Triangular numbers: Difference between revisions
Added Perl
Thundergnat (talk | contribs) m (→{{header|Raku}}: Math::Root now includes the r-simplex root routines) |
SqrtNegInf (talk | contribs) (Added Perl) |
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tetrahedral-root : 44355.777376558433
pentatopic -root : 4321.000000000000
</pre>
=={{header|Perl}}==
{{trans|Raku}}
<syntaxhighlight lang="perl" line>
use v5.36;
use experimental <builtin for_list>;
use Math::AnyNum <binomial cbrt max round>;
sub table { my $t = 6 * (my $c = 1 + length max @_); ( sprintf( ('%'.$c.'d')x@_, @_) ) =~ s/.{1,$t}\K/\n/gr }
sub triangular_root ($x) {
round( (sqrt(8 * $x + 1) - 1) / 2, -3);
}
sub tetrahedral_root ($x) {
round(
cbrt(3 * $x + sqrt 9 * $x**2 - 1/27) +
cbrt(3 * $x - sqrt 9 * $x**2 - 1/27) - 1,
-3)
}
sub pentatopic_root ($x) {
round( (sqrt(5 + 4 * sqrt 24 * $x + 1) - 3) / 2, -3)
}
sub polytopic ($r, @range) { map { binomial $_ + $r - 1, $r } @range }
for my($r,$label) (2, 'triangular', 3, 'tetrahedral', 4, 'pentatopic', 12, '12-simplex') {
say "First 30 $label numbers:\n" . table polytopic $r, 0..29
}
for (7140, 21408696, 26728085384, 14545501785001) {
printf "Roots of $_:
triangular-root: %s
tetrahedral-root: %s
pentatopic-root: %s\n\n",
triangular_root($_), tetrahedral_root($_), pentatopic_root($_);
}
</syntaxhighlight>
{{out}}
<pre>
First 30 triangular numbers:
0 1 3 6 10 15
21 28 36 45 55 66
78 91 105 120 136 153
171 190 210 231 253 276
300 325 351 378 406 435
First 30 tetrahedral numbers:
0 1 4 10 20 35
56 84 120 165 220 286
364 455 560 680 816 969
1140 1330 1540 1771 2024 2300
2600 2925 3276 3654 4060 4495
First 30 pentatopic numbers:
0 1 5 15 35 70
126 210 330 495 715 1001
1365 1820 2380 3060 3876 4845
5985 7315 8855 10626 12650 14950
17550 20475 23751 27405 31465 35960
First 30 12-simplex numbers:
0 1 13 91 455 1820
6188 18564 50388 125970 293930 646646
1352078 2704156 5200300 9657700 17383860 30421755
51895935 86493225 141120525 225792840 354817320 548354040
834451800 1251677700 1852482996 2707475148 3910797436 5586853480
Roots of 7140:
triangular-root: 119
tetrahedral-root: 34
pentatopic-root: 18.877
Roots of 21408696:
triangular-root: 6543
tetrahedral-root: 503.561
pentatopic-root: 149.061
Roots of 26728085384:
triangular-root: 231205.406
tetrahedral-root: 5432
pentatopic-root: 893.442
Roots of 14545501785001:
triangular-root: 5393607.158
tetrahedral-root: 44355.777
pentatopic-root: 4321
</pre>
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