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Effective Methods for Systems of Algebraic Partial Differential Equations

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Effective Methods in Algebraic Geometry

Part of the book series: Progress in Mathematics ((PM,volume 94))


As a matter of fact, despite the fast progress of computer algebra during the last ten years, only a few steps have been done towards the use of symbolic computers for studying systems of partial differential equations (PDE) ([2], [13]). In particular, one must notice a few modern tentatives for dealing with algebraic PDE through differential algebraic techniques [19] or differential elimination techniques [16], [18] or exterior calculus ([1], Novosibirsk school), but these methods, being absolutely dependent on the coordinate system as they rely on old works ([6], [14], [18]), do not seem to go far inside the intrinsic structure of the system. Despite this point, these methods have been applied with success to control theory during the last five years ([3], [12]).

“God created integers, men made the remaining” (KRONECKER)

…but it is surely the Devil who let them conceive partial differential equations!

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© 1991 Springer Science+Business Media New York

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Pommaret, JF., Haddak, A. (1991). Effective Methods for Systems of Algebraic Partial Differential Equations. In: Mora, T., Traverso, C. (eds) Effective Methods in Algebraic Geometry. Progress in Mathematics, vol 94. Birkhäuser, Boston, MA.

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