ALGEBRAIC RECASTING OF NONLINEAR-SYSTEMS OF ODES INTO UNIVERSAL FORMATS

It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known th at this goal may imply an increase in the dimension of the system. Thi s is what happens if in this new representation the vector field has a lower degree of nonlinearity or a smaller number of nonlinear contrib utions. Until now both issues have been treated separately, rather uns ystematically and, in some cases, at the expense of an excessive incre ase in the number of dimensions. We unify here the treatment of both i ssues in a common algebraic framework. This allows us to proceed algor ithmically in terms of simple matrix operations.