Description of fast matrix multiplication algorithm: ⟨9×11×16:996⟩

Algorithm type

4 X^{4} Y^{6} Z^{4} + 13 X^{4} Y^{5} Z^{4} + X^{4} Y^{6} Z^{2} + 47 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + X^{9} Y Z + 3 X^{6} Y^{3} Z^{2} + 4 X^{4} Y^{5} Z^{2} + 5 X^{3} Y^{4} Z^{4} + 2 X^{2} Y^{7} Z^{2} + 3 X^{2} Y^{5} Z^{4} + 4 X^{2} Y^{3} Z^{6} + 8 X Y Z^{9} + 26 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 36 X^{2} Y^{6} Z^{2} + 32 X^{2} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{6} + 5 X Y^{8} Z + X^{7} Y Z + 3 X^{5} Y^{2} Z^{2} + 2 X^{4} Y^{3} Z^{2} + 7 X^{2} Y^{6} Z + 30 X^{2} Y^{5} Z^{2} + 38 X^{2} Y^{3} Z^{4} + 4 X Y^{7} Z + 3 X Y^{6} Z^{2} + 9 X Y^{4} Z^{4} + 20 X Y^{2} Z^{6} + X^{6} Y Z + 4 X^{4} Y^{2} Z^{2} + 3 X^{2} Y^{5} Z + 71 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{2} Z^{4} + 27 X Y^{6} Z + 8 X Y^{5} Z^{2} + 4 X Y^{3} Z^{4} + 10 X Y Z^{6} + 24 X^{3} Y^{3} Z + 15 X^{3} Y^{2} Z^{2} + 6 X^{3} Y Z^{3} + 4 X^{2} Y^{4} Z + 25 X^{2} Y^{3} Z^{2} + 14 X Y^{5} Z + 37 X Y^{4} Z^{2} + 16 X Y^{3} Z^{3} + 7 X Y^{2} Z^{4} + 13 X^{3} Y^{2} Z + 21 X^{3} Y Z^{2} + 9 X^{2} Y^{3} Z + 61 X^{2} Y^{2} Z^{2} + 25 X Y^{4} Z + 43 X Y^{3} Z^{2} + 15 X Y^{2} Z^{3} + 19 X^{3} Y Z + 3 X^{2} Y^{2} Z + 2 X^{2} Y Z^{2} + 25 X Y^{3} Z + 30 X Y^{2} Z^{2} + 30 X Y Z^{3} + 7 X^{2} Y Z + 29 X Y^{2} Z + 8 X Y Z^{2} + 5 X Y Z

Algorithm definition

The algorithm ⟨9×11×16:996⟩ 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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