Euler's identity: Difference between revisions
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</pre>
=={{header|Prolog}}==
Symbolically manipulates Euler's identity until it can't be further reduced (and we get zero :)
<lang Prolog>
% reduce() keeps on simplifying until the expression can no longer be simplified;
% prints the intermediate results so that one can see Prolog "thinking."
%
reduce(A, C) :-
simplify(A, B),
(B = A -> C = A; io:format("= ~w~n", [B]), reduce(B, C)).
simplify(exp(i*X), cos(X) + i*sin(X)) :- !.
simplify(0 + A, A) :- !.
simplify(A + 0, A) :- !.
simplify(A + B, C) :-
integer(A),
integer(B), !,
C is A + B.
simplify(A + B, C + D) :- !,
simplify(A, C),
simplify(B, D).
simplify(0 * _, 0) :- !.
simplify(_ * 0, 0) :- !.
simplify(1 * A, A) :- !.
simplify(A * 1, A) :- !.
simplify(A * B, C) :-
integer(A),
integer(B), !,
C is A * B.
simplify(A * B, C * D) :- !,
simplify(A, C),
simplify(B, D).
simplify(cos(0), 1) :- !.
simplify(sin(0), 0) :- !.
simplify(cos(pi), -1) :- !.
simplify(sin(pi), 0) :- !.
simplify(X, X).
</lang>
{{Out}}
<pre>
?- reduce(exp(i*pi)+1, X).
= cos(pi)+i*sin(pi)+1
= -1+i*0+1
= -1+0+1
= -1+1
= 0
X = 0.
</pre>
=={{header|Python}}==
<lang python>>>> import math
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