Data update

Task/Arithmetic-derivative/00-TASK.txt

@@ -4,21 +4,21 @@ factorization, by analogy with the product rule for the derivative of a function
 used in mathematical analysis. Accordingly, for natural numbers n, the arithmetic 
 derivative D(n) is defined as follows:
 
-;*D(0) = D(1) = 0.
-;*D(p) = 1 for any prime p.
-;*D(mn) = D(m)n + mD(n) for any m,n ∈ N. (Leibniz rule for derivatives).
+;*<math>D(0) = D(1) = 0</math>.
+;*<math>D(p) = 1 \;\text{for any prime}\; p</math>.
+;*<math>D(mn) = D(m)n + mD(n) \;\text{for any}\; m,n \in N</math>. (Leibniz rule for derivatives).
 
-Additionally, for negative integers the arithmetic derivative may be defined as -D(-n) (n < 0).
+Additionally, for negative integers the arithmetic derivative may be defined as <math>-D(-n) \;\text{for}\; (n < 0)</math>.
 
 ; Examples
 
-D(2) = 1 and D(3) = 1 (both are prime) so if mn = 2 * 3, D(6) = (1)(3) + (1)(2) = 5.
+<math>D(2) = 1</math> and <math>D(3) = 1</math> (both are prime) so if <math>mn = 2 \cdot 3</math>, then <math>D(6) = D(2\cdot 3) = D(2)\cdot 3 + 2\cdot D(3) = 1\cdot 3 + 2\cdot 1 = 5</math>.
 
-D(9) = D(3)(3) + D(3)(3) = 6
+<math>D(9) = D(3)\cdot 3 + 3\cdot D(3) = 1\cdot 3 + 3\cdot 1 = 6</math>
 
-D(27) = D(3)*9 + D(9)*3 = 9 + 18 = 27
+<math>D(27) = D(3)\cdot 9 + 3\cdot D(9) = 1\cdot 9 + 3\cdot 6 = 27</math>
 
-D(30) = D(5)(6) + D(6)(5) = 6 + 5 * 5 = 31.
+<math>D(30) = D(5)\cdot 6 + 5\cdot D(6) = 1\cdot 6 + 5 \cdot 5 = 31</math>.
 
 ; Task
 
@@ -26,7 +26,7 @@ Find and show the arithmetic derivatives for -99 through 100.
 
 ; Stretch task
 
-Find (the arithmetic derivative of 10^m) then divided by 7, where m is from 1 to 20.
+Find (the arithmetic derivative of <math>10^m</math>) then divided by 7, where m is from 1 to 20.
 
 ; See also
 

Task/Arithmetic-derivative/Arturo/arithmetic-derivative.arturo

@@ -0,0 +1,20 @@
+D: $[x][
+    when [
+        x < 0 -> neg D neg x
+        x = 0 -> 0
+        x = 1 -> 0
+        prime? x -> 1
+        any [
+            m: 2
+            while [0 <> x % m] -> inc 'm
+            n: x / m
+            (n * D m) + m * D n
+        ]
+    ]
+]
+
+(neg 99)..100 | map => D
+              | split.every:10
+              | loop => [loop & 'n -> prints pad to :string n 5 print ""]
+print ""
+loop 20 'n -> print ~"D(10^|n|)/7 = |div D 10^n 7|"

Task/Arithmetic-derivative/C-sharp/arithmetic-derivative.cs

@@ -0,0 +1,30 @@
+using System.Numerics;
+
+static BigInteger Derivative(BigInteger k)
+{
+    if (k < 0) return -Derivative(-k);
+    if (k < 2) return 0;
+    if (k.IsEven) return 2 * Derivative(k / 2) + k / 2;
+    BigInteger m = 3;
+
+    while (m * m <= k && (k % m) != 0)
+        m += 2;
+
+    var n = k / m;
+    if (m * n != k || m == 1 || n == 1) return 1;
+    return n * Derivative(m) + m * Derivative(n);
+}
+
+for (var i = -99; i <= 100; i++)
+{
+    Console.Write($"{Derivative(i),6}");
+    if (i % 10 == 0) Console.WriteLine();
+}
+
+BigInteger p = 1;
+
+for (var n = 1; n <= 20; n++)
+{
+    p *= 10;
+    Console.WriteLine($"⅐ D(10^{n}) = {Derivative(p) / 7}");
+}

Task/Arithmetic-derivative/EasyLang/arithmetic-derivative.easy

@@ -1,18 +1,12 @@
 func lagarias n .
-   if n < 0
-      return -lagarias -n
-   .
-   if n = 0 or n = 1
-      return 0
-   .
+   if n < 0 : return -lagarias -n
+   if n = 0 or n = 1 : return 0
    f = 2
    while n mod f <> 0
       f += 1
    .
    q = n / f
-   if q = 1
-      return 1
-   .
+   if q = 1 : return 1
    return q * lagarias f + f * lagarias q
 .
 for n = -99 to 100