1 Introduction
  
  The LinBox C++ library (http://www.linalg.org) performs exact linear algebra
  and  provides  a set of routines for the solution of linear algebra problems
  such  as  rank, determinant, and the solution of linear systems. It provides
  representations  for both sparse and dense matrices over integers and finite
  fields.  It has a particular emphasis on black-box matrix methods (which are
  very  efficient  over  sparse  matrices),  but  increasingly  also  provides
  elimination-based  routines  for  dense matrices using the industry-standard
  BLAS numeric routines.
  
  GAP  (http://www.gap-system.org)  is  a  system  for  computational discrete
  algebra, with particular emphasis on Computational Group Theory. It provides
  good implementations of exact linear algebra routines on dense matrices over
  all  common  fields  and  the integers. Typically, GAP's versions are faster
  than  LinBox  for small finite fields (i.e. order less than 256), but LinBox
  is much faster for larger finite fields and the integers.
  
  The  linboxing  (LinBox-in-GAP)  package provides an interface to the LinBox
  C++ library from GAP. It provides alternative versions of GAP linear algebra
  routines  which are mapped through to the equivalent LinBox library routines
  at  the  GAP kernel level. The result is linear algebra routines in GAP that
  are,  in  the  majority  of  cases,  considerably faster than the native GAP
  versions, and which scale better with matrix size. See the linboxing website
  at  http://www.maths.nuigalway.ie/~pas/CHA/linboxing/index.shtml  for timing
  examples  and speedup estimates. As is typical, this speed is at the expense
  of  memory,  since  the GAP matrices and vector must be copied into a memory
  format that LinBox can use.
  
  The  functions  provided  by the linboxing package are named the same as the
  GAP  equivalents, but are all contained within the LinBox record, and so are
  prefixed with `LinBox.'. The functions provided are
  
  --    LinBox.Determinant (3.1-1)
  
  --    LinBox.Rank (3.1-2)
  
  --    LinBox.Trace (3.1-3)
  
  --    LinBox.SolutionMat (3.1-4)
  
  over the integers and prime fields.