numtheory(3tcl)
NAME
math::numtheory - Number Theory
SYNOPSIS
package require Tcl ?8.5? package require math::numtheory ?1.0? math::numtheory::isprime N ?option value ...? ______________________________________________________________________________
DESCRIPTION
This package is for collecting various number-theoretic operations,
though at the moment it only provides that of testing whether an
integer is a prime.
math::numtheory::isprime N ?option value ...?
The isprime command tests whether the integer N is a prime,
returning a boolean true value for prime N and a boolean false
value for non-prime N. The formal definition of prime' used is
the conventional, that the number being tested is greater than 1
and only has trivial divisors.
To be precise, the return value is one of 0 (if N is definitely
not a prime), 1 (if N is definitely a prime), and on (if N is
probably prime); the latter two are both boolean true values.
The case that an integer may be classified as "probably prime"
arises because the Miller-Rabin algorithm used in the test
implementation is basically probabilistic, and may if we are
unlucky fail to detect that a number is in fact composite.
Options may be used to select the risk of such "false positives"
in the test. 1 is returned for "small" N (which currently means
N < 118670087467), where it is known that no false positives are
possible.
The only option currently defined is:
-randommr repetitions
which controls how many times the Miller-Rabin test
should be repeated with randomly chosen bases. Each
repetition reduces the probability of a false positive by
a factor at least 4. The default for repetitions is 4.
Unknown options are silently ignored.
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math :: numtheory of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas for enhancements you may have for either package and/or documentation.
KEYWORDS
number theory, prime
CATEGORY
Mathematics
COPYRIGHT
Copyright (c) 2010 Lars Hellstrm <Lars dot Hellstrom at residenset dot net>
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