Gro^¨ bner基方法验证乘法器的Maple实现

Maple Implementation of Verification Multiplier Based on Gro^¨ bner Basis

摘要: 乘法器电路验证问题是一项极其重要而又极具挑战性的难题。当前主流的方法是先将其建模成交换代数中的理想成员问题，然后使用Mathematica、Singular等计算机代数系统中的Gröbner基方法进行判定。本文使用计算机代数系统Maple对这一方法给出了全新实现并在计算机上进行了对比实验。实验结果表明：Maple的实现在某种程度上具有更高的验证效率，可成为乘法器电路强有力的验证平台。

Abstract: The verification of multiplier circuit is a very important and challenging problem. At present, the mainstream method is to model the ideal member problem in commutative algebra, and then use the Gröbner basis method in Mathematica, Singular and other computer algebra systems to determine. In this paper, a new implementation of this method is given by using the computer algebra system Maple, and a comparative experiment is carried out on the computer. The experimental results show that the implementation of maple has higher verification efficiency to some extent, and can be a powerful verification platform for multiplier circuits.