Description of fast matrix multiplication algorithm: ⟨9×9×16:822⟩

Algorithm type

4 X^{6} Y^{4} Z^{4} + 2 X^{9} Y^{2} Z^{2} + 16 X^{2} Y^{6} Z^{5} + 28 X^{4} Y^{4} Z^{4} + 16 X^{2} Y^{5} Z^{5} + 24 X Y^{6} Z^{5} + 4 X^{3} Y^{4} Z^{4} + 8 X Y^{5} Z^{5} + 24 X^{6} Y^{2} Z^{2} + 10 X^{2} Y^{6} Z^{2} + 38 X^{2} Y^{4} Z^{4} + 14 X^{2} Y^{2} Z^{6} + 2 X Y^{8} Z + 8 X Y^{5} Z^{4} + 8 X Y^{4} Z^{5} + 2 X Y Z^{8} + 10 X^{2} Y^{5} Z^{2} + 3 X^{2} Y^{3} Z^{4} + X^{2} Y^{2} Z^{5} + 2 X Y^{7} Z + 11 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 12 X Y^{2} Z^{6} + 70 X^{4} Y^{2} Z^{2} + 9 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{3} Z^{3} + 19 X^{2} Y^{2} Z^{4} + X Y^{6} Z + 2 X Y^{5} Z^{2} + 2 X Y^{3} Z^{4} + 6 X Y Z^{6} + 6 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 5 X^{3} Y Z^{3} + 5 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 6 X Y^{5} Z + 14 X Y^{4} Z^{2} + 6 X Y^{3} Z^{3} + 18 X Y^{2} Z^{4} + 5 X Y Z^{5} + 3 X^{3} Y^{2} Z + 7 X^{3} Y Z^{2} + 22 X^{2} Y^{3} Z + 85 X^{2} Y^{2} Z^{2} + 22 X^{2} Y Z^{3} + 4 X Y^{4} Z + 18 X Y^{3} Z^{2} + 10 X Y^{2} Z^{3} + 6 X Y Z^{4} + 3 X^{3} Y Z + 18 X^{2} Y^{2} Z + 23 X^{2} Y Z^{2} + 28 X Y^{3} Z + 31 X Y^{2} Z^{2} + 24 X Y Z^{3} + 11 X^{2} Y Z + 23 X Y^{2} Z + 27 X Y Z^{2} + 15 X Y Z

Algorithm definition

The algorithm ⟨9×9×16:822⟩ 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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