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.