Completion of Linear Differential Systems to Involution

摘要: In this paper we generalize the involutive methods and algorithms have been devised for polynomial ideals to differential ones generated by a finite set of linear polynomials in ring over zero characteristic field. Given ranking derivative terms an division, formulate involutivity conditions which form basis algorithms. We present algorithm computation minimal basis. Its correctness termination hold any constructive noetherian division. As two important applications consider posing initial value problem system providing uniqueness its solution Lie symmetry analysis nonlinear equations. particular, allows determine structure arbitrariness general systems thereby find size group.