3 Function Reference
  
  
  3.1 Replacements for GAP functions
  
  3.1-1 LinBox.Determinant
  
  > LinBox.Determinant( M ) __________________________________________function
  > LinBox.DeterminantMat( M ) _______________________________________function
  > LinBox.DeterminantIntMat( M ) ____________________________________function
  
  Returns  the  determinant  of  the square matrix M. The entries of M must be
  integers or over a prime field.
  
  ---------------------------  Example  ----------------------------
    gap> LinBox.DeterminantMat([[1,2,3],[4,5,6],[7,8,9]]);
    0
  ------------------------------------------------------------------
  
  3.1-2 LinBox.Rank
  
  > LinBox.Rank( M ) _________________________________________________function
  > LinBox.RankMat( M ) ______________________________________________function
  
  Returns the maximal number of linearly-independent rows of the matrix M. The
  entries of M must be integers or over a prime field.
  
  ---------------------------  Example  ----------------------------
    gap> LinBox.RankMat([[1,2,3],[4,5,6],[7,8,9]]);
    2
  ------------------------------------------------------------------
  
  3.1-3 LinBox.Trace
  
  > LinBox.Trace( M ) ________________________________________________function
  > LinBox.TraceMat( M ) _____________________________________________function
  
  For  a square matrix M, returns the sum of the diagonal entries. The entries
  of  M must be integers or over a prime field. Note that this version (unlike
  the others in this package) is typically slower than the GAP equivalent, but
  is provided for completeness.
  
  ---------------------------  Example  ----------------------------
    gap> LinBox.TraceMat([[1,2,3],[4,5,6],[7,8,9]]);
    15
  ------------------------------------------------------------------
  
  3.1-4 LinBox.SolutionMat
  
  > LinBox.SolutionMat( M, b ) _______________________________________function
  
  Returns  a  row vector x that is a solution of the equation xM=b, or fail if
  no  solution  exists.  If  the  system is consistent, a random solution x is
  returned.  The  entries  of M must be integers or over a prime field, but if
  they are integers then the solution may include rationals.
  
  ---------------------------  Example  ----------------------------
    gap> LinBox.SolutionMat([[1,2,3],[4,5,6],[7,8,9]], [2,1,0]);
    [ -1, -1, 1 ]
    gap> LinBox.SolutionMat([[1,2,3],[4,5,6],[7,8,9]], [2,1,0]);
    [ -5/4, -1/2, 3/4 ]
  ------------------------------------------------------------------
  
  
  3.2 Miscellaneous functions
  
  3.2-1 LinBox.SetMessages
  
  > LinBox.SetMessages( on ) _________________________________________function
  
  Turns  on or off the printing of the LinBox library commentator messages. If
  the  boolean  argument on is set to true then messages will be printed, else
  no messages will be displayed.
  
  3.2-2 MakeLinboxingDoc
  
  > MakeLinboxingDoc( [make-internal] ) ______________________________function
  
  Builds  this  documentation  from  the  linboxing package source files. This
  should  not  normally  need  doing:  the  current documentation is built and
  included with the package release.
  
  If  the  optional  boolean  argument make-internal is true then the internal
  (undocumented!) functions are included in this manual.
  
  3.2-3 TestLinboxing
  
  > TestLinboxing( [num-tests] ) _____________________________________function
  
  Test  the  installation  of  linboxing and print profiling information. This
  tries  all  the  linboxing  package's  algorithms  with  random  vectors and
  matrices  over  random  fields  (covering  all  the distinct supported field
  types).  The results are compared with the equivalent GAP functions, and the
  relative times displayed.
  
  The  optional  argument num-tests specifies how many times to run each test:
  the default is 5 times.