Computing representations for radicals of finitely generated differential ideals
From MaRDI portal
Publication:1015366
DOI10.1007/s00200-009-0091-7zbMath1185.12003OpenAlexW2054452549MaRDI QIDQ1015366
Michel Petitot, François Boulier, Daniel Lazard, François Ollivier
Publication date: 8 May 2009
Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00200-009-0091-7
Symbolic computation and algebraic computation (68W30) Computational aspects and applications of commutative rings (13P99) Differential algebra (12H05) Modules of differentials (13N05)
Related Items
Algorithms yield upper bounds in differential algebra ⋮ Singularities of algebraic differential equations ⋮ A generalization of the Boulier-Buchberger criterion for the computation of characteristic sets of differential ideals ⋮ Effective bounds for the consistency of differential equations ⋮ Mode discernibility and bounded-error state estimation for nonlinear hybrid systems ⋮ Recent progress in an algebraic analysis approach to linear systems ⋮ The Differential Dimension Polynomial for Characterizable Differential Ideals ⋮ An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner bases ⋮ Model reduction of chemical reaction systems using elimination ⋮ Validation of simulation models without knowledge of parameters using differential algebra ⋮ New order bounds in differential elimination algorithms ⋮ Rational general solutions of systems of first-order algebraic partial differential equations ⋮ On integro-differential algebras. ⋮ The Maple package TDDS for computing Thomas decompositions of systems of nonlinear PDEs ⋮ Differential Elimination for Dynamical Models via Projections with Applications to Structural Identifiability ⋮ Jacobi's bound: Jacobi's results translated in Kőnig's, Egerváry's and Ritt's mathematical languages ⋮ On the partial differential Lüroth's theorem ⋮ Membership problem for differential ideals generated by a composition of polynomials ⋮ Algorithmic Thomas decomposition of algebraic and differential systems ⋮ New effective differential Nullstellensatz ⋮ Thomas Decomposition and Nonlinear Control Systems ⋮ On Symbolic Approaches to Integro-Differential Equations ⋮ Sur le problème d’équivalence de Cartan ⋮ Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms ⋮ Elimination of unknowns for systems of algebraic differential-difference equations ⋮ An equivalence theorem for regular differential chains ⋮ A bound for a typical differential dimension of systems of linear differential equations ⋮ Universal characteristic decomposition of radical differential ideals ⋮ A normal form algorithm for regular differential chains ⋮ Thomas Decomposition of Algebraic and Differential Systems ⋮ Differential algebra for derivations with nontrivial commutation rules ⋮ A bound for orders in differential Nullstellensatz ⋮ Some effective approaches to check the identifiability of uncontrolled nonlinear systems ⋮ Probabilistic algorithms for computing resolvent representations of regular differential ideals ⋮ Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits ⋮ A geometric index reduction method for implicit systems of differential algebraic equations ⋮ Characteristic sets for ordinary differential equations ⋮ Symmetry-based algorithms for invertible mappings of polynomially nonlinear PDE to linear PDE ⋮ Automatic pre- and postconditions for partial differential equations ⋮ On the integrability of homogeneous scalar evolution equations ⋮ Computing all identifiable functions of parameters for ODE models ⋮ On the Coalgebra of Partial Differential Equations ⋮ Computing differential characteristic sets by change of ordering ⋮ Accelerated tower arithmetic
Uses Software
Cites Work
- On an installation of Buchberger's algorithm
- Solving zero-dimensional algebraic systems
- A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
- The differential ideal \([P : M^ \infty\).]
- The low power theorem for partial differential polynomials
- Contribution to the Picard-Vessiot Theory of Homogeneous Linear Differential Equations
- Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
- Reduction of systems of nonlinear partial differential equations to simplified involutive forms
- Differential Elimination–Completion Algorithms for DAE and PDAE
- Abstract Differential Algebra and the Analytic Case
- Abstract Differential Algebra and the Analytic Case. II
- Specializations in Differential Algebra
- On the translation of languages from left to right
- Some Basic Theorems in Differential Algebra (Characteristic p, Arbitrary)
- Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item