Description of fast matrix multiplication algorithm: ⟨8×15×16:1185⟩

Algorithm type

48 X^{4} Y^{8} Z^{4} + 24 X^{2} Y^{12} Z^{2} + 2 X^{4} Y^{4} Z^{6} + 24 X Y^{12} Z + 24 X^{4} Y^{4} Z^{5} + 24 X^{6} Y^{4} Z^{2} + 13 X^{4} Y^{4} Z^{4} + 48 X^{2} Y^{8} Z^{2} + 6 X^{6} Y^{2} Z^{3} + 3 X^{4} Y^{4} Z^{3} + 4 X^{2} Y^{6} Z^{3} + 6 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{4} Z^{2} + 2 X^{2} Y^{6} Z^{2} + 42 X^{2} Y^{4} Z^{4} + 32 X^{2} Y^{2} Z^{6} + 11 X^{4} Y^{2} Z^{3} + 62 X^{2} Y^{4} Z^{3} + 14 X^{2} Y^{2} Z^{5} + 9 X Y^{6} Z^{2} + 7 X^{4} Y^{2} Z^{2} + 24 X^{3} Y^{4} Z + 32 X^{2} Y^{4} Z^{2} + 31 X^{2} Y^{2} Z^{4} + 3 X Y^{6} Z + X Y^{4} Z^{3} + 12 X Y Z^{6} + 20 X^{3} Y^{2} Z^{2} + 20 X^{3} Y Z^{3} + 2 X^{2} Y^{4} Z + 39 X^{2} Y^{2} Z^{3} + 58 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 18 X Y^{2} Z^{4} + 4 X Y Z^{5} + 4 X^{3} Y^{2} Z + 2 X^{3} Y Z^{2} + 127 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 16 X Y^{4} Z + X Y^{3} Z^{2} + 42 X Y^{2} Z^{3} + 4 X Y Z^{4} + 50 X^{3} Y Z + 15 X^{2} Y^{2} Z + 3 X^{2} Y Z^{2} + 49 X Y^{3} Z + 37 X Y^{2} Z^{2} + 37 X Y Z^{3} + 9 X^{2} Y Z + 20 X Y^{2} Z + 55 X Y Z^{2} + 8 X Y Z

Algorithm definition

The algorithm ⟨8×15×16:1185⟩ 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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