  The construction of the general solution sequence of row-finite linear
systems is accomplished by implementing -ad infinitum- the Gauss-Jordan
algorithm under a rightmost pivot elimination strategy. The algorithm generates
a basis (finite or Schauder) of the homogeneous solution space for row-finite
systems. The infinite Gaussian elimination part of the algorithm solves linear
difference equations with variable coefficients of regular order, including
equations of constant order and of ascending order. The general solution thus
obtained can be expressed as a single Hessenbergian.
