论文标题
Newton-Puiseux算法和有效的代数系列
The Newton-Puiseux algorithm and effective algebraic series
论文作者
论文摘要
我们解释了如何通过有限量的数据来编码代数序列，即其最小的多项式，总顺序及其相对于此顺序的第一个术语，以及如何在这些编码级别上进行有效的算术。推理基于牛顿 - 普寿岛算法和代数系列的有效平等测试。我们还解释了如何得出有关代数系列的支持的信息，即其支撑凸壳的顶点和有限面。此外，我们展示了如何识别多项式方程的多项式和合理解。
We explain how to encode an algebraic series by a finite amount of data, namely its minimal polynomial, a total order and its first terms with respect to this order, and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorithm and an effective equality test for algebraic series. We also explain how to derive information about the support of an algebraic series, that is, the vertices and bounded faces of the convex hull of its support. Furthermore, we show how to identify the polynomial and rational solutions of a polynomial equation.
