  
  
                                     [1m[4m[31m[1mCircle[1m[4m[31m[0m
  
  
                   [1m[4m[31mAdjoint groups of finite radical algebras[0m
  
  
                                  Version 1.1
  
  
                                  August 2006
  
  
                              Alexander Konovalov
  
                               Panagiotis Soules
  
  
  
  Alexander Konovalov
      Email:    [34mmailto:konovalov@member.ams.org[0m
      Homepage: [34mhttp://homepages.vub.ac.be/~okonoval/[0m
      Address:  Department of Mathematics
                Zaporozhye National University
                Zaporozhye, 69063 Ukraine
                Current address:
                Department of Mathematics
                Vrije Universiteit Brussel
                Pleinlaan 2, Brussels
                B-1050 Belgium
  
  
  Panagiotis Soules
      Email:    [34mmailto:psoules@math.uoa.gr[0m
      Address:  Department of Mathematics
                National and Capodistrian University of Athens
                Panepistimioupolis, GR-15784, Athens, Greece
  
  
  
  -------------------------------------------------------
  [1m[4m[31mAbstract[0m
  The  [1mGAP[0m4  package  [1mCircle[0m extends the [1mGAP[0m functionality for computations in
  adjoint  groups of associative rings. It provides functionality to construct
  circle  objects  that will respect the circle multiplication r * s = r + s +
  rs,  create  multiplicative  groups,  generated by such objects, and compute
  groups  of  elements,  invertible with respect to this operation, for finite
  radical algebras and finite associative rings without one.
  
  
  -------------------------------------------------------
  [1m[4m[31mCopyright[0m
  (C) 2006 by Alexander Konovalov and Panagiotis Soules
  
  [1mCircle[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.      For      details,      see      the     FSF's     own     site
  [34mhttp://www.gnu.org/licenses/gpl.html[0m.
  
  If  you  obtained [1mCircle[0m, we would be grateful for a short notification sent
  to one of the authors.
  
  If  you  publish  a  result  which  was partially obtained with the usage of
  [1mCircle[0m, please cite it in the following form:
  
  A.  Konovalov,  P.  Soules.  [22m[36mCircle --- Adjoint groups of associative rings,
  Version 1.1;[0m 2006 ([34mhttp://homepages.vub.ac.be/~okonoval/circle.htm[0m).
  
  
  -------------------------------------------------------
  [1m[4m[31mAcknowledgements[0m
  We acknowledge very much Alexander Hulpke for helpful comments and advise.
  
  
  -------------------------------------------------------
  
  
  [1m[4m[31mContent (Circle)[0m
  
  1. Introduction
    1.1 General aims
    1.2 Installation and system requirements
  2. [1mCircle[0m functions
    2.1 Circle objects
      2.1-1 CircleObject
      2.1-2 UnderlyingRingElement
      2.1-3 IsCircleObject
      2.1-4 IsPositionalObjectOneSlotRep
      2.1-5 CircleFamily
    2.2 Operations with circle objects
      2.2-1 OneOp
      2.2-2 InverseOp
      2.2-3 IsUnit
      2.2-4 IsCircleUnit
    2.3 Construction of the adjoint group
      2.3-1 AdjointGroup
    2.4 Service functions
      2.4-1 InfoCircle
      2.4-2 CIRCLEBuildManual
      2.4-3 CIRCLEBuildManualHTML
  3. A sample computation with [1mCircle[0m
  
  
  -------------------------------------------------------
