The fundamental theorem of tropical differential algebra for formal Puiseux series
Research Square (Research Square)(2023)
摘要
The fundamental theorem of tropical differential algebra has been established
for formal power series solutions of systems of algebraic differential
equations. It has been shown that the direct extension to formal Puiseux series
solutions fails. In this paper, we overcome this issue by transforming the
given differential system and such a generalization is presented. Moreover, we
explain why such transformations do not work for generalizing the fundamental
theorem to transseries solutions, but show that one inclusion still holds for
this case even without using any transformation.
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关键词
tropical differential algebra
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