Description of fast matrix multiplication algorithm: ⟨9×16×16:1380⟩

Algorithm type

16 X^{4} Y^{6} Z^{4} + 33 X^{4} Y^{5} Z^{4} + 65 X^{4} Y^{4} Z^{4} + 9 X^{9} Y Z + 9 X Y Z^{9} + 48 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 92 X^{2} Y^{6} Z^{2} + 71 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 6 X^{6} Y^{2} Z + 38 X^{4} Y^{3} Z^{2} + 46 X^{2} Y^{5} Z^{2} + 36 X^{2} Y^{3} Z^{4} + 6 X Y^{2} Z^{6} + 3 X^{6} Y Z + 22 X^{4} Y^{2} Z^{2} + 129 X^{2} Y^{4} Z^{2} + 19 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 3 X Y Z^{6} + 6 X^{3} Y^{3} Z + 6 X^{3} Y^{2} Z^{2} + 18 X^{3} Y Z^{3} + 6 X^{2} Y^{4} Z + 3 X^{2} Y^{3} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 14 X Y^{5} Z + 70 X Y^{4} Z^{2} + 6 X Y^{3} Z^{3} + 42 X^{3} Y^{2} Z + 3 X^{3} Y Z^{2} + 90 X^{2} Y^{3} Z + 102 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 55 X Y^{4} Z + 36 X Y^{3} Z^{2} + 42 X Y^{2} Z^{3} + 9 X^{3} Y Z + 9 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 6 X Y^{3} Z + 11 X Y^{2} Z^{2} + 9 X Y Z^{3} + 12 X^{2} Y Z + 9 X Y^{2} Z

Algorithm definition

The algorithm ⟨9×16×16:1380⟩ 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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