Transseries for beginners
Transseries for beginners
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适合初学者的 TransSeries
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. A. Edgar
中科院分区：
文献类型：
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作者：
G. A. Edgar
从最简单的角度来看，跨级数是实值函数的一种新的展开式。但是transseries构成的远不止这些--它们有非常丰富的（代数的、组合的、分析的）结构。transseries集合是一个大的有序域，它是真实的数域的扩展，并赋予了指数、对数、导数、积分、复合等额外的运算。在过去的20年左右，transseries已经出现在数学的几个领域：渐近分析，模型论，计算机代数，超实数。这篇论文是为非专业数学家准备的。
所有数学家需要知道，以应用transseries。
From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than that--they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries is a large ordered field, extending the real number field, and endowed with additional operations such as exponential, logarithm, derivative, integral, composition. Over the course of the last 20 years or so, transseries have emerged in several areas of mathematics: asymptotic analysis, model theory, computer algebra, surreal numbers. This paper is an exposition for the non-specialist mathematician.
All a mathematician needs to know in order to apply transseries.