This is an automated email from the git hooks/post-receive script. ppm-guest pushed a commit to annotated tag v0.36 in repository libmath-prime-util-perl.
commit 08a2f59d1829e17c67946bbebe0553579340ecef Author: Dana Jacobsen <[email protected]> Date: Sat Dec 28 01:46:50 2013 -0800 Fix PP test issues --- lib/Math/Prime/Util.pm | 5 +++-- lib/Math/Prime/Util/PP.pm | 17 +++++++++++++++++ util.c | 2 +- 3 files changed, 21 insertions(+), 3 deletions(-) diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm index 4fb7262..e3d9468 100644 --- a/lib/Math/Prime/Util.pm +++ b/lib/Math/Prime/Util.pm @@ -1721,8 +1721,9 @@ sub _generic_znorder { sub _generic_znprimroot { my($n) = @_; + $n = -$n if defined $n && $n =~ /^-\d+/; # TODO: fix this for string bigints _validate_num($n) || _validate_positive_integer($n); - return if $n <= 0; + return if $n == 0; return $n-1 if $n <= 4; my $a = 1; my $phi = euler_phi($n); @@ -2570,7 +2571,7 @@ __END__ =encoding utf8 -=for stopwords forprimes forcomposites fordivisors Möbius Deléglise totient moebius mertens liouville znorder irand primesieve uniqued k-tuples von SoE pari yafu fonction qui compte le nombre nombres voor PhD superset sqrt(N) gcd(A^M k-th (10001st primegen libtommath +=for stopwords forprimes forcomposites fordivisors Möbius Deléglise totient moebius mertens liouville znorder irand primesieve uniqued k-tuples von SoE pari yafu fonction qui compte le nombre nombres voor PhD superset sqrt(N) gcd(A^M k-th (10001st primegen libtommath kronecker znprimroot =head1 NAME diff --git a/lib/Math/Prime/Util/PP.pm b/lib/Math/Prime/Util/PP.pm index 9911658..f116c35 100644 --- a/lib/Math/Prime/Util/PP.pm +++ b/lib/Math/Prime/Util/PP.pm @@ -2764,6 +2764,23 @@ The following conditions must hold: - C<< k >= 0 >> - C<< n >= 2 >> +=head2 kronecker + +Returns the Kronecker symbol C<(a|n)> for two integers. The possible +return values with their meanings for odd positive C<n> are: + + 0 a = 0 mod n + 1 a is a quadratic residue modulo n (a = x^2 mod n for some x) + -1 a is a quadratic non-residue modulo n + +and the return value is congruent to C<a^((n-1)/2)>. The Kronecker +symbol is an extension of the Jacobi symbol to all integer values of +C<n> from its domain of positive odd values of C<n>. The Jacobi +symbol is itself an extension of the Legendre symbol, which is +only defined for odd prime values of C<n>. This corresponds to Pari's +C<kronecker(a,n)> function and Mathematica's C<KroneckerSymbol[n,m]> +function. + =head1 UTILITY FUNCTIONS diff --git a/util.c b/util.c index 9032028..d2c18e7 100644 --- a/util.c +++ b/util.c @@ -1008,7 +1008,7 @@ UV znorder(UV a, UV n) { } return k; } - + UV znprimroot(UV n) { UV fac[MPU_MAX_FACTORS+1]; UV exp[MPU_MAX_FACTORS+1]; -- 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 [email protected] http://lists.alioth.debian.org/cgi-bin/mailman/listinfo/pkg-perl-cvs-commits
