Abstract
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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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. https://doi.org/10.1007/978-1-4612-0441-1_27
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DOI: https://doi.org/10.1007/978-1-4612-0441-1_27
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