Data commit

Task/Faulhabers-triangle/Prolog/faulhabers-triangle.pro

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+ft_rows(Lz) :-
+    lazy_list(ft_row, [], Lz).
+
+ft_row([], R1, R1) :- R1 = [1].
+ft_row(R0, R2, R2) :-
+    length(R0, P),
+    Jmax is 1 + P, numlist(2, Jmax, Qs),
+    maplist(term(P), Qs, R0, R1),
+    sum_list(R1, S), Bk is 1 - S, % Bk is Bernoulli number
+    R2 = [Bk | R1].
+
+term(P, Q, R, S) :- S is R * (P rdiv Q).
+
+show(N) :-
+    ft_rows(Rs),
+    length(Rows, N), prefix(Rows, Rs),
+    forall(
+        member(R, Rows),
+            (format(string(S), "~w", [R]),
+             re_replace(" rdiv "/g, "/", S, T),
+             re_replace(","/g, ", ", T, U),
+             write(U), nl)).
+
+sum(N, K, S) :- % sum I=1,N (I ** K)
+    ft_rows(Rows), drop(K, Rows, [Coefs|_]),
+    reverse([0|Coefs], Poly),
+    foldl(horner(N), Poly, 0, S).
+
+horner(N, A, S0, S1) :-
+    S1 is N*S0 + A.
+
+drop(N, Lz1, Lz2) :-
+    append(Pfx, Lz2, Lz1), length(Pfx, N), !.