  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  
  [1X1.1 [33X[0;0YPhilosophy[133X[101X
  
  [33X[0;0YThis  package  implements  a complete infrastructure for vectors over finite
  fields.  The  basic idea is, that one can store an element of a finite field
  using  only  a  few  bits rather than a full machine word. Therefore one can
  pack more than one finite field element in a machine word. This approach not
  only saves memory but also allows fast arithmetic.[133X
  
  [33X[0;0YContrary  to  other implementations this package uses long word instructions
  for  arithmetic  and  other  operations  rather  than table lookups, because
  modern  microprocessor  designs seem to support faster memory access in this
  way  and  memory  access  is  the main limiting factor for computations over
  finite  fields. This approach also allows for bigger finite fields with more
  than  256  elements.  For  a  more  detailed descriptions of this design see
  Chapter [14X3[114X.[133X
  
  [33X[0;0YThe  main  purpose  of  this  implementation  is  to  use it in [5XMeatAxe[105X-like
  applications,  that  is,  working  with  matrices  consisting  of compressed
  vectors   over   finite  fields,  doing  linear  algebra  calculations  like
  nullspaces,  spinning of vectors, multiplying and inverting matrices and the
  like.  Another  purpose  could be matrix group calculations. Usually in such
  computations,  the  base  field  does  not  change  too  often  and not many
  different  lengths  of  vectors occur. This implementation is optimized with
  these  applications  in  mind  and  might  not  be  very efficient for other
  purposes like using compressed vectors as coefficient lists of polynomials.[133X
  
  [33X[0;0YAnother  important  point  is that compressed vectors in this package do not
  even  try  to  behave exactly like [5XGAP[105X lists. To the contrary, they disallow
  many  operations  that are possible for [5XGAP[105X lists for example changing their
  length  or  assigning  arbitrary [5XGAP[105X objects to positions in the vector. The
  reason  for  this is that the chosen data structure does not allow to assign
  anything  but  elements of the one base field to positions in the vector and
  the  option to change the representation [21Xon the fly[121X is not desirable in most
  applications.  On  the  other  hand  one  can be relatively sure not to [21Xlose
  compression[121X along the way.[133X
  
  
  [1X1.2 [33X[0;0YOverview over this manual[133X[101X
  
  [33X[0;0YChapter  [14X2[114X  describes  the installation of this package. Chapter [14X3[114X describes
  the basic design and all the data structures used in this package, including
  the external representation of matrices on storage. These descriptions might
  be  very  valuable  to  understand  the  behaviour of the implementation and
  various  performance  issues. Those and other performance issues are covered
  in  Chapter  [14X7[114X, where you mainly find hints on how to tune your own programs
  that  use this package. Chapters [14X4[114X to [14X5[114X describe the available functionality
  for  vectors  and  matrices  respectively.  Chapter  [14X8[114X  describes,  how  the
  functionality in this package is or is not usable in connection with the [5XGAP[105X
  library. Finally, Chapter [14X9[114X shows instructive examples for the usage of this
  package.[133X
  
  
  [1X1.3 [33X[0;0YFeedback[133X[101X
  
  [33X[0;0YFor  bug  reports,  feature  requests  and suggestions, please use our issue
  tracker ([7Xhttps://github.com/gap-packages/cvec/issues[107X).[133X
  
