ In = [2, x]. %% ?- add_terms([2, x^3], [x^3], In). %@ In = [3, x^3]. %% ?- add_terms([2, x^3], [3, x^3], In). %@ In = [5, x^3]. %% ?- add_terms([2, x^3], [3, x^2], In). %@ false. %% 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]. %% 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), %% Ensure there is a coeficient term_to_canon(L, L2), [N | In] = L2, %% (-)/1 is an operator, needs to be evaluated, otherwise %% it gives a symbolic result, which messes with further processing N2 is -N, %% Convert the term back from canonic form term_to_canon(L3, [N2 | In]), %% Reverse the order of the list, because converting %% implicitly reverses it reverse(L3, L4), term_to_list(T2, L4), !. %% Tests: %% ?- negate_term(1, In). %@ In = -1. %% ?- negate_term(x, In). %@ In = -x. %% ?- negate_term(-x, In). %@ In = x. %% ?- negate_term(x^2, In). %@ In = -x^2. %% ?- negate_term(3*x*y^2, In). %@ In = -3*y^2*x. %% 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), %% Canonize terms maplist(term_to_canon, L2, L3), %% Append C to the start of each sublist maplist(cons(C), L3, L4), %% Convert to a list of terms maplist(term_to_list, L5, L4), %% Simplify the resulting polynomial simplify_polynomial_as_list(L5, L6), %% Return as a simplified polynomial list_to_polynomial(L6, 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: %% ?- cons(C, L, L2). %@ L2 = [C|L]. %% 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.