Description of fast matrix multiplication algorithm: ⟨2×7×7:76⟩

Algorithm type

2 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{5} Z^{2} + 3 X Y^{7} Z + 4 X^{2} Y^{4} Z^{2} + X Y^{6} Z + 3 X^{2} Y^{3} Z^{2} + 17 X Y^{5} Z + 9 X^{2} Y^{2} Z^{2} + 6 X Y^{4} Z + X^{2} Y Z^{2} + 9 X Y^{3} Z + 5 X Y^{2} Z + 12 X Y Z

Algorithm definition

The algorithm ⟨2×7×7:76⟩ is taken from:

Manuel Kauers and Issaac Wood. Exploring the meta flip graph for matrix multiplication. Technical Report 2510.19787, arXiv, October 2025. [ arXiv ]

Algorithm description

Algorithm symmetries

The following group of 2 isotropies acts as a permutation group on algorithm tensor representation:

maple tensor representation (compressed by bzip2);

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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