P-Adic numbers, basic: Difference between revisions

Line 1,602:

<lang perl6># 20210225 Raku programming solution

#!/usr/bin/env raku

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class Padic { has @.v is default([]) is rw ;

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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;

while +self.v < d {

my %d = ^p Z=> (( $x «-« ^p ) »/» p )».&{ .denominator % p };

my %d = ^p Z=> (( $x «-« ^p ) »/» p )».&{ .denominator % p }; # .kv

for %d.keys { self.v.unshift: $_ and last if %d{$_} != 0 }

$x = ($x - self.v.first) / p

}

self.v

self

}

method add (Padic \x, \p) {

my $div = 0;

return Padic.new:

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reverse gather for ( self.v.reverse Z x.v.reverse )».sum {

~~take ( $_ + $div ) %~~ p ~~and $div~~ = ~~$_ div~~ p

p => p,

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v => reverse gather for ( self.v.reverse Z x.v.reverse )».sum

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}

{ take ( $_ + $div ) % p and $div = $_ div p } # .polymod

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}

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{$_} }

}

~~given~~ my $a = ~~Padic.new { say .r2pa:~~ 5/8, 7, 11 }

my \DATA = < 5/8 353/30809 47 11 > ;

given my $a = Padic.new { say .r2pa: DATA[0], DATA[2], DATA[3] }

given my $b = Padic.new { say .r2pa: ~~353/30809~~, 7, 11 }

given my $b = Padic.new { say .r2pa: DATA[1], DATA[2], DATA[3] }

say $a.add: $b, 7;

say $a.add: $b, DATA[2] ;

given my $c = Padic.new { say .r2pa: ~~47099/10977~~, 7, 11 }

given my $c = Padic.new { say .r2pa: DATA[0]+DATA[1] , DATA[2], DATA[3] }

</lang>

<pre>[4 2 4 2 4 2 4 2 4 2 5]

<pre>… 29 17 29 17 29 17 29 17 29 17 30 ₄₇

[2 3 6 6 3 6 4 3 4 5 5]

… 4 13 42 28 43 43 34 36 25 20 1 ₄₇

(6 6 4 2 1 2 1 6 2 1 3)

… 33 31 24 46 26 14 17 7 7 37 31 ₄₇

[6 6 4 2 1 2 1 6 2 1 3]</pre>

… 33 31 24 46 26 14 17 7 7 37 31 ₄₇</pre>

=={{header|Wren}}==