Description of fast matrix multiplication algorithm: ⟨9×9×9:486⟩

Algorithm type

27 X^{4} Y^{4} Z^{4} + 12 X^{4} Y^{2} Z^{3} + 18 X^{2} Y^{4} Z^{3} + 18 X^{2} Y^{2} Z^{5} + 42 X^{4} Y^{2} Z^{2} + 9 X^{2} Y^{4} Z^{2} + 9 X^{2} Y^{2} Z^{4} + 6 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 10 X^{2} Y^{3} Z + 66 X^{2} Y^{2} Z^{2} + 30 X^{2} Y Z^{3} + 6 X Y^{3} Z^{2} + 27 X^{3} Y Z + 12 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 10 X Y^{3} Z + 24 X Y^{2} Z^{2} + 30 X Y Z^{3} + 2 X^{2} Y Z + 12 X Y^{2} Z + 24 X Y Z^{2} + 56 X Y Z

Algorithm definition

The algorithm ⟨9×9×9:486⟩ is taken from:

Andrew I. Perminov. FastMatrixMultiplication, GitHub, February 2026. [ GitHub repository ]

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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