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Task/P-Adic-numbers-basic/Raku/p-adic-numbers-basic.raku

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+# 20210225 Raku programming solution
+
+#!/usr/bin/env raku
+
+class Padic { has ($.p is default(2), %.v is default({})) is rw ;
+
+   method r2pa (Rat $x is copy, \p, \d) { # Reference: math.stackexchange.com/a/1187037
+      self.p = p ;
+      $x += p**d if $x < 0 ;  # complement
+
+      my $lowerest = 0;
+      my ($num,$den) = $x.nude;
+      while ($den % p) == 0 { $den /= p and $lowerest-- }
+      $x = $num / $den;
+
+      while +self.v < d {
+         my %d = ^p Z=> (( $x «-« ^p ) »/» p )».&{ .denominator % p }; # .kv
+         for %d.keys { self.v.{$lowerest++} = $_ and last if %d{$_} != 0 }
+         $x = ($x - self.v.{$lowerest-1}) / p ;
+      }
+      self
+   }
+
+   method add (Padic \x, \d) {
+      my $div = 0;
+      my $lowerest = (self.v.keys.sort({.Int}).first,
+                         x.v.keys.sort({.Int}).first  ).min ;
+      return Padic.new:
+         p => self.p,
+         v => gather for ^d {
+            my $power = $lowerest + $_;
+            given ((self.v.{$power}//0)+(x.v.{$power}//0)+$div).polymod(x.p)
+               { take ($power, .[0]).Slip and $div = .[1] }
+         }
+   }
+
+   method gist {
+      # en.wikipedia.org/wiki/P-adic_number#Notation
+      # my %H = (0..9) Z=> ('₀'..'₉'); # (0x2080 .. 0x2089);
+      # '⋯ ' ~ self.v ~ ' ' ~ [~] self.p.comb».&{ %H{$_} }
+
+      # express as a series
+      my %H = ( 0…9 ,'-') Z=> ( '⁰','¹','²','³','⁴'…'⁹','⁻');
+      [~] self.v.keys.sort({.Int}).map: {
+         ' + ' ~ self.v.{$_} ~ '*' ~ self.p ~ [~] $_.comb».&{ %H{$_}} }
+      }
+}
+
+my @T;
+for my \D = (
+#`[[ these are not working
+   < 26/25 -109/125 5 4 >,
+   < 6/7 -5/7 10 7 >,
+   < 2/7 -3/7 10 7 >,
+   < 2/7 -1/7 10 7 >,
+   < 34/21 -39034/791 10 9 >,
+#]]