Description of fast matrix multiplication algorithm: ⟨6×7×9:268⟩

Algorithm type

6 X^{4} Y^{4} Z^{4} + 6 X^{3} Y^{3} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{5} Z^{2} + 5 X^{2} Y^{4} Z^{2} + 21 X^{2} Y^{2} Z^{4} + X Y^{5} Z^{2} + 2 X^{2} Y^{3} Z^{2} + X Y^{3} Z^{3} + 43 X^{2} Y^{2} Z^{2} + X Y^{4} Z + 13 X Y^{3} Z^{2} + X^{2} Y^{2} Z + 3 X^{2} Y Z^{2} + 19 X Y^{3} Z + 20 X Y^{2} Z^{2} + X Y Z^{3} + 30 X Y^{2} Z + 42 X Y Z^{2} + 44 X Y Z

Algorithm definition

The algorithm ⟨6×7×9:268⟩ is taken from:

Andrew I. Perminov. Fast matrix multiplication via ternary meta flip graphs. Technical report, arXiv, November 2025. [ arXiv ]

Algorithm description

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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