Description of fast matrix multiplication algorithm: ⟨8×9×16:735⟩

Algorithm type

3 X^{4} Y^{4} Z^{6} + 7 X^{4} Y^{4} Z^{5} + 35 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{4} Z^{6} + 3 X^{2} Y^{6} Z^{3} + 2 X^{2} Y^{4} Z^{5} + 12 X Y^{9} Z + 13 X^{6} Y^{2} Z^{2} + 39 X^{2} Y^{6} Z^{2} + 14 X^{2} Y^{4} Z^{4} + 16 X^{2} Y^{2} Z^{6} + X^{4} Y^{2} Z^{3} + 28 X^{2} Y^{4} Z^{3} + 16 X^{2} Y^{2} Z^{5} + 6 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 7 X Y^{2} Z^{6} + 2 X^{4} Y^{2} Z^{2} + 46 X^{2} Y^{4} Z^{2} + 29 X^{2} Y^{2} Z^{4} + 19 X Y^{6} Z + 8 X Y^{4} Z^{3} + 5 X Y^{2} Z^{5} + 12 X Y Z^{6} + 12 X^{3} Y^{3} Z + 3 X^{3} Y^{2} Z^{2} + 17 X^{2} Y^{2} Z^{3} + 19 X Y^{4} Z^{2} + 5 X Y^{3} Z^{3} + 20 X Y^{2} Z^{4} + 6 X Y Z^{5} + 16 X^{3} Y^{2} Z + X^{3} Y Z^{2} + 62 X^{2} Y^{2} Z^{2} + 9 X^{2} Y Z^{3} + 10 X Y^{4} Z + 13 X Y^{3} Z^{2} + 37 X Y^{2} Z^{3} + 2 X Y Z^{4} + 21 X^{3} Y Z + 2 X^{2} Y^{2} Z + X^{2} Y Z^{2} + 22 X Y^{3} Z + 47 X Y^{2} Z^{2} + 29 X Y Z^{3} + X^{2} Y Z + 14 X Y^{2} Z + 32 X Y Z^{2} + 5 X Y Z

Algorithm definition

The algorithm ⟨8×9×16:735⟩ 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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