论文标题
从头开始的Brill-Noether方法的证明
A proof of the Brill-Noether method from scratch
论文作者
论文摘要
1874年，布里尔（Brill and Noether）设计了一种用于计算Riemann-Roch空间基础的开创性几何方法。从那时起，他们的方法导致了几种算法，其中一些方法正在计算机代数系统中实现。通常的证据通常依赖于代数几何和交换代数的抽象概念。在本文中，我们提供了一个简短的独立且基本的证据，表明大多数需要牛顿多边形，远足，双变量结果和中国剩余。
In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being implemented in computer algebra systems. The usual proofs often rely on abstract concepts of algebraic geometry and commutative algebra. In this paper we present a short self-contained and elementary proof that mostly needs Newton polygons, Hensel lifting, bivariate resultants, and Chinese remaindering.
