DifferentialAlgebra Refereences
The DifferentialAlgebra package is based on the Bibliotheques Lilloises d'Algebre Differentielle (BLAD) software developed by F. Boulier. For more information about BLAD, visit http://www.lifl.fr/%7Eboulier/pmwiki/pmwiki.php?n=Main.BLAD. The redesign of the interface of BLAD to DifferentialAlgebra was done by F. Boulier and E. S. Cheb-Terrab in Maple 14.
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The papers and the books cited in this bibliography are mentioned in the help pages, or, correspond to some very related work.
ALM99Philippe Aubry, Daniel Lazard, Marc Moreno Maza. On the theories of triangular sets. Journal of Symbolic Computation. 1999BKM01Driss Bouziane, Abdelillah Kandri Rody, Hamid Maarouf. Unmixed-Dimensional Decomposition of a Finitely Generated Perfect Differential Ideal. Journal of Symbolic Computation. 2001B09Francois Boulier. The BLAD libraries.BLOP95Francois Boulier, Daniel Lazard, Francois Ollivier, Michel Petitot. Representation for the radical of a finitely generated differential ideal. ISSAC. 1995BLOP09Francois Boulier, Daniel Lazard, Francois Ollivier, Michel Petitot. Computing representations for radicals of finitely generated differential ideals. Journal of AAECC. 2009BLLM07Francois Boulier, Marc Lefranc, Francois Lemaire, Pierre-Emmanuel Morant. Model Reduction of Chemical Reaction Systems using Elimination. MACIS. 2007BL00Francois Boulier, Francois Lemaire. Computing canonical representatives of regular differential ideals. ISSAC. 2000BLM06Francois Boulier, Francois Lemaire, Marc Moreno Maza. Well known theorems on triangular systems and the D5 principle. TC. 2006BLM10Francois Boulier, Francois Lemaire, Marc Moreno Maza. Computing differential characteristic sets by change of ordering. Journal of Symbolic Computation. To appear in 2010.BC99Alexandru Buium, Phyllis Cassidy. Differential Algebraic Geometry and Differential Algebraic Groups: From Algebraic Differential Equations To Diophantine Geometry. American Mathematical Society. 1999.DL84Jan Denef, Leonard Lipshitz. Power Series Solutions of Algebraic Differential Equations. Mathematische Annalen. 1984GKO09Oleg Golubitsky, Marina Kondratieva, Alexey Ovchinnikov. Algebraic transformation of differential characteristic decompositions from one ranking to another. Journal of Symbolic Computation. 2009BMO91Giovanni Gallo, Bubaneshwar Mishra, Francois Ollivier. Some constructions in rings of differential polynomials. AAECC. 1991H99Evelyne Hubert. Essential Components of an Algebraic Differential Equation. Journal of Symbolic Computation. 1999.H00Evelyne Hubert. Factorization free decomposition algorithms in differential algebra. Journal of Symbolic Computation. 2000HW96Ernst Hairer, Gerhard Wanner. Solving ordinary differential equations II. Stiff and Differential-Algebraic Problems. Springer-Verlag. 1996K73Ellis Robert Kolchin. Differential Algebra and Algebraic groups. Academic Press. 1973LW99Ziming Li, Dongming Wang. Coherent, regular and simple systems in zero decompositions of partial differential systems. Systems Science and Mathematical Sciences. 1999M91Elizabeth L. Mansfield. Differential Groebner Bases. PhD thesis. 1991MMM00Marc Moreno Maza. On Triangular Decompositions of Algebraic Varieties. MEGA. 2000.M99Sally Morrison. The Differential Ideal [P]:M. Journal of Symbolic Computation. 1999RWB96Gregory J. Reid, Allan D. Wittkopf, Alan Boulton. Reduction of systems of nonlinear partial differential equations to simplified involutive forms European Journal of Applied Math. 1996RLW01Gregory J. Reid, Ping Lin, Allan D. Wittkopf. Differential Elimination-Completion Algorithms for DAE and PDAE. Studies in Applied Mathematics. 2001R50Joseph Fels Ritt. Differential Algebra. Dover Publications Inc. 1950R59Azriel Rosenfeld. Specializations in differential algebra. TAMS. 1959S56Abraham Seidenberg. An elimination theory for differential algebra. Univ. California Publ. Math. (New Series). 1956S02William Sit, The Ritt-Kolchin theory for differential polynomials. DART. 2002Wu89Wenjun Wu. On the foundation of algebraic differential geometry. Mechanization of Mathematics. 1989W98Dongming Wang. Decomposing polynomial systems into simple systems. Journal of Symbolic Computation. 1998W03Dongming Wang. Elimination Practice: Software Tools and Applications. Imperial College Press. 2003