95 lines
2.6 KiB
Raku
95 lines
2.6 KiB
Raku
# 20210225 Raku programming solution
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#!/usr/bin/env raku
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class Padic { has ($.p is default(2), %.v is default({})) is rw ;
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method r2pa (Rat $x is copy, \p, \d) { # Reference: math.stackexchange.com/a/1187037
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self.p = p ;
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$x += p**d if $x < 0 ; # complement
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my $lowerest = 0;
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my ($num,$den) = $x.nude;
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while ($den % p) == 0 { $den /= p and $lowerest-- }
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$x = $num / $den;
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while +self.v < d {
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my %d = ^p Z=> (( $x «-« ^p ) »/» p )».&{ .denominator % p }; # .kv
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for %d.keys { self.v.{$lowerest++} = $_ and last if %d{$_} != 0 }
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$x = ($x - self.v.{$lowerest-1}) / p ;
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}
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self
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}
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method add (Padic \x, \d) {
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my $div = 0;
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my $lowerest = (self.v.keys.sort({.Int}).first,
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x.v.keys.sort({.Int}).first ).min ;
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return Padic.new:
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p => self.p,
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v => gather for ^d {
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my $power = $lowerest + $_;
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given ((self.v.{$power}//0)+(x.v.{$power}//0)+$div).polymod(x.p)
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{ take ($power, .[0]).Slip and $div = .[1] }
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}
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}
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method gist {
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# en.wikipedia.org/wiki/P-adic_number#Notation
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# my %H = (0..9) Z=> ('₀'..'₉'); # (0x2080 .. 0x2089);
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# '⋯ ' ~ self.v ~ ' ' ~ [~] self.p.comb».&{ %H{$_} }
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# express as a series
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my %H = ( 0…9 ,'-') Z=> ( '⁰','¹','²','³','⁴'…'⁹','⁻');
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[~] self.v.keys.sort({.Int}).map: {
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' + ' ~ self.v.{$_} ~ '*' ~ self.p ~ [~] $_.comb».&{ %H{$_}} }
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}
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}
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my @T;
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for my \D = (
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#`[[ these are not working
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< 26/25 -109/125 5 4 >,
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< 6/7 -5/7 10 7 >,
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< 2/7 -3/7 10 7 >,
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< 2/7 -1/7 10 7 >,
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< 34/21 -39034/791 10 9 >,
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#]]
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#`[[[[[ Works
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< 11/4 679001/207 2 43>,
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< 11/4 679001/207 3 27 >,
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< 5/19 -101/384 2 12>,
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< -22/7 46071/379 7 13 >,
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< -7/5 99/70 7 4> ,
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< -101/109 583376/6649 61 7>,
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< 122/407 -517/1477 7 11>,
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< 2/1 1/1 2 4>,
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< 4/1 3/1 2 4>,
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< 4/1 3/1 2 5>,
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< 4/9 8/9 5 4>,
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< 11/4 679001/207 11 13 >,
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< 1/4 9263/2837 7 11 >,
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< 49/2 -4851/2 7 6 >,
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< -9/5 27/7 3 8>,
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< -22/7 46071/379 2 37 >,
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< -22/7 46071/379 3 23 >,
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< -101/109 583376/6649 2 40>,
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< -101/109 583376/6649 32749 3>,
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< -25/26 5571/137 7 13>,
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#]]]]]
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< 5/8 353/30809 7 11 >,
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) -> \D {
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given @T[0] = Padic.new { say D[0]~' = ', .r2pa: D[0],D[2],D[3] }
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given @T[1] = Padic.new { say D[1]~' = ', .r2pa: D[1],D[2],D[3] }
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given @T[0].add: @T[1], D[3] {
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given @T[2] = Padic.new { .r2pa: D[0]+D[1], D[2], D[3] }
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say "Addition result = ", $_.gist; #
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unless ( $_.v.Str eq @T[2].v.Str ) {
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say 'but ' ~ (D[0]+D[1]).nude.join('/') ~ ' = ' ~ @T[2].gist
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}
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}
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}
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