Description of fast matrix multiplication algorithm: ⟨8×13×16:1054⟩

Algorithm type

6 X^{4} Y^{8} Z^{4} + 8 X^{4} Y^{6} Z^{4} + 16 X^{4} Y^{5} Z^{4} + 36 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{4} Z^{6} + 2 X^{4} Y^{3} Z^{4} + 9 X^{2} Y^{7} Z^{2} + 40 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 10 X^{2} Y^{2} Z^{6} + X Y^{7} Z^{2} + 36 X^{2} Y^{5} Z^{2} + 3 X Y^{7} Z + 2 X^{3} Y^{4} Z + 52 X^{2} Y^{4} Z^{2} + 40 X^{2} Y^{2} Z^{4} + 6 X Y^{4} Z^{3} + 76 X^{2} Y^{3} Z^{2} + 26 X Y^{4} Z^{2} + 4 X Y^{3} Z^{3} + 122 X^{2} Y^{2} Z^{2} + 87 X Y^{4} Z + 16 X Y^{3} Z^{2} + 7 X^{3} Y Z + 9 X^{2} Y Z^{2} + 114 X Y^{3} Z + 4 X Y^{2} Z^{2} + 12 X Y Z^{3} + 3 X^{2} Y Z + 98 X Y^{2} Z + 56 X Y Z^{2} + 119 X Y Z

Algorithm definition

The algorithm ⟨8×13×16:1054⟩ 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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