Package COM.INFORMATIMAGO.COMMON-LISP.ARITHMETIC.PRIMES


Compute primes and factorize numbers.


License:

    AGPL3

    Copyright Pascal J. Bourguignon 2003 - 2012

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU Affero General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Affero General Public License for more details.

    You should have received a copy of the GNU Affero General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>

(compute-primes-to n)

function

DO:     Compute an Eratostene sieve to find all prime numbers up to N.
RETURN: An array of prime numbers.

(divisors n)

function

RETURN: a list of divisors of N from 1 to N.

(factorize n &optional primes)

function

N:        an INTEGER
PRIMES:   a VECTOR of prime factors sorted in increasing order.
RETURN:   a SEXP of the form: (* uncomensurate-factor
                                 [ prime | (EXPT prime exponent) ]… [ -1 ] )

(print-factorization exponents primes)

function

EXPONENTS:  A sequence: ( uncommensurate-factor  exponents… )
PRIMES:     A sequence: ( prime-factors… )
PRE:        (= (LENGTH EXPONENTS) (1+ (LENGTH PRIMES)))
DO:         Prints on *STANDARD-OUTPUT* an expression of the number.

(str-decode num primes)

function

RETURN:  A string decoding the integer NUM factorized with the PRIMES.

(str-encode str primes)

function

RETURN:  An integer encoding the string STR factorized with the PRIMES.