P-Adic numbers, basic: Difference between revisions
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<lang perl6># 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.
$x = ($x - self.v.
}
self
}
method add (Padic \x, \
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 =>
my $power = $lowerest +
given ((self.v.{$power}//0)+(x.v.{$power}//0)+$div).polymod(x.p)
{ take ($power, .[0]).Slip and $div = .[1] }
}
}
method gist {
# en.wikipedia.org/wiki/P-adic_number#Notation
# '⋯ ' ~ self.v ~ ' ' ~ [~] self.p.comb».&{ %H{$_} }
# 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 = (
#`
<
< 26/25 -109/125 5 5 >,▼
< 5/19 -101/384 2 12>,▼
< 6/7 -5/7 10 7 >,
< 2/7 -3/7 10 7 >,
< 2/7 -1/7 10 7 >,
< 34/21 -39034/791 10 9 >,
#`[[[[[ Works
< 11/4 679001/207 2 43>,
< 11/4 679001/207 3 27 >,
< -22/7 46071/379 7 13 >,
< -101/109 583376/6649 61 7>,
< 122/407 -517/1477 7 11>,
▲# ]]]]]
< 2/1 1/1 2 4>,
< 4/1 3/1 2 4>,
Line 1,656 ⟶ 1,676:
< -22/7 46071/379 2 37 >,
< -22/7 46071/379 3 23 >,
< -101/109 583376/6649 2 40>,
< -101/109 583376/6649 32749 3>,
< -25/26 5571/137 7 13>,
#
< 5/8 353/30809 7 11 >,
Line 1,665 ⟶ 1,686:
given @T[0] = Padic.new { say D[0]~' = ', .r2pa: D[0],D[2],D[3] }
given @T[1] = Padic.new { say D[1]~' = ', .r2pa: D[1],D[2],D[3] }
given @T[0].add: @T[1], D[
given @T[2] = Padic.new { .r2pa: D[0]+D[1], D[2], D[3] }
say "Addition result = ", $_.gist
unless (
say 'but ' ~ (D[0]+D[1]).nude.join('/') ~ ' = ' ~ @T[2].gist
}
}
}
</lang>
{{out}}
<pre>
5/8 = + 5*7⁰ + 2*7¹ + 4*7² + 2*7³ + 4*7⁴ + 2*7⁵ + 4*7⁶ + 2*7⁷ + 4*7⁸ + 2*7⁹ + 4*7¹⁰
353/30809 = + 5*7⁰ + 5*7¹ + 4*7² + 3*7³ + 4*7⁴ + 6*7⁵ + 3*7⁶ + 6*7⁷ + 6*7⁸ + 3*7⁹ + 2*7¹⁰
Addition result = + 3*7⁰ + 1*7¹ + 2*7² + 6*7³ + 1*7⁴ + 2*7⁵ + 1*7⁶ + 2*7⁷ + 4*7⁸ + 6*7⁹ + 6*7¹⁰
</pre>
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