  
  [1X3 Function Reference[0X
  
  
  [1X3.1 Replacements for [5XGAP[1X functions[0X
  
  [1X3.1-1 LinBox.Determinant[0m
  
  [2X> LinBox.Determinant( [0X[3XM[0X[2X ) __________________________________________[0Xfunction
  [2X> LinBox.DeterminantMat( [0X[3XM[0X[2X ) _______________________________________[0Xfunction
  [2X> LinBox.DeterminantIntMat( [0X[3XM[0X[2X ) ____________________________________[0Xfunction
  
  Returns  the  determinant  of  the square matrix [3XM[0m. The entries of [3XM[0m must be
  integers or over a prime field.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> LinBox.DeterminantMat([[1,2,3],[4,5,6],[7,8,9]]);[0X
    [4X0[0X
  [4X------------------------------------------------------------------[0X
  
  [1X3.1-2 LinBox.Rank[0m
  
  [2X> LinBox.Rank( [0X[3XM[0X[2X ) _________________________________________________[0Xfunction
  [2X> LinBox.RankMat( [0X[3XM[0X[2X ) ______________________________________________[0Xfunction
  
  Returns the maximal number of linearly-independent rows of the matrix [3XM[0m. The
  entries of [3XM[0m must be integers or over a prime field.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> LinBox.RankMat([[1,2,3],[4,5,6],[7,8,9]]);[0X
    [4X2[0X
  [4X------------------------------------------------------------------[0X
  
  [1X3.1-3 LinBox.Trace[0m
  
  [2X> LinBox.Trace( [0X[3XM[0X[2X ) ________________________________________________[0Xfunction
  [2X> LinBox.TraceMat( [0X[3XM[0X[2X ) _____________________________________________[0Xfunction
  
  For  a square matrix [3XM[0m, returns the sum of the diagonal entries. The entries
  of  [3XM[0m must be integers or over a prime field. Note that this version (unlike
  the others in this package) is typically slower than the [5XGAP[0m equivalent, but
  is provided for completeness.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> LinBox.TraceMat([[1,2,3],[4,5,6],[7,8,9]]);[0X
    [4X15[0X
  [4X------------------------------------------------------------------[0X
  
  [1X3.1-4 LinBox.SolutionMat[0m
  
  [2X> LinBox.SolutionMat( [0X[3XM, b[0X[2X ) _______________________________________[0Xfunction
  
  Returns  a  row vector [3Xx[0m that is a solution of the equation xM=b, or [9Xfail[0m if
  no  solution  exists.  If  the  system is consistent, a random solution [3Xx[0m is
  returned.  The  entries  of [3XM[0m must be integers or over a prime field, but if
  they are integers then the solution may include rationals.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> LinBox.SolutionMat([[1,2,3],[4,5,6],[7,8,9]], [2,1,0]);[0X
    [4X[ -1, -1, 1 ][0X
    [4Xgap> LinBox.SolutionMat([[1,2,3],[4,5,6],[7,8,9]], [2,1,0]);[0X
    [4X[ -5/4, -1/2, 3/4 ][0X
  [4X------------------------------------------------------------------[0X
  
  
  [1X3.2 Miscellaneous functions[0X
  
  [1X3.2-1 LinBox.SetMessages[0m
  
  [2X> LinBox.SetMessages( [0X[3Xon[0X[2X ) _________________________________________[0Xfunction
  
  Turns  on or off the printing of the LinBox library commentator messages. If
  the  boolean  argument [3Xon[0m is set to [9Xtrue[0m then messages will be printed, else
  no messages will be displayed.
  
  [1X3.2-2 MakeLinboxingDoc[0m
  
  [2X> MakeLinboxingDoc( [0X[3X[make-internal][0X[2X ) ______________________________[0Xfunction
  
  Builds  this  documentation  from  the  [5Xlinboxing[0m 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 [3Xmake-internal[0m is [9Xtrue[0m then the internal
  (undocumented!) functions are included in this manual.
  
  [1X3.2-3 TestLinboxing[0m
  
  [2X> TestLinboxing( [0X[3X[num-tests][0X[2X ) _____________________________________[0Xfunction
  
  Test  the  installation  of  [5Xlinboxing[0m and print profiling information. This
  tries  all  the  [5Xlinboxing[0m  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 [5XGAP[0m functions, and the
  relative times displayed.
  
  The  optional  argument [3Xnum-tests[0m specifies how many times to run each test:
  the default is 5 times.
  
