Taylor and Lyubeznik resolutions via Gröbner bases
Journal of Symbolic Computation
Involutive upgrades of Navier-Stokes solvers
International Journal of Computational Fluid Dynamics
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Thomas decomposition of algebraic and differential systems
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Macaulay inverse systems revisited
Journal of Symbolic Computation
Involutive division generated by an antigraded monomial ordering
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Consistency analysis of finite difference approximations to PDE systems
MMCP'11 Proceedings of the 2011 international conference on Mathematical Modeling and Computational Science
Programming and Computing Software
On polynomial solutions of linear partial differential and (q-)difference equations
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Computing hopf bifurcations in chemical reaction networks using reaction coordinates
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Comprehensive involutive systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Quasi-stability versus genericity
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Involutive bases algorithm incorporating F5 criterion
Journal of Symbolic Computation
Systems of generators for ideals of algebra of convergent differential series
Programming and Computing Software
| Hi-index | 0.00 |
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. It presents for the first time in book form the theory of Pommaret bases, a special kind of Grbner bases closely related to Koszul homology, and contains an extensive discussion of the existence and uniqueness of solutions of formally well-posed initial value problems and a novel presentation of Vessiot's dual version of the Cartan-Khler theory. Special emphasis is put on a constructive approach leading to effective algorithms.