Description of fast matrix multiplication algorithm: ⟨9×10×16:916⟩

Algorithm type

64 X^{4} Y^{6} Z^{6} + 44 X^{3} Y^{6} Z^{6} + 48 X^{2} Y^{6} Z^{6} + 4 X Y^{6} Z^{6} + 6 X^{4} Y^{4} Z^{4} + 2 X^{5} Y^{4} Z^{2} + 32 X^{5} Y^{3} Z^{3} + 6 X^{3} Y^{4} Z^{4} + 4 X^{5} Y^{3} Z^{2} + 6 X^{5} Y^{2} Z^{3} + X^{4} Y^{4} Z^{2} + 64 X^{4} Y^{3} Z^{3} + 15 X^{5} Y^{2} Z^{2} + 3 X^{4} Y^{3} Z^{2} + 6 X^{4} Y^{2} Z^{3} + X^{3} Y^{4} Z^{2} + 176 X^{3} Y^{3} Z^{3} + 27 X^{4} Y^{2} Z^{2} + X^{3} Y^{4} Z + 2 X^{3} Y^{3} Z^{2} + 93 X^{2} Y^{3} Z^{3} + 10 X^{5} Y Z + X^{3} Y^{3} Z + 26 X^{3} Y^{2} Z^{2} + 21 X^{3} Y Z^{3} + 2 X^{2} Y^{4} Z + 3 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 37 X Y^{3} Z^{3} + 16 X^{4} Y Z + X^{3} Y^{2} Z + 4 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 28 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + X Y^{4} Z + 2 X Y^{2} Z^{3} + 41 X^{3} Y Z + 4 X^{2} Y^{2} Z + 8 X^{2} Y Z^{2} + 6 X Y^{2} Z^{2} + 6 X Y Z^{3} + 60 X^{2} Y Z + X Y^{2} Z + 2 X Y Z^{2} + 23 X Y Z

Algorithm definition

The algorithm ⟨9×10×16:916⟩ 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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