[libmath-prime-util-perl] 10/18: Documentation formatting
Partha P. Mukherjee
ppm-guest at moszumanska.debian.org
Thu May 21 18:48:03 UTC 2015
This is an automated email from the git hooks/post-receive script.
ppm-guest pushed a commit to annotated tag v0.26
in repository libmath-prime-util-perl.
commit c9ce3694252ddbf48e85c0aa90a70d17fd6f66d3
Author: Dana Jacobsen <dana at acm.org>
Date: Mon Apr 15 00:32:38 2013 -0700
Documentation formatting
---
lib/Math/Prime/Util.pm | 60 ++++++++++++++++++++++++++------------------------
1 file changed, 31 insertions(+), 29 deletions(-)
diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm
index ce49022..e023cb2 100644
--- a/lib/Math/Prime/Util.pm
+++ b/lib/Math/Prime/Util.pm
@@ -2822,9 +2822,9 @@ A certificate is an array holding an C<n-cert>. An C<n-cert> is one of:
currently means smaller than 2^64.
n,"Pratt",[n-cert, ...],a
- A Pratt certificate. We are given n, the method "Pratt" or "Lucas",
- a list of n-certs that indicate all the unique factors of n-1, and
- an 'a' value to be used in the Lucas primality test.
+ A Pratt certificate. We are given n, the method "Pratt" or
+ "Lucas", a list of n-certs that indicate all the unique factors
+ of n-1, and an 'a' value to be used in the Lucas primality test.
The certificate passes if:
1 all factor n-certs can be verified
2 all n-certs are factors of n-1 and none are missing
@@ -2834,17 +2834,18 @@ A certificate is an array holding an C<n-cert>. An C<n-cert> is one of:
n,"n-1",[n-cert, ...],[a,...]
An n-1 certificate suitable for the generalized Pocklington or the
- BLS75 (Brillhart-Lehmer-Selfridge 1975, theorem 5) test. The proof
- is performed using BLS75 theorem 5 which requires n-1 to be factored
- up to (n/2)^1/3. If n-1 is factored to more than sqrt(n), then the
- conditions are identical to the generalized Pocklington test.
+ BLS75 (Brillhart-Lehmer-Selfridge 1975, theorem 5) test. The
+ proof is performed using BLS75 theorem 5 which requires n-1 to be
+ factored up to (n/2)^1/3. If n-1 is factored to more than
+ sqrt(n), then the conditions are identical to the generalized
+ Pocklington test.
The certificate passes if:
1 all factor n-certs can be verified
2 all factor n-certs are factors of n-1
3 there must be a corresponding 'a' for each factor n-cert
- 4 given A (the factored part of n-1), B = (n-1)/A (the unfactored
- part), s = int(B/(2A)), r = B-s*2A:
- - n < (A+1)(2*A*A+(r-a)A+a) [ n-1 factored to (n/2)^1/3 ]
+ 4 given A (the factored part of n-1), B = (n-1)/A (the
+ unfactored part), s = int(B/(2A)), r = B-s*2A:
+ - n < (A+1)(2*A*A+(r-a)A+a) [ n-1 factored to (n/2)^1/3 ]
- s = 0 or r*r-8s not a perfect square
- A and B are coprime
5 for each pair (f,a) representing a factor n-cert and its 'a':
@@ -2853,10 +2854,10 @@ A certificate is an array holding an C<n-cert>. An C<n-cert> is one of:
n,"AGKM",[ec-block],[ec-block],...
An Elliptic Curve certificate. We are given n, the method "AGKM"
- or "ECPP", and a one or more 6-element blocks representing a standard
- ECPP or Atkin-Goldwasser-Kilian-Morain certificate. The format of
- this n-cert is non-recursive so it can be easily used for similar
- programs such as Sage and GMP-ECPP.
+ or "ECPP", and a one or more 6-element blocks representing a
+ standard ECPP or Atkin-Goldwasser-Kilian-Morain certificate.
+ The format of this n-cert is non-recursive so it can be easily
+ used for similar programs such as Sage and GMP-ECPP.
Every ec-block has 6 elements:
N the N value this block proves prime if q is prime
a value describing the elliptic curve to be used
@@ -3305,25 +3306,26 @@ the configuration, so changing it has no effect. The settings include:
Allows setting of some parameters. Currently the only parameters are:
- xs Allows turning off the XS code, forcing the Pure Perl code
- to be used. Set to 0 to disable XS, set to 1 to re-enable.
- You probably will never want to do this.
+ xs Allows turning off the XS code, forcing the Pure Perl
+ code to be used. Set to 0 to disable XS, set to 1 to
+ re-enable. You probably will never want to do this.
gmp Allows turning off the use of L<Math::Prime::Util::GMP>,
- which means using Pure Perl code for big numbers. Set to
- 0 to disable GMP, set to 1 to re-enable.
+ which means using Pure Perl code for big numbers. Set
+ to 0 to disable GMP, set to 1 to re-enable.
You probably will never want to do this.
- assume_rh Allows functions to assume the Riemann hypothesis is true
- if set to 1. This defaults to 0. Currently this setting
- only impacts prime count lower and upper bounds, but could
- later be applied to other areas such as primality testing.
- A later version may also have a way to indicate whether
- no RH, RH, GRH, or ERH is to be assumed.
-
- irand Takes a code ref to an irand function returning a uniform
- number between 0 and 2**32-1. This will be used for all
- random number generation in the module.
+ assume_rh Allows functions to assume the Riemann hypothesis is
+ true if set to 1. This defaults to 0. Currently this
+ setting only impacts prime count lower and upper
+ bounds, but could later be applied to other areas such
+ as primality testing. A later version may also have a
+ way to indicate whether no RH, RH, GRH, or ERH is to
+ be assumed.
+
+ irand Takes a code ref to an irand function returning a
+ uniform number between 0 and 2**32-1. This will be
+ used for all random number generation in the module.
=head1 FACTORING FUNCTIONS
--
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