论文标题
热带部分差分代数几何的基本定理
The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry
论文作者
论文摘要
热带差异代数几何形状认为微分方程中的困难甚至是棘手的问题，并试图从输入的限制结构中提取其解决方案的信息。热带差异代数几何形状的基本定理指出，可以通过求解所谓的热带差异化系统来获得具有正式功率序列系数的普通微分方程系统解决方案解决方案的支持。热带化微分方程在完全不同的代数结构上工作，这可能有助于理论和计算问题。我们表明，通过引入牛顿多边形的顶点集，可以将基本定理扩展到部分微分方程系统的情况。
Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of Tropical Differential Algebraic Geometry states that the support of solutions of systems of ordinary differential equations with formal power series coefficients over an uncountable algebraically closed field of characteristic zero can be obtained by solving a so-called tropicalized differential system. Tropicalized differential equations work on a completely different algebraic structure which may help in theoretical and computational questions. We show that the Fundamental Theorem can be extended to the case of systems of partial differential equations by introducing vertex sets of Newton polygons.
