Description of fast matrix multiplication algorithm: ⟨10×16×16:1560⟩

Algorithm type

8 X^{8} Y^{8} Z^{4} + 25 X^{4} Y^{8} Z^{4} + 5 X^{4} Y^{6} Z^{6} + 4 X^{4} Y^{4} Z^{8} + 8 X^{8} Y^{4} Z^{2} + 21 X^{4} Y^{8} Z^{2} + 26 X^{4} Y^{6} Z^{4} + 2 X^{4} Y^{4} Z^{6} + 2 X^{4} Y^{2} Z^{8} + 5 X^{2} Y^{8} Z^{4} + 12 X^{2} Y^{9} Z^{2} + 5 X^{6} Y^{4} Z^{2} + 7 X^{4} Y^{6} Z^{2} + 49 X^{4} Y^{4} Z^{4} + 5 X^{4} Y^{2} Z^{6} + 4 X^{2} Y^{9} Z + 60 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{7} Z^{3} + 10 X^{2} Y^{6} Z^{4} + 12 X^{2} Y^{4} Z^{6} + 5 X^{2} Y^{8} Z + 17 X^{2} Y^{7} Z^{2} + 2 X^{2} Y^{6} Z^{3} + 16 X Y^{9} Z + 5 X Y^{8} Z^{2} + 7 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 14 X^{4} Y^{2} Z^{4} + 5 X^{2} Y^{7} Z + 71 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{5} Z^{3} + 10 X^{2} Y^{4} Z^{4} + 35 X Y^{8} Z + 4 X Y^{7} Z^{2} + 4 X Y^{6} Z^{3} + 16 X^{4} Y^{4} Z + 21 X^{2} Y^{5} Z^{2} + 7 X^{2} Y^{4} Z^{3} + 5 X^{2} Y^{3} Z^{4} + 26 X Y^{7} Z + 13 X Y^{6} Z^{2} + 10 X^{4} Y^{2} Z^{2} + 5 X^{3} Y^{4} Z + 6 X^{2} Y^{5} Z + 110 X^{2} Y^{4} Z^{2} + 4 X^{2} Y^{3} Z^{3} + 33 X Y^{6} Z + 6 X Y^{5} Z^{2} + 16 X Y^{4} Z^{3} + 9 X^{3} Y^{3} Z + 8 X^{2} Y^{4} Z + 66 X^{2} Y^{3} Z^{2} + 8 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + 33 X Y^{5} Z + 6 X Y^{4} Z^{2} + 24 X^{2} Y^{3} Z + 119 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 66 X Y^{4} Z + 16 X Y^{2} Z^{3} + 22 X^{3} Y Z + 44 X^{2} Y Z^{2} + 109 X Y^{3} Z + 38 X Y^{2} Z^{2} + 20 X^{2} Y Z + 90 X Y^{2} Z + 110 X Y Z

Algorithm definition

The algorithm ⟨10×16×16:1560⟩ 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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