math::numtheory(3tcl)						 Tcl Math Library					     math::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 inte-
       ger 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 proba-
	      bly  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.

KEYWORDS

       number theory, prime

CATEGORY

       Mathematics

COPYRIGHT

       Copyright (c) 2010 Lars Hellstrom <Lars dot Hellstrom at residenset dot net>

math									1.0						     math::numtheory(3tcl)