Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for a large number of schemes a pairwise equivalence check becomes cumbersome. In this paper we propose an algorithm to compute a normal form of matrix multiplication schemes. This allows us to decide pairwise equivalence of a larger number of schemes efficiently.
翻译:小矩阵精确乘法方案有一个大对称组。 这个组界定了一组乘法方案的等同关系。 有算法可以决定两种方案是否等同。 但是,对于许多方案,对等等制检查变得累赘。 在本文中,我们建议一种算法来计算一种正常的矩阵乘法方案。 这样我们就可以有效地决定对等制更多的方案。