Involution: The Formal Theory of Differential Equations and its Applications in Computer AlgebraSpringer Science & Business Media, 26 okt 2009 - 650 pagina's The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas. |
Inhoudsopgave
| 1 | |
| 9 | |
3 Involution I Algebraic Theory | 63 |
4 Completion to Involution | 105 |
5 Structure Analysis of Polynomial Modules | 167 |
6 Involution II Homological Theory | 235 |
7 Involution III Differential Theory | 263 |
8 The Size of the Formal Solution Space | 329 |
9 Existence and Uniqueness of Solutions | 357 |
Overige edities - Alles bekijken
Involution: The Formal Theory of Differential Equations and its Applications ... Werner M. Seiler Geen voorbeeld beschikbaar - 2012 |
Involution: The Formal Theory of Differential Equations and its Applications ... Werner M. Seiler Geen voorbeeld beschikbaar - 2009 |
Veelvoorkomende woorden en zinsdelen
Algorithm arbitrary assume assumption autoreduced bases basis H coefficients comodule computation consider construction contained coordinates corresponding decomposition defined definition degree q derivatives differential equation Rq elements equivalent Example exists fibred manifold fields finite first formal power series formally integrable generalised geometric given Gr¨obner basis Hence Hilbert function implies independent variables initial value problem integrability conditions involutive basis involutive division involutively head isomorphism Janet division jet bundle leading terms Lemma lexicographic order linear system matrix minimal module monoid monoid ideal monomial multi index multiplicative Noetherian non-multiplicative obtain Obviously one-form ordinary differential equations polynomial ring Pommaret basis principal symbol prolongation proof Proposition R-module Remark representation respect right hand side sequence Spencer cohomology submanifold subset syzygy tangent term order Theorem theory tion trivial unique vanish vector field vector space Vessiot distribution yields