Arithmetic derivative: Difference between revisions
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D(10000000000000000) / 7 = 16000000000000000
D(100000000000000000) / 7 = 170000000000000000
</pre>
=={{header|MiniScript}}==
{{Trans|ALGOL 68|via Lua}}
<syntaxhighlight lang="miniscript">
lagarias = function (n) // Lagarias arithmetic derivative
if n < 0 then
return -lagarias (-n)
else if n == 0 or n == 1 then
return 0
else
smallPf = function (j, k) // Smallest prime factor
if j % k == 0 then
return k
else
return smallPf (j, k + 1)
end if
end function
f = smallPf (n, 2)
q = floor (n / f)
if q == 1 then
return 1
else
return q * lagarias (f) + f * lagarias (q)
end if
end if
end function
fmt6 = function (n) // return a 6 character string representation of n
s = str( n )
if s.len > 5 then
return s
else
return ( " " * ( 6 - s.len ) ) + s
end if
end function
ad = ""
for n in range( -99, 100 )
ad = ad + " " + fmt6( lagarias (n) )
if n % 10 == 0 then
print( ad )
ad = ""
end if
end for
print()
for n in range( 1, 17 ) // 18, 19 and 20 would overflow ????? TODO: check
m = 10 ^ n
print( "D(" + str(m) + ") / 7 = " + str( floor (lagarias (m) / 7) ) )
end for
</syntaxhighlight>
{{out}}
<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
0 1 1 4 1 5 1 12 6 7
1 16 1 9 8 32 1 21 1 24
10 13 1 44 10 15 27 32 1 31
1 80 14 19 12 60 1 21 16 68
1 41 1 48 39 25 1 112 14 45
20 56 1 81 16 92 22 31 1 92
1 33 51 192 18 61 1 72 26 59
1 156 1 39 55 80 18 71 1 176
108 43 1 124 22 45 32 140 1 123
20 96 34 49 24 272 1 77 75 140
D(10) / 7 = 1
D(100) / 7 = 20
D(1000) / 7 = 300
D(10000) / 7 = 4000
D(100000) / 7 = 50000
D(1000000) / 7 = 600000
D(10000000) / 7 = 7000000
D(100000000) / 7 = 80000000
D(1000000000) / 7 = 900000000
D(10000000000) / 7 = 10000000000
D(100000000000) / 7 = 110000000000
D(1000000000000) / 7 = 1200000000000
D(10000000000000) / 7 = 13000000000000
D(100000000000000) / 7 = 140000000000000
D(1000000000000000) / 7 = 1500000000000000
D(10000000000000000) / 7 = 16000000000000000
D(100000000000000000) / 7 = 170000000000000000
D(1000000000000000000) / 7 = 1800000000000000000
D(10000000000000000000) / 7 = 19000000000000000000
D(100000000000000000000) / 7 = 200000000000000000000
</pre>
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