论文标题
一个计算策略和计划，以解决矩阵三元的Gerstenhaber问题
A computing strategy and programs to resolve the Gerstenhaber Problem for commuting triples of matrices
论文作者
论文摘要
我们描述了一个MATLAB程序，该程序可以通过建造三个通勤$ n \ times n $矩阵$ a，b，c $在field $ f $上的$ n \ times n $ n $ f $来产生负面答案。在Gerstenhaber令人惊讶的结果（Annals Math。）$ \ dim f [a，b] \ le n $中，任何两个通勤矩阵$ a，b $ to $ \ dim f [a，b] \ le n $。该属性因四个或多个通勤矩阵而失败。我们还可以免费提供MATLAB文件。
We describe a MATLAB program that could produce a negative answer to the Gerstenhaber Problem by the construction of three commuting $n \times n$ matrices $A,B,C$ over a field $F$ such that the subalgebra $F[A,B,C]$ they generate has dimension greater than $n$. This problem has remained open for nearly 60 years, following Gerstenhaber's surprising result (Annals Math.) that $\dim F[A,B] \le n$ for any two commuting matrices $A,B$. The property fails for four or more commuting matrices. We also make the MATLAB files freely available.
