Data commit

Task/Farey-sequence/Jq/farey-sequence.jq

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+include "rational" ;  # actually, only `r/2` and `gcd/2` are actually needed
+
+# Emit an ordered stream of the Farey sequence of order $order
+# by recursively generating the mediants
+def FS($order):
+  def f($l; $r; $n):
+    r($l.n + $r.n; $l.d + $r.d) as $m
+    | select($m.d <= $n)
+    | f($l; $m; $n), $m, f($m; $r; $n);
+
+  r(0;1) as $l
+  | r(1;1) as $r
+  | $l, f($l; $r; .), $r;
+
+# Pretty-print Farey sequences of order $min up to and including order $max
+def FareySequences($min; $max):
+  def rpp: "\(.n)/\(.d)";
+  def pp(s): [s|rpp] | join(" ");
+  range($min;$max+1)
+  | "F(\(.)): " + pp(FS(.));
+
+# Use `count/1` for counting to save space
+def count(s): reduce s as $_ (0; .+1);
+def FareySequenceMembers($N):
+  count(FS($N));
+
+# The tasks:
+FareySequences(1;11),
+"",
+(range(100; 1001; 100) | "F\(.): \(FareySequenceMembers(.)|length) members" )