矩阵交换三元组Gerstenhaber问题的计算策略及程序
A computing strategy and programs to resolve the Gerstenhaber Problem for commuting triples of matrices
摘要：
我们描述了一个MATLAB程序，可以产生一个否定的答案Gerstenhaber问题的建设三个交换$n \times n$矩阵$A,B,C$在一个字段$F$，使他们产生的子代数$F[A,B,C]$的维数大于$n$。这个问题一直悬而未决近60年，继Gerstenhaber的令人惊讶的结果（年鉴数学。对于任何两个交换矩阵$A,B$，都有$\dim F[A,B] \le n$。对于四个或更多的交换矩阵，该性质失效。我们还免费提供MATLAB文件。
英文摘要：
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.
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