math::numtheory(n) Tcl Math Library math::numtheory(n)______________________________________________________________________________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
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 repe‐
tition 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 Hellstr�m <Lars dot Hellstrom at residenset dot net>
math 1.0 math::numtheory(n)
