Arithmetic derivative: Difference between revisions

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      110000000000      1200000000000      13000000000000      140000000000000      1500000000000000
 16000000000000000 170000000000000000 1800000000000000000 19000000000000000000 200000000000000000000</syntaxhighlight>
+=={{header|jq}}==
+For this task, gojq (the Go implementation of jq) is used
+for numerical accuracy.
+See [[Prime_decomposition#jq]] for the def of factors/0 used here.
+<syntaxhighlight lang="jq">
+To take advantage of gojq's arbitrary-precision integer arithmetic:
+def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
+# In case gojq is used:
+def _nwise($n):
+  def nw: if length <= $n then . else .[0:$n] , (.[$n:] | nw) end;
+  nw;
+def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
+def D($n):
+    if   $n < 0 then -D(- $n)
+    elif $n < 2 then 0
+    else [$n | factors] as $f
+    | ($f|length) as $c
+    | if   $c <= 1 then 1
+      elif $c == 2 then $f[0] + $f[1]
+      else ($n / $f[0]) as $d
+      | D($d) * $f[0] + $d
+      end
+    end ;
+def task:
+  def task1:
+    reduce range(-99; 101) as $n ([]; .[$n+99] = D($n))
+    | _nwise(10) | map(lpad(4)) | join(" ");
+  def task2:
+    range(1; 21) as $i
+    | "D(10^\($i)) / 7 = \( D(10|power($i))/7 )" ;
+  task1, "", task2 ;
+task
+</syntaxhighlight>
+{{Output}}
+<pre>
+ -75  -77   -1 -272  -24  -49  -34  -96  -20 -123
+  -1 -140  -32  -45  -22 -124   -1  -43 -108 -176
+  -1  -71  -18  -80  -55  -39   -1 -156   -1  -59
+ -26  -72   -1  -61  -18 -192  -51  -33   -1  -92
+  -1  -31  -22  -92  -16  -81   -1  -56  -20  -45
+ -14 -112   -1  -25  -39  -48   -1  -41   -1  -68
+ -16  -21   -1  -60  -12  -19  -14  -80   -1  -31
+  -1  -32  -27  -15  -10  -44   -1  -13  -10  -24
+  -1  -21   -1  -32   -8   -9   -1  -16   -1   -7
+  -6  -12   -1   -5   -1   -4   -1   -1    0    0
+1    1    4    1    5    1   12    6    7
+16    1    9    8   32    1   21    1   24
+13    1   44   10   15   27   32    1   31
+80   14   19   12   60    1   21   16   68
+41    1   48   39   25    1  112   14   45
+56    1   81   16   92   22   31    1   92
+33   51  192   18   61    1   72   26   59
+156    1   39   55   80   18   71    1  176
+43    1  124   22   45   32  140    1  123
+96   34   49   24  272    1   77   75  140
+D(10^1) / 7 = 1
+D(10^2) / 7 = 20
+D(10^3) / 7 = 300
+D(10^4) / 7 = 4000
+D(10^5) / 7 = 50000
+D(10^6) / 7 = 600000
+D(10^7) / 7 = 7000000
+D(10^8) / 7 = 80000000
+D(10^9) / 7 = 900000000
+D(10^10) / 7 = 10000000000
+D(10^11) / 7 = 110000000000
+D(10^12) / 7 = 1200000000000
+D(10^13) / 7 = 13000000000000
+D(10^14) / 7 = 140000000000000
+D(10^15) / 7 = 1500000000000000
+D(10^16) / 7 = 16000000000000000
+D(10^17) / 7 = 170000000000000000
+D(10^18) / 7 = 1800000000000000000
+D(10^19) / 7 = 19000000000000000000
+D(10^20) / 7 = 200000000000000000000
+</pre>
 =={{header|Julia}}==