  
  
                                    [1X[5XFactInt[0m[1X[0m
  
  
                    [1XAdvanced Methods for Factoring Integers[0m
  
  
                                 Version 1.5.3
  
  
                                 June 16, 2011
  
  
                                  Stefan Kohl
  
  
  
  Stefan Kohl
      Email:    [7Xmailto:stefan@mcs.st-and.ac.uk[0m
      Homepage: [7Xhttp://www.gap-system.org/DevelopersPages/StefanKohl/[0m
      Address:  Department of Mathematics
                University of Vlora
                Lagjja: Pavaresia
                Vlore / Albania
  
  
  
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  [1XAbstract[0m
  This  package  for  [5XGAP[0m 4  provides  a general-purpose integer factorization
  routine,  which  makes  use  of  a  combination  of  factoring  methods.  In
  particular it contains implementations of the following algorithms:
  
  --    Pollard's p-1
  
  --    Williams' p+1
  
  --    Elliptic Curves Method (ECM)
  
  --    Continued Fraction Algorithm (CFRAC)
  
  --    Multiple Polynomial Quadratic Sieve (MPQS)
  
  It  also  contains code by Frank Lübeck for making use of Richard P. Brent's
  tables  of  factors  of integers of the form b^k pm 1. [5XFactInt[0m is completely
  written in the [5XGAP[0m language and contains / requires no external binaries. It
  needs  [5XGAPDoc[0m 1.0  [LN07]  or  higher.  [5XFactInt[0m must be installed in the [11Xpkg[0m
  subdirectory of the [5XGAP[0m distribution.
  
  
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  [1XCopyright[0m
  © 1999 - 2011 by Stefan Kohl.
  
  [5XFactInt[0m is free software: you can redistribute it and/or modify it under the
  terms  of  the  GNU General Public License as published by the Free Software
  Foundation,  either  version 2 of the License, or (at your option) any later
  version.
  
  [5XFactInt[0m  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  General Public License for more
  details.
  
  For  a  copy  of the GNU General Public License, see the file [11XGPL[0m in the [11Xetc[0m
  directory       of       the       [5XGAP[0m       distribution       or       see
  [7Xhttp://www.gnu.org/licenses/gpl.html[0m.
  
  
  -------------------------------------------------------
  [1XAcknowledgements[0m
  I  would  like  to thank Bettina Eick and Steve Linton for their support and
  many interesting discussions.
  
  
  -------------------------------------------------------
  
  
  [1XContents (FactInt)[0X
  
  1 Preface
  2 The General Factorization Routine
    2.1 The method for [10XFactors[0m
      2.1-1 Factors
      2.1-2 FactInt
    2.2 Getting information about the factoring process
      2.2-1 InfoFactInt
  3 The Routines for Specific Factorization Methods
    3.1 Trial division
      3.1-1 FactorsTD
    3.2 Pollard's p-1
      3.2-1 FactorsPminus1
    3.3 Williams' p+1
      3.3-1 FactorsPplus1
    3.4 The Elliptic Curves Method (ECM)
      3.4-1 FactorsECM
    3.5 The Continued Fraction Algorithm (CFRAC)
      3.5-1 FactorsCFRAC
    3.6 The Multiple Polynomial Quadratic Sieve (MPQS)
      3.6-1 FactorsMPQS
  4 How much Time does a Factorization take?
    4.1 Timings for the general factorization routine
    4.2 Timings for the ECM
    4.3 Timings for the MPQS
  
  
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