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 Hellström <Lars dot Hellstrom at residenset dot net>

math                                                   1.0                                 math::numtheory(3tcl)