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Pure Mathematics 2025
基于Groebner基的单项式生成理想仿射代数簇维数计算
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Abstract:
研究代数簇的维数可以帮助深入理解代数结构与几何对象。论文研究了从单项式生成理想所对应代数簇的维数计算，通过找出单项式生成理想的Groebner基，并在此基础上探讨多种单项式理想对应簇的维数，得出了一个计算单项式生成理想簇的维数的公式，并利用Maple软件进行算法实现，得到计算代数簇维数的一种方法。
Studying the dimension of algebraic varieties aids in gaining a deeper understanding of algebraic structures and geometric objects. This paper investigates the computation of the dimension of algebraic varieties corresponding to ideals generated by monomials. By identifying the Groebner basis of the ideal generated by monomials, the paper further explores the dimensions of varieties corresponding to various monomial ideals. It derives a formula for calculating the dimension of the variety corresponding to an ideal generated by monomials and implements the algorithm using Maple software, thereby providing a method for computing the dimension of algebraic varieties.
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