Abstract
Deciding the unsolvability of a system of algebraic differential equations ∑ is one of the basic problems in differential algebra. We use the construction of Mayr and Meyer to show that the algorithms based on effective methods such as differential Groebner Bases, or Ritt's algorithm to test whether 1 belongs to the differential ideal generated by ∑, have at least doubly exponential worst case complexity in the linear case.
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Sadik, B. (1995). The complexity of formal resolution of linear partial differential equations. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_31
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DOI: https://doi.org/10.1007/3-540-60114-7_31
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