Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra

摘要: The book provides a self-contained account of the formal theory general, i.e. also under- and overdetermined, systems differential equations which in its central notion involution combines geometric, algebraic, homological combinatorial ideas. It presents for first time form Pommaret bases, special kind Grbner bases closely related to Koszul homology, contains an extensive discussion existence uniqueness solutions formally well-posed initial value problems novel presentation Vessiot's dual version Cartan-Khler theory. Special emphasis is put on constructive approach leading effective algorithms.