[libmath-prime-util-perl] 10/40: Documentation updates

[Partha P. Mukherjee]

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ppm-guest pushed a commit to annotated tag v0.30
in repository libmath-prime-util-perl.

commit be92b208a50c414b9f323bd2bcfb44af089c7c95
Author: Dana Jacobsen <dana at acm.org>
Date:   Mon Jun 24 15:57:19 2013 -0700

    Documentation updates
---
 lib/Math/Prime/Util.pm    | 13 ++++++++++---
 lib/Math/Prime/Util/PP.pm | 10 +++++++++-
 2 files changed, 19 insertions(+), 4 deletions(-)

diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm
index 4278d5a..a06f5b1 100644
--- a/lib/Math/Prime/Util.pm
+++ b/lib/Math/Prime/Util.pm
@@ -2737,6 +2737,7 @@ L</is_prime> return probable prime results using the strong Baillie-PSW test,
 which has had no counterexample found since it was published in 1980.
 
 
+
 =head2 primes
 
 Returns all the primes between the lower and upper limits (inclusive), with
@@ -2985,7 +2986,7 @@ function.
 
 =head2 miller_rabin
 
-An alias for C<is_strong_pseudoprime>.  This name is being deprecated.
+An alias for C<is_strong_pseudoprime>.  This name is deprecated.
 
 =head2 is_lucas_pseudoprime
 
@@ -3008,12 +3009,18 @@ L<OEIS A217255|http://oeis.org/A217255>.
 
 Takes a positive number as input, and returns 1 if the input passes the extra
 strong Lucas test (as defined in
-L<Grantham 2000|http://www.ams.org/mathscinet-getitem?mr=1680879>).
+L<Grantham 2000|http://www.ams.org/mathscinet-getitem?mr=1680879>).  Parameter
+selection is done by incrementing C<P> from C<3> until C<jacobi(D,n) = -1>.
 This has slightly more restrictive conditions than the strong Lucas test,
 but uses different starting parameters so is not directly comparable.
 Removing primes, this produces the sequence
 L<OEIS A217719|http://oeis.org/A217719>.
 
+The extra strong Lucas test typically performs 20 to 30% faster than the
+strong Lucas test, and produces fewer pseudoprimes.  There are no
+counterexamples below C<2^64> with BPSW using any of the Lucas tests, and
+no published counterexamples of any size.
+
 =head2 is_frobenius_underwood_pseudoprime
 
 Takes a positive number as input, and returns 1 if the input passes the minimal
@@ -3211,7 +3218,7 @@ However AKS in general is far too slow to be of practical use.  R.P. Brent,
 
   my($U, $V, $Qk) = lucas_sequence($n, $P, $Q, $k)
 
-Computes C<U_k>, C<V_k>, and C<Q_k> for the Lucas seqence defined by
+Computes C<U_k>, C<V_k>, and C<Q_k> for the Lucas sequence defined by
 C<P>,C<Q>, modulo C<n>.  The modular Lucas sequence is used in a
 number of primality tests and proofs.
 
diff --git a/lib/Math/Prime/Util/PP.pm b/lib/Math/Prime/Util/PP.pm
index 8aab410..8a60270 100644
--- a/lib/Math/Prime/Util/PP.pm
+++ b/lib/Math/Prime/Util/PP.pm
@@ -2842,6 +2842,14 @@ L<Grantham 2000|http://www.ams.org/mathscinet-getitem?mr=1680879>).
 This has slightly more restrictive conditions than the strong Lucas test,
 but uses different starting parameters so is not directly comparable.
 
+=head2 is_frobenius_underwood_pseudoprime
+
+Takes a positive number as input, and returns 1 if the input passes the minimal
+lambda+2 test (see Underwood 2012 "Quadratic Compositeness Tests"), where
+C<(L+2)^(n-1) = 5 + 2x mod (n, L^2 - Lx + 1)>.  The computational cost for this
+is between the cost of 2 and 3 strong pseudoprime tests.  There are no known
+counterexamples, but this is not a well studied test.
+
 =head2 is_aks_prime
 
 Takes a positive number as input, and returns 1 if the input can be proven
@@ -2866,7 +2874,7 @@ composite, though it should not be anywhere near as long as the Lucas test.
 
   my($U, $V, $Qk) = lucas_sequence($n, $P, $Q, $k)
 
-Computes C<U_k>, C<V_k>, and C<Q_k> for the Lucas seqence defined by
+Computes C<U_k>, C<V_k>, and C<Q_k> for the Lucas sequence defined by
 C<P>,C<Q>, modulo C<n>.  The modular Lucas sequence is used in a
 number of primality tests and proofs.
 

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