  
  
                                     [1m[4m[31m[1mCircle[1m[4m[31m[0m
  
  
                   [1m[4m[31mAdjoint groups of finite radical algebras[0m
  
  
                                  Version 1.2
  
  
                                   April 2007
  
  
                              Alexander Konovalov
  
                               Panagiotis Soules
  
  
  
  Alexander Konovalov
      Email:    [34mmailto:konovalov@member.ams.org[0m
      Homepage: [34mhttp://www.cs.st-andrews.ac.uk/~alexk/[0m
      Address:  School of Computer Science
                University of St Andrews
                Jack Cole Building, North Haugh,
                St Andrews, Fife, KY16 9SX, Scotland
  
  
  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, and to compute adjoint semigroups and adjoint groups of finite rings.
  
  
  -------------------------------------------------------
  [1m[4m[31mCopyright[0m
  (C) 2006-2007 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 1.2;[0m 2007 ([34mhttp://www.cs.st-andrews.ac.uk/~alexk/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. Implementing circle objects
    2.1 First attempts
    2.2 Defining circle objects
    2.3 Installing operations for circle objects
  3. [1mCircle[0m functions
    3.1 Circle objects
      3.1-1 CircleObject
      3.1-2 UnderlyingRingElement
      3.1-3 IsCircleObject
      3.1-4 IsPositionalObjectOneSlotRep
      3.1-5 CircleFamily
    3.2 Operations with circle objects
      3.2-1 One
      3.2-2 InverseOp
      3.2-3 IsUnit
      3.2-4 IsCircleUnit
    3.3 Construction of the adjoint semigroup and adjoint group
      3.3-1 AdjointSemigroup
      3.3-2 AdjointGroup
    3.4 Service functions
      3.4-1 InfoCircle
      3.4-2 CIRCLEBuildManual
      3.4-3 CIRCLEBuildManualHTML
  4. A sample computation with [1mCircle[0m
  
  
  -------------------------------------------------------
