参数Groebner系统广泛应用于机器证明、几何定理自动推理及各类参数系统，研究参数Groebner系统的算法具有重要的理论意义和应用价值。本项目主要研究参数Groebner系统的相关算法及其在化学系统中的应用。在算法研究方面，首先解决含参向量组的线性相关性判定问题，基于该关键问题及FGLM算法和MMM算法，给出零维参数理想的参数Groebner系统在不同项序下的转换算法，参数Groebner系统的零维分支在不同项序下的转换算法及计算两个零维参数理想的交理想的参数Groebner系统的算法，并在软件Maple中编程实现。在化学系统中的应用方面，重点研究化学反应系统“单电子转移还原反应”，从数学角度给出该参数系统的准确描述，并应用参数Groebner系统探索产量最大化的参数设置，预测最高理论产量以及确定最优的反应条件。

Comprehensive Groebner system is widely used in areas of mechanical theorem-proving, automated geometry theorem proving and various parametric systems. Thus the research on algorithms of comprehensive Groebner systems and their applications in systems plays an important role in theory studying and applications. The core aims of the project are to study the revelant algorithms of comprehensive Groebner systems and their applications to chemical systems. As to the research on algorithms, we first solve the basic problem: checking the linear dependence of parametric vectors. Based on this typical solution and the two algorithms of FGLM and MMM, we propose three algorithms: the algorithm of comprehensive Groebner system transformation between different orderings for zero-dimensional parametric ideals, the algorithm of comprehensive Groebner system transformation between different orderings for zero-dimensional branch of comprehensive Groebner systems, and the algorithm to compute comprehensive Groebner systems for the intersection ideal of two zero-dimensional parametric ideals. These algorithms will be implemented in Maple. As to the applications, we focus on the chemical reaction “single electron transfer reaction”. From the mathematical view, we give a precise description for this parametric system, and study the maximum output and determine the parameters. We also give the theoretical expectation of maximum output and optimal conditons for this reaction.