48 lines
1.3 KiB
Raku
48 lines
1.3 KiB
Raku
my @primes := 2, |grep *.is-prime, (3,5,7...*);
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sub factor($a is copy) {
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gather {
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for @primes -> $p {
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my $j = 0;
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while $a %% $p {
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$a div= $p;
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$j++;
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}
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take $p => $j if $j > 0;
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last if $a < $p * $p;
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}
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take $a => 1 if $a > 1;
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}
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}
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sub mo-prime($a, $p, $e) {
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my $m = $p ** $e;
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my $t = ($p - 1) * ($p ** ($e - 1)); # = Phi($p**$e) where $p prime
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my @qs = 1;
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for factor($t) -> $f {
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@qs = flat @qs.map(-> $q { (0..$f.value).map(-> $j { $q * $f.key ** $j }) });
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}
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@qs.sort.first(-> $q { expmod( $a, $q, $m ) == 1});
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}
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sub mo($a, $m) {
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$a gcd $m == 1 || die "$a and $m are not relatively prime";
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[lcm] flat 1, factor($m).map(-> $r { mo-prime($a, $r.key, $r.value) });
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}
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sub MAIN("test") {
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use Test;
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for (10, 21, 25, 150, 1231, 123141, 34131) -> $n {
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is ([*] factor($n).map(-> $pair { $pair.key ** $pair.value })), $n, "$n factors correctly";
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}
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is mo(37, 1000), 100, 'mo(37,1000) == 100';
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my $b = 10**20-1;
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is mo(2, $b), 3748806900, 'mo(2,10**20-1) == 3748806900';
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is mo(17, $b), 1499522760, 'mo(17,10**20-1) == 1499522760';
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$b = 100001;
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is mo(54, $b), 9090, 'mo(54,100001) == 9090';
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}
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