摘要
亏格是代数曲线的重要不变量.文章给出计算一类平面代数曲线亏格上界的符号-数值混合算法.首先通过数值稳定的符号-数值混合算法把代数曲线的定义多项式系统约化到几何对合形式,然后考察奇点的性质.如果曲线的奇点是寻常的,那么由奇点的重数可以计算出代数曲线的亏格;否则算法仅给出亏格的一个上界.
Genus is a fundamental invariant of algebraic curves.We present a symbolic-numeric algorithm to compute the genus upper bounds for plane algebraic curves.We first compute the singular points of an algebraic curve by a method based on symbolic-numeric reduction to geometric involutive form.With the multiplicities of these singular points,the genus can be found under the assumption that these singular points are ordinary ones.Otherwise,we obtain an upper bound for the genus.
作者
吴晓丽
WU Xiao-li(Higher Education Press,Beijing 100029,China)
出处
《大学数学》
2021年第4期5-9,共5页
College Mathematics
基金
国家自然科学基金(61772203)。