- Added the Number is_imprimitive_carmichael(n).

Returns true if `n` is an imprimitive Carmichael numbers, as defined by OEIS: A328935. Example: say 325533792014488126487416882038879701391121.is_imprimitive_carmichael # true The method efficiently tries to factorize large Carmichael numbers, using the `miller_factor(n)` method.
trizen · Aug 26, 2020 · d435c38 · d435c38
1 parent cd9d3ce
commit d435c38
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diff --git a/lib/Sidef/Types/Number/Number.pm b/lib/Sidef/Types/Number/Number.pm
@@ -14494,6 +14494,61 @@ package Sidef::Types::Number::Number {
           : Sidef::Types::Bool::Bool::FALSE;
     }
 
+    sub is_imprimitive_carmichael {    # OEIS: A328935
+        my ($n) = @_;
+
+        __is_int__($$n) || return Sidef::Types::Bool::Bool::FALSE;
+        $n = _any2mpz($$n) // return Sidef::Types::Bool::Bool::FALSE;
+        Math::GMPz::Rmpz_cmp_ui($n, 294409) >= 0 or return Sidef::Types::Bool::Bool::FALSE;
+
+        if ($HAS_PRIME_UTIL && Math::GMPz::Rmpz_fits_ulong_p($n)) {
+
+            $n = Math::GMPz::Rmpz_get_ui($n);
+            Math::Prime::Util::is_carmichael($n) || return Sidef::Types::Bool::Bool::FALSE;
+            my @factors = map { $_ - 1 } Math::Prime::Util::factor($n);
+
+            my $gcd = Math::Prime::Util::gcd(@factors);
+            my $lcm = Math::Prime::Util::lcm(@factors);
+
+            return (
+                    (($gcd * $gcd) > $lcm)
+                    ? Sidef::Types::Bool::Bool::TRUE
+                    : Sidef::Types::Bool::Bool::FALSE
+                   );
+        }
+
+        Math::Prime::Util::GMP::is_carmichael($n) || return Sidef::Types::Bool::Bool::FALSE;
+
+        my @factors = map { $$_ } @{(bless \$n)->miller_factor};
+        my @primes;
+
+        foreach my $k (@factors) {
+            if (Math::Prime::Util::GMP::is_prob_prime($k)) {
+                push @primes, $k;
+            }
+            else {
+                push @primes, Math::Prime::Util::GMP::factor($k);
+            }
+        }
+
+        @factors = map { Math::Prime::Util::GMP::subint($_, 1) } @primes;
+
+        my $gcd = Math::Prime::Util::GMP::gcd(@factors);
+        my $lcm = Math::Prime::Util::GMP::lcm(@factors);
+
+        state $x = Math::GMPz::Rmpz_init_nobless();
+        state $y = Math::GMPz::Rmpz_init_nobless();
+
+        Math::GMPz::Rmpz_set_str($x, $gcd, 10);
+        Math::GMPz::Rmpz_set_str($y, $lcm, 10);
+
+        Math::GMPz::Rmpz_mul($x, $x, $x);
+
+        (Math::GMPz::Rmpz_cmp($x, $y) > 0)
+          ? Sidef::Types::Bool::Bool::TRUE
+          : Sidef::Types::Bool::Bool::FALSE;
+    }
+
     sub is_lucas_carmichael {    # OEIS: A006972
         my ($n) = @_;
 

diff --git a/lib/Sidef/Types/Number/Number.pod b/lib/Sidef/Types/Number/Number.pod
@@ -2406,6 +2406,14 @@ Return the
 
 =cut
 
+=head2 is_imprimitive_carmichael
+
+Number.is_imprimitive_carmichael() -> I<Obj>
+
+Return the
+
+=cut
+
 =head2 is_inf
 
 Number.is_inf() -> I<Obj>
@@ -3250,6 +3258,16 @@ Aliases: I<mfactorial>, I<multi_factorial>
 
 =cut
 
+=head2 miller_factor
+
+Number.miller_factor() -> I<Obj>
+
+Return the
+
+Aliases: I<miller_rabin_factor>
+
+=cut
+
 =head2 miller_rabin_random
 
 Number.miller_rabin_random() -> I<Obj>