Description of fast matrix multiplication algorithm: ⟨8×13×15:992⟩

Algorithm type

X^{6} Y^{6} Z^{4} + X^{4} Y^{8} Z^{4} + 5 X^{6} Y^{5} Z^{4} + 8 X^{4} Y^{3} Z^{8} + 12 X^{6} Y^{4} Z^{4} + 3 X^{4} Y^{6} Z^{4} + 3 X^{2} Y^{8} Z^{4} + X^{6} Y^{3} Z^{4} + 2 X^{4} Y^{7} Z^{2} + 11 X^{4} Y^{5} Z^{4} + 2 X^{2} Y^{7} Z^{4} + 5 X^{6} Y^{2} Z^{4} + 6 X^{4} Y^{6} Z^{2} + 15 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{6} Z^{4} + 4 X^{2} Y^{2} Z^{8} + X Y^{9} Z^{2} + 6 X^{6} Y^{3} Z^{2} + 3 X^{4} Y^{5} Z^{2} + X^{3} Y^{6} Z^{2} + X^{2} Y^{8} Z + 2 X^{2} Y^{7} Z^{2} + 5 X^{2} Y^{5} Z^{4} + 2 X^{2} Y^{3} Z^{6} + 4 X^{2} Y Z^{8} + X Y^{8} Z^{2} + 18 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 10 X^{3} Y^{5} Z^{2} + 2 X^{2} Y^{7} Z + 14 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 10 X Y^{8} Z + 3 X Y^{7} Z^{2} + 14 X^{4} Y^{3} Z^{2} + 17 X^{3} Y^{4} Z^{2} + 5 X^{2} Y^{6} Z + 52 X^{2} Y^{5} Z^{2} + 6 X^{2} Y^{3} Z^{4} + 9 X Y^{7} Z + 6 X Y^{6} Z^{2} + 8 X^{4} Y^{3} Z + 14 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{3} Z^{2} + 11 X^{2} Y^{5} Z + 36 X^{2} Y^{4} Z^{2} + 7 X Y^{6} Z + 22 X Y^{5} Z^{2} + 4 X Y^{3} Z^{4} + 4 X^{4} Y^{2} Z + 12 X^{3} Y^{3} Z + 20 X^{3} Y^{2} Z^{2} + 17 X^{2} Y^{4} Z + 49 X^{2} Y^{3} Z^{2} + 2 X^{2} Y Z^{4} + 12 X Y^{5} Z + 21 X Y^{4} Z^{2} + 5 X Y^{3} Z^{3} + 5 X Y^{2} Z^{4} + 42 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 36 X^{2} Y^{3} Z + 51 X^{2} Y^{2} Z^{2} + 7 X Y^{4} Z + 27 X Y^{3} Z^{2} + 9 X Y^{2} Z^{3} + 3 X Y Z^{4} + 18 X^{3} Y Z + 49 X^{2} Y^{2} Z + 4 X^{2} Y Z^{2} + 36 X Y^{3} Z + 22 X Y^{2} Z^{2} + 4 X Y Z^{3} + 14 X^{2} Y Z + 72 X Y^{2} Z + 5 X Y Z^{2} + 33 X Y Z

Algorithm definition

The algorithm ⟨8×13×15:992⟩ 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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