math::numtheory(n)             Tcl Math Library             math::numtheory(n)



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NAME
       math::numtheory - Number Theory

SYNOPSIS
       package require Tcl  ?8.5?

       package require math::numtheory  ?1.0?

       math::numtheory::isprime N ?option value ...?

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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.

KEYWORDS
       number theory, prime

CATEGORY
       Mathematics

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




math                                  1.0                   math::numtheory(n)
