Description of fast matrix multiplication algorithm: ⟨10×14×16:1398⟩

Algorithm type

8 X^{4} Y^{8} Z^{8} + X^{6} Y^{6} Z^{4} + 48 X^{4} Y^{4} Z^{8} + 2 X^{8} Y^{3} Z^{4} + X^{6} Y^{5} Z^{4} + 9 X^{4} Y^{7} Z^{4} + 10 X^{4} Y^{6} Z^{4} + 16 X^{2} Y^{8} Z^{4} + 8 X^{2} Y^{4} Z^{8} + X^{6} Y^{3} Z^{4} + X^{4} Y^{5} Z^{4} + 3 X^{2} Y^{9} Z^{2} + 3 X^{2} Y^{7} Z^{4} + 4 X^{6} Y^{4} Z^{2} + X^{6} Y^{2} Z^{4} + 5 X^{4} Y^{6} Z^{2} + 10 X^{4} Y^{4} Z^{4} + X^{3} Y^{7} Z^{2} + 17 X^{2} Y^{8} Z^{2} + 17 X^{2} Y^{6} Z^{4} + 56 X^{2} Y^{2} Z^{8} + X Y^{9} Z^{2} + 2 X^{4} Y^{5} Z^{2} + 6 X^{4} Y^{3} Z^{4} + 4 X^{3} Y^{6} Z^{2} + 4 X^{2} Y^{8} Z + 25 X^{2} Y^{7} Z^{2} + 3 X^{2} Y^{3} Z^{6} + 4 X Y^{9} Z + 3 X Y^{8} Z^{2} + 3 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{5} Z^{2} + 2 X^{2} Y^{7} Z + 54 X^{2} Y^{6} Z^{2} + X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 4 X Y^{7} Z^{2} + 8 X Y Z^{8} + 4 X^{4} Y^{3} Z^{2} + 2 X^{3} Y^{5} Z + 3 X^{3} Y^{4} Z^{2} + 16 X^{2} Y^{6} Z + 18 X^{2} Y^{5} Z^{2} + 2 X^{2} Y^{3} Z^{4} + 19 X Y^{7} Z + 6 X Y^{6} Z^{2} + 16 X Y^{4} Z^{4} + X^{4} Y^{2} Z^{2} + 10 X^{3} Y^{4} Z + 5 X^{3} Y^{3} Z^{2} + 4 X^{2} Y^{5} Z + 55 X^{2} Y^{4} Z^{2} + 42 X^{2} Y^{2} Z^{4} + 60 X Y^{6} Z + 3 X Y^{5} Z^{2} + 4 X Y^{4} Z^{3} + 16 X Y^{3} Z^{4} + 5 X^{4} Y Z^{2} + 6 X^{3} Y^{3} Z + 4 X^{3} Y^{2} Z^{2} + 4 X^{2} Y^{4} Z + 62 X^{2} Y^{3} Z^{2} + 18 X Y^{5} Z + 5 X Y^{4} Z^{2} + 8 X Y^{3} Z^{3} + 6 X^{3} Y^{2} Z + 5 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 140 X^{2} Y^{2} Z^{2} + 65 X Y^{4} Z + 14 X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 40 X Y Z^{4} + 16 X^{2} Y^{2} Z + 20 X^{2} Y Z^{2} + 99 X Y^{3} Z + 2 X Y^{2} Z^{2} + 10 X Y Z^{3} + 49 X Y^{2} Z + 26 X Y Z^{2} + 130 X Y Z

Algorithm definition

The algorithm ⟨10×14×16:1398⟩ 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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