GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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  1 Introduction
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  1.1 General aims
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  Let  R  be  an  associative  ring,  not necessarily with one. The set of all
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  elements  of  R  forms  a monoid with the neutral element 0 from R under the
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  operation r ⋅ s = r + s + rs defined for all r and s of R. This operation is
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  called  the  circle  multiplication,  and  it  is  also  known  as  the star
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  multiplication.  The monoid of elements of R under the circle multiplication
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  is  called  the  adjoint semigroup of R and is denoted by R^ad. The group of
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  all  invertible elements of this monoid is called the adjoint group of R and
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  is denoted by R^*.
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  These  notions  naturally lead to a number of questions about the connection
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  between  a  ring and its adjoint group, for example, how the ring properties
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  will  determine  properties of the adjoint group; which groups can appear as
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  adjoint groups of rings; which rings can have adjoint groups with prescribed
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  properties, etc.
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  For  example,  V. O. Gorlov in [Gor95] gives a full list of finite nilpotent
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  algebras R, such that R^2 ne 0 and the adjoint group of R is metacyclic (but
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  not cyclic).
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  S.  V.  Popovich  and  Ya.  P. Sysak in [PS97] characterize all quasiregular
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  algebras   such  that  all  subgroups  of  their  adjoint  group  are  their
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  subalgebras.  In  particular,  they  show that all algebras of such type are
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  nilpotent with nilpotency index at most three.
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  Various  connections between properties of a ring and its adjoint group were
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  considered by O. D. Artemovych and Yu. B. Ishchuk in [AI97].
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  B.  Amberg  and  L.  S.  Kazarin  in  [AK00]  give  the  description  of all
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  nonisomorphic  finite  p-groups  that can occur as the adjoint group of some
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  nilpotent p-algebra of the dimension at most 5.
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  In  [AS01]  B.  Amberg  and Ya. P. Sysak give a survey of results on adjoint
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  groups  of  radical rings, including such topics as subgroups of the adjoint
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  group;  nilpotent  groups  which are isomorphic to the adjoint group of some
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  radical  ring;  adjoint groups of finite nilpotent $p$-algebras. The authors
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  continued their investigations in further papers [AS02] and [AS04].
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  In  [KS04]  L. S. Kazarin and P. Soules study associative nilpotent algebras
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  over  a  field  of  positive  characteristic whose adjoint group has a small
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  number of generators.
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  The  main objective of the proposed GAP4 package Circle is to extend the GAP
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  functionality  for  computations  in  adjoint groups of associative rings to
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  make  it  possible  to use the GAP system for the investigation of the above
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  described questions.
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  Circle  provides functionality to construct circle objects that will respect
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  the  circle  multiplication  r  ⋅  s  =  r  +  s + rs, create multiplicative
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  structures,  generated  by  such objects, and compute adjoint semigroups and
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  adjoint groups of finite rings.
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  Also  we hope that the package will be useful as an example of extending the
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  GAP  system  with new multiplicative objects. Relevant details are explained
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  in the next chapter of the manual.
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  1.2 Installation and system requirements
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  Circle  does  not  use  external  binaries  and,  therefore,  works  without
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  restrictions  on  the  type  of  the  operating  system. This version of the
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  package  is  designed for GAP4.5 and no compatibility with previous releases
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  of GAP4 is guaranteed.
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  To  use  the  Circle online help it is necessary to install the GAP4 package
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  GAPDoc  by  Frank Lübeck and Max Neunhöffer, which is available from the GAP
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  site or from http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/.
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  Circle  is  distributed  in  standard  formats  (tar.gz,  tar.bz2,  zip  and
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  -win.zip)          and          can         be         obtained         from
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  http://www.cs.st-andrews.ac.uk/~alexk/circle/  or  from the GAP homepage. To
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  install  the package, unpack its archive in the pkg subdirectory of your GAP
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  installation.
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