神经理想的Gröbner基与典范形式集  

The Gröbner Bases and Canonical Form of Neural Ideal

作　　者：郑丽翠[1] 张艺耀 刘金旺[1] ZHENG Licui;ZHANG Yiyao;LIU Jinwang(School of Mathematics and Computing Sciences,Hunan University of Science and Technology,Xiangtan 411201)

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭411201

出　　处：《系统科学与数学》2024年第5期1303-1310,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(12201204,11971161,12271154);湖南省自然科学基金(2023JJ40275,2022JJ30234)资助课题.

摘　　要：神经环和神经理想这一概念是由Curto等(2013)提出的,它们是用于整理和分析神经编码中复杂组合信息的一种有用的代数方法.文章主要研究了神经理想的典范形式集与Gröbner基之间的关系,并根据Gröbner基中的元素给出了3种新类型的RF-关系.As presented by Curto,et al.(2013),neural rings and ideals serve as powerful algebraic constructs that facilitate the systematic organization and analysis of combinatorial data within neural codes.In this paper,we present the relationship between the Gröbner basis and canonical form of the neural ideal.Some new RF-relationships are given by analyzing the forms of elements in neural ideals.

关 键 词：神经理想 Gröbner基 典范形式集 

分 类 号：O15[理学—数学]