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commit 3caff7ceadaa1bfee0adb6ce4ea3f1975e7299cc Author: Dana Jacobsen <d...@acm.org> Date: Wed Feb 27 09:42:14 2013 -0800 Slight doc change for moebius/phi/lambda/M --- lib/Math/Prime/Util.pm | 26 +++++++++++++------------- t/80-pp.t | 6 +++++- 2 files changed, 18 insertions(+), 14 deletions(-) diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm index f63495f..7e76610 100644 --- a/lib/Math/Prime/Util.pm +++ b/lib/Math/Prime/Util.pm @@ -2414,8 +2414,8 @@ primality tests. say "$n is square free" if moebius($n) != 0; $sum += moebius($_) for (1..200); say "Mertens(200) = $sum"; -Returns the Möbius function (also called the Moebius, Mobius, or MoebiusMu -function) for a non-negative integer input. This function is 1 if +Returns μ(n), the Möbius function (also called the Moebius, Mobius, or +MoebiusMu function) for a non-negative integer input. This function is 1 if C<n = 1>, 0 if C<n> is not square free (i.e. C<n> has a repeated factor), and C<-1^t> if C<n> is a product of C<t> distinct primes. This is an important function in prime number theory. Like SAGE, we define @@ -2432,7 +2432,7 @@ which is a segmented version of Lioen and van de Lune (1994) algorithm 3.2. say "Mertens(10M) = ", mertens(10_000_000); # = 1037 -Returns the Mertens function of the positive non-zero integer input. This +Returns M(n), the Mertens function for a non-negative integer input. This function is defined as C<sum(moebius(1..n))>. This is a much more efficient solution for larger inputs. For example, computing Mertens(100M) takes: @@ -2457,10 +2457,10 @@ algorithms can lead to a faster solution. say "The Euler totient of $n is ", euler_phi($n); -Returns the Euler totient function (also called Euler's phi or phi function) -for an integer value. This is an arithmetic function that counts the number -of positive integers less than or equal to C<n> that are relatively prime to -C<n>. Given the definition used, C<euler_phi> will return 0 for all +Returns φ(n), the Euler totient function (also called Euler's phi or phi +function) for an integer value. This is an arithmetic function that counts +the number of positive integers less than or equal to C<n> that are relatively +prime to C<n>. Given the definition used, C<euler_phi> will return 0 for all C<n E<lt> 1>. This follows the logic used by SAGE. Mathematic/WolframAlpha also returns 0 for input 0, but returns C<euler_phi(-n)> for C<n E<lt> 0>. @@ -2486,12 +2486,12 @@ the Dedikind psi function, where C<psi(n) = J(2,n) / J(1,n)>. say "exp(lambda($_)) = ", exp_mangoldt($_) for 1 .. 100; -The Mangoldt function Λ(n) (also known as von Mangoldt's function) is equal -to log p if n is prime or a power of a prime, and 0 otherwise. We return -the exponential so all results are integers. Hence the return value -for C<exp_mangoldt> is: - C<p> if C<n = p^m> for some prime C<p> and integer C<m E<gt>= 1> - 1 otherwise. +Returns Λ(n), the Mangoldt function (also known as von Mangoldt's function) for +an integer value. It is equal to log p if n is prime or a power of a prime, +and 0 otherwise. We return the exponential so all results are integers. + Hence the return value for C<exp_mangoldt> is: + C<p> if C<n = p^m> for some prime C<p> and integer C<m E<gt>= 1> + 1 otherwise. =head2 divisor_sum diff --git a/t/80-pp.t b/t/80-pp.t index 1ec86d5..06f7c92 100644 --- a/t/80-pp.t +++ b/t/80-pp.t @@ -226,7 +226,7 @@ plan tests => 1 + 1 + 1 + # factor 8 + 4*3 + # factoring subs 10 + # AKS - 0; + 1; use Math::Prime::Util qw/primes prime_count_approx prime_count_lower/; use Math::BigInt try => 'GMP'; @@ -253,6 +253,8 @@ require_ok 'Math::Prime::Util::PP'; ############################################################################### +$_ = 'this should not change'; + { my %small_primes = map { $_ => 1 } @small_primes; my @isprime = map { is_prime($_) } (0 .. 1086); @@ -471,6 +473,8 @@ SKIP: { is( is_aks_prime(74513), 0, "AKS: 74513 is composite (failed anr test)" ); } +is( $_, 'this should not change', "Nobody clobbered \$_" ); + ############################################################################### sub parse_range { -- Alioth's /usr/local/bin/git-commit-notice on /srv/git.debian.org/git/pkg-perl/packages/libmath-prime-util-perl.git _______________________________________________ Pkg-perl-cvs-commits mailing list Pkg-perl-cvs-commits@lists.alioth.debian.org http://lists.alioth.debian.org/cgi-bin/mailman/listinfo/pkg-perl-cvs-commits