GENERIC INTERFACE GaussElim (Elem);
(*
  Gaussian elimination on matrices of "Elem.T"s.

  Created 95-02-27 by J. Stolfi.
  Last edited by stolfi *)

PROCEDURE Triangularize(VAR m: ARRAY OF ARRAY OF Elem.T; total: BOOLEAN := FALSE);
  (*
    Reduces "m" to upper triangular form by elementary row
    operations. 
    
    A matrix "m" is {\em upper tr1iangular}  if the elements
    "m[i][j]" with "i > j" are all zero.

    An {\em elementary row operation} consists of adding a multiple
    of one row to another row; a {\em row swap} consists of exchanging
    two rows and negating one of them.  Observe that these operations
    are equivalent to premultiplying the matrix by a square matrix
    with unit determinant.
    
    If "total" is true, the procedure keeps applying elementary row 
    operations until "m" is {\em totally reduced}, that is,
    each row that is not entirely zero has at least one more leading 
    zero than the preceding row. *)

END GaussElim.