Computation of normal forms (Q1263255)

The computation of normal (i.e. simple or canonical) forms for a differential system is particularly useful in nonlinear dynamics problems. The method of \textit{R. H. Rand} and \textit{W. L.Keith} [Applications of computer algebra, 309-328 (1985; Zbl 0653.65004)] is simple but assumes that the ``form'' of a fixed normal form is already known. Related to it, the present paper gives: first, a method and a program to compute the ``form'' of a fixed normal form; after, a method to compute the normal form for the differential system (having computed the normal form for the matrix of the linear term). A program using the symbolic manipulator MACSYMA is applied in several examples.