  
  [1X1 Introduction[0X
  
  This  package, named GBNP for Gröbner Bases for Non-commutative Polynomials,
  is  intended  for computing in (associative) non-commutative algebras with a
  finite  presentation.  Starting  from a free algebra A on a finite number of
  generating  variables,  the reader can specify a finite set G of polynomials
  in  these  variables,  in  order  to  study the quotient algebra of A by the
  (2-sided) ideal of A generated by G.
  
  This  documentation gives a short description of the mathematical content in
  Chapter  [14X2[0m, explains the functions of the package in Chapter [14X3[0m, and provides
  more than twenty four worked out examples in Appendix [14XA.[0m. It is available as
  an HTML document at [7Xhttp://mathdox.org/products/gbnp/[0m and as an pdf document
  at [7Xhttp://mathdox.org/products/gbnp/manual.pdf[0m.
  
  
  [1X1.1 Installation[0X
  
  To        install       GBNP,       first       download       it       from
  [7Xhttp://mathdox.org/products/gbnp/GBNP-1.0.1.tar.gz[0m,        then       unpack
  [11XGBNP-1.0.1.tar.gz[0m  in  the  [10Xpkg[0m subdirectory of your [5XGAP[0m installation (or in
  the  [10Xpkg[0m subdirectory of any other [5XGAP[0m root directory, for example one added
  with   the   [10X-l[0m   argument)   with   the   following   command:   [10Xtar  -xvzf
  GBNP-1.0.1.tar.gz[0m.
  
  GBNP is then loaded with the GAP command
  
  [4X------------------------------------------------------------------[0X
    [4Xgap> LoadPackage( "GBNP" ); [0X
  [4X------------------------------------------------------------------[0X
  
  Those   who   want   to   download   this   documentation  can  find  it  at
  [7Xhttp://mathdox.org/products/gbnp/GBNPdoc-1.0.1.tar.gz[0m  and  extract  it with
  [10Xtar -xvzf GBNPdoc-1.0.1.tar.gz[0m. It is also included in the package.
  
  
  [1X1.2 Using the package[0X
  
  If   you   wish   to   compute  a  Gröbner  basis,  create  a  list  of  NPs
  (non-commutative  polynomials  in  NP  format), as described in Section [14X2.1[0m.
  This  can  be  done  either  directly  or by use of the transition functions
  described  in  Section  [14X3.1[0m. To run the standard algorithm use the functions
  from  Section  [14X3.4[0m.  With  these  functions,  you can try and find a Gröbner
  basis.  The word try is included because the algorithm for computing Gröbner
  bases  is not guaranteed to terminate. Printing issues for polynomials in NP
  format  are  discussed in Section [14X3.2[0m. If the Gröbner basis is found and the
  dimension  of  the  quotient  algebra Q (see Section [14X2.9[0m) is finite, you can
  find  a  basis  of  monomials for Q with the functions in Section [14X3.5[0m. For a
  more  advanced  analysis  of  Q,  such  as  a  proof  of  finite or infinite
  dimensionality, or for determining its growth or its partial Hilbert series,
  use the functions from Section [14X3.6[0m .
  
  There  are  three  variants  of  the  Gröbner basis algorithm, the truncated
  version,  the  trace  version,  and  the  module  version. In the (weighted)
  homogeneous case (described in Section [14X2.6[0m), the truncated version, given by
  the functions described in Section [14X3.8[0m, computes the part of a Gröbner basis
  up  to  an  indicated  weight. The trace version (described in Section [14X2.5[0m),
  given  by  the functions described in Section [14X3.7[0m, computes an expression of
  the  polynomials  of  the  Gröbner  basis  found  in  terms  of the original
  generators.  The  module  version (described in Sections [14X2.2[0m, [14X2.7[0m, and [14X2.8[0m),
  given  by  the  functions described in Section [14X3.9[0m, computes a Gröbner basis
  for a submodule of a free Q-module of finite rank.
  
  Read  the  example  files  in  Chapter [14XA.[0m for inspiration. The source of the
  files  can  be  perused for auxiliary functions, which are often used in the
  main functions but not deemed necessary for a first time user.
  
  
  [1X1.3 Further documentation[0X
  
  The  reports [Coh07], [Kro03], and [Kno04] can be downloaded from the web at
  these addresses:
  
  The  report  "Non-commutative  polynomial  computations",  by Arjeh M. Cohen
  (with  support  of Dié Gijsbers, Jan Willem Knopper, and Chris Krook) can be
  downloaded from [7Xhttp://mathdox.org/products/gbnp/gbnp.pdf[0m.
  
  The  report  "Dimensionality  of  quotient  algebras", by Chris Krook can be
  downloaded from [7Xhttp://mathdox.org/products/gbnp/dqa.pdf[0m.
  
  The  report  "GBNP  and  vector  enumeration",  by Jan Willem Knopper can be
  downloaded from [7Xhttp://mathdox.org/products/gbnp/knopper.pdf[0m.
  
