Triangular numbers

use Math::Root:ver<0.0.4>;

sub binomial { [×] ($^n … 0) Z/ 1 .. $^p }

sub polytopic (Int $r, @range) { @range.map: { binomial $_ + $r - 1, $r } }

sub display (@values) {
    my $c = @values.max.chars;
    @values.batch(6)».fmt("%{$c}d").join: "\n";
}

for 2, 'triangular', 3, 'tetrahedral', 4, 'pentatopic', 12, '12-simplex'
  -> $r, $name { say "\nFirst 30 $name numbers:\n" ~ display polytopic $r, ^30 }

say '';

my \ε = FatRat.new: 1, 10**24;

for 7140, 21408696, 26728085384, 14545501785001 {
  say qq:to/R/;
  Roots of $_:
    triangular-root: {.&triangular-root.round:  ε}
   tetrahedral-root: {.&tetrahedral-root.round: ε}
    pentatopic-root: {.&pentatopic-root.round:  ε}
  R
}

Output:

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: 18.876646615928006607901783

Roots of 21408696:
  triangular-root: 6543
 tetrahedral-root: 503.56182697463651404819613
  pentatopic-root: 149.060947375265867484387575

Roots of 26728085384:
  triangular-root: 231205.405565255836957291031961
 tetrahedral-root: 5432
  pentatopic-root: 893.442456751684869888466212

Roots of 14545501785001:
  triangular-root: 5393607.158145172316497304724655
 tetrahedral-root: 44355.777384073256052620916903
  pentatopic-root: 4321