Arithmetic derivative: Difference between revisions

=={{header|Perl}}==

{{trans|J}}

{{libheader|ntheory}}

<lang perl>use v5.36;

use bigint;

no warnings 'uninitialized';

use List::Util <sum max>;

use ntheory 'factor';

sub table ($c, @V) { my $t = $c * (my $w = 2 + length max @V); ( sprintf( ('%'.$w.'d')x@V, @V) ) =~ s/.{1,$t}\K/\n/gr }

sub D ($n) {

my %f;

return 0 if $n == 0;

$f{$_}++ for factor (my $nabs = abs $n);

my $s = sum map { $nabs * $f{$_} / $_ } keys %f;

$n > 0 ? $s : -$s;

}

say table map { D $_ } -99 .. 100;

say join "\n", map { sprintf('D(10**%-2d) / 7 == ', $_) . D(10**$_) / 7 } 1 .. 20;

</lang>

{{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**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>