高维多项式理想的实根计算  

Computing the real radicals of higher-dimensional polynomial ideals

作　　者：杨雪英 肖水晶[1] YANG Xueying;XIAO Shuijing(School of Science,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学理学院,江西南昌330031

出　　处：《南昌大学学报（理科版）》2021年第5期409-415,共7页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11561046,12161057)。

摘　　要：研究高维多项式理想实根的计算。对于给定的高维多项式理想,首先通过一个典范同态映射将其转化为扩张多项式环中的零维理想。基于零维实根是实极大理想的交集的结论,该扩张理想的实根可以在新的多项式环中计算。最后,通过理想的收缩,把实根收缩回原多项式环,便可得到高维多项式理想的实根。It focuses on the computation of the real radicals of higher-dimensional polynomial ideals.For a given higher-dimensional ideal of polynomials,it was firstly transformed into a zero-dimensional ideal in an extended polynomial ring via an injection.Based on the conclusion that a zero-dimensional real radical is an intersection of real maximal ideals,the real radical of this extension ideal can be computed in the new polynomial ring.Finally,with the aid of the contraction to the original polynomial ring,the real radical of the considered polynomial ideal can be obtained.

关 键 词：多项式理想 根理想 实根理想 零维理想 高维理想 理想的收缩与扩张 

分 类 号：O174.14[理学—数学]