The DifferentialAlgebra package implements algebraic and differential elimination algorithms which are key for simplifying systems of polynomial differential equations and computing formal power series solutions for them. The underlying theory is the differential algebra of Joseph Fels Ritt and Ellis Robert Kolchin [R50, K73] (see References). The main functionality of the package is provided by the RosenfeldGroebner function, which permits triangularizing a differential equation system so that it can be solved eliminating one variable at a time, simplifying the system with respect to its integrability conditions, or determining its singular cases. Commands are also provided to solve related problems, such as BelongsTo for deciding membership to a differential ideal, and ReducedForm for reducing a system with respect to another one. The command for computing formal power series solutions to differential equation systems is PowerSeriesSolution. Other commands for analyzing mathematical properties of differential systems or performing algebraic manipulation and related programming are listed below.
Keywords for this software
References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Verdière, N.; Zhu, S.; Denis-Vidal, L.: A distribution input-output polynomial approach for estimating parameters in nonlinear models. Application to a chikungunya model (2018)
- Boulier, François; Lemaire, François; Lallemand, Joseph; Regensburger, Georg; Rosenkranz, Markus: Additive normal forms and integration of differential fractions (2016)
- Boulier, François; Lefranc, Marc; Lemaire, François; Morant, Pierre-Emmanuel: Model reduction of chemical reaction systems using elimination (2011)
- Boulier, François; Lemaire, François; Sedoglavic, Alexandre: On the regularity property of differential polynomials modulo regular differential chains (2011)
- Boulier, François; Lemaire, François: A normal form algorithm for regular differential chains (2010)