5 Internal Function Reference
  
  These  are  functions  that  are used internally in the LinBox package. They
  should  not  be  needed  by  users  of  the  package,  but  may be useful to
  developers and are provided for completeness
  
  
  5.1 Kernel Module Functions
  
  These functions are implemented directly in C or C++ in the kernel module.
  
  5.1-1 LinBox.DETERMINANT
  
  > LinBox.DETERMINANT( M, field-id ) ________________________________function
  
  Kernel  module  function to calculate the determinant of a matrix. Called by
  the  wrapper LinBox.DeterminantMat (3.1-1). The field-id parameter should be
  0 for a matrix of integers, or the size of the field if the matrix is over a
  finite field.
  
  5.1-2 LinBox.RANK
  
  > LinBox.RANK( M, field-id ) _______________________________________function
  
  Kernel  module  function  to  calculate  the rank of a matrix. Called by the
  wrapper  LinBox.RankMat  (3.1-2).  The  field-id parameter should be 0 for a
  matrix  of integers, or the size of the field if the matrix is over a finite
  field.
  
  5.1-3 LinBox.TRACE
  
  > LinBox.TRACE( M, field-id ) ______________________________________function
  
  Kernel  module  function to calculate the determinant of a matrix. Called by
  the  wrapper LinBox.TraceMat (3.1-3). The field-id parameter should be 0 for
  a  matrix  of  integers,  or  the  size of the field if the matrix is over a
  finite field.
  
  5.1-4 LinBox.SOLVE
  
  > LinBox.SOLVE( M, b, field-id ) ___________________________________function
  
  Kernel  module function to calculate the solution of a matrix. Called by the
  wrapper  LinBox.SolutionMat (3.1-4). The field-id parameter should be 0 when
  the  matrix  and  vector  contains integers, or the size of the field if the
  matrix  and vector are over a finite field (which must naturally be the same
  for both).
  
  5.1-5 LinBox.TEST_INT_CONVERSION_INTERNAL
  
  > LinBox.TEST_INT_CONVERSION_INTERNAL( z ) _________________________function
  
  Tests  the GAP-LinBox and LinBox-GAP integer conversion. Returns the integer
  z  (which  may  be large) after it has been converted into LinBox format and
  then back.
  
  5.1-6 LinBox.TEST_VECTOR_CONVERSION_INTERNAL
  
  > LinBox.TEST_VECTOR_CONVERSION_INTERNAL( v, field-id ) ____________function
  
  Tests  the GAP-LinBox and LinBox-GAP vector conversion. Returns the vector v
  after  it  has been converted into LinBox format and then back. The field-id
  parameter  should be 0 for a vector of integers, or the size of the field if
  the   vector   is   over   a  finite  field.  This  function  is  called  by
  LinBox.TEST_VECTOR_CONVERSION (5.1-11).
  
  5.1-7 LinBox.TEST_MATRIX_CONVERSION_INTERNAL
  
  > LinBox.TEST_MATRIX_CONVERSION_INTERNAL( M, field-id ) ____________function
  
  Tests  the GAP-LinBox and LinBox-GAP matrix conversion. Returns the matrix v
  after  it  has been converted into LinBox format and then back. The field-id
  parameter  should be 0 for a matrix of integers, or the size of the field if
  the   matrix   is   over   a  finite  field.  This  function  is  called  by
  LinBox.TEST_MATRIX_CONVERSION (5.1-12).
  
  5.1-8 LinBox.MAX_GAP_SMALL_INT
  
  > LinBox.MAX_GAP_SMALL_INT(  ) _____________________________________function
  
  Kernel  module  function  which returns the size of the largest integer that
  the  LinBox  kernel module thinks can be represented as a GAP small integer.
  This  number  is  different  on  32- or 64-bit machines, but LinBox tries to
  check with GAP when it compiles to find out which value to use.
  
  ---------------------------  Example  ----------------------------
      gap> z := LinBox.MAX_GAP_SMALL_INT();
      1152921504606846975
      gap> IsSmallIntRep(z);
      true
      gap> IsSmallIntRep(z+1);
      
  ------------------------------------------------------------------
  
  5.1-9 LinBox.FIELD_DATA
  
  > LinBox.FIELD_DATA( M ) ___________________________________________function
  
  Checks  that the field of the matrix M is one that is accepted by the kernel
  module, and if so returns data on the field for the kernel module to use. if
  the field is not compatible, then an error is thrown.
  
  The field data is a plain record with three elements: .field is the field of
  the  matrix  (using DefaultFieldOfMatrix (Reference: DefaultFieldOfMatrix));
  id  is  the field id read by the kernel module, which is zero for an integer
  (or  rationals)  matrix, or the fieldsize otherwise; the last element one is
  the one of the field.
  
  If  the matrix is over the integers or the rationals, then zero is returned.
  It is assumed that the matrix is over the integers (since we can't cope with
  rationals),  but we check that each element is an integer when we convert it
  in the kernel module and throw an error if it is not.
  
  5.1-10 LinBox.TEST_INT_CONVERSION
  
  > LinBox.TEST_INT_CONVERSION( z ) __________________________________function
  
  Convert  the  integer  z  into  the  internal  LinBox format and back again,
  returning the result.
  
  5.1-11 LinBox.TEST_VECTOR_CONVERSION
  
  > LinBox.TEST_VECTOR_CONVERSION( v ) _______________________________function
  
  Convert  the  vector  v  into  the  internal  LinBox  format and back again,
  returning the result.
  
  5.1-12 LinBox.TEST_MATRIX_CONVERSION
  
  > LinBox.TEST_MATRIX_CONVERSION( M ) _______________________________function
  
  Convert  the  matrix  M  into  the  internal  LinBox  format and back again,
  returning the result.