Description of fast matrix multiplication algorithm: ⟨11×15×16:1605⟩

Algorithm type

X^{6} Y^{4} Z^{6} + 8 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{4} Z^{8} + 8 X^{2} Y^{12} Z^{2} + X^{8} Y^{4} Z^{3} + X^{6} Y^{4} Z^{5} + 8 X^{4} Y^{4} Z^{7} + 2 X^{8} Y^{4} Z^{2} + X^{6} Y^{4} Z^{4} + 11 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{4} Z^{8} + 8 X Y^{12} Z + 2 X^{6} Y^{4} Z^{3} + 3 X^{6} Y^{2} Z^{5} + 13 X^{4} Y^{4} Z^{5} + 2 X^{2} Y^{4} Z^{7} + 2 X^{2} Y^{2} Z^{9} + X^{6} Y^{4} Z^{2} + 3 X^{6} Y^{2} Z^{4} + 66 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{6} + 8 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 15 X^{2} Y^{2} Z^{8} + 4 X^{9} Y Z + 6 X^{4} Y^{4} Z^{3} + 5 X^{4} Y^{2} Z^{5} + 8 X^{3} Y^{4} Z^{4} + 2 X^{3} Y^{2} Z^{6} + 2 X^{2} Y^{6} Z^{3} + 17 X^{2} Y^{4} Z^{5} + 14 X^{2} Y^{2} Z^{7} + 4 X Y^{9} Z + 3 X Y^{2} Z^{8} + 2 X Y Z^{9} + 4 X^{8} Y Z + 41 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{4} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{4} Z^{3} + X^{3} Y^{2} Z^{5} + 5 X^{3} Y Z^{6} + 39 X^{2} Y^{6} Z^{2} + 34 X^{2} Y^{4} Z^{4} + 59 X^{2} Y^{2} Z^{6} + 5 X Y^{4} Z^{5} + 2 X Y^{2} Z^{7} + 15 X Y Z^{8} + 4 X^{7} Y Z + 2 X^{6} Y^{2} Z + 13 X^{5} Y^{2} Z^{2} + 3 X^{4} Y^{4} Z + 5 X^{4} Y^{2} Z^{3} + 7 X^{3} Y^{4} Z^{2} + 8 X^{3} Y^{2} Z^{4} + 2 X^{3} Y Z^{5} + 4 X^{2} Y^{6} Z + 40 X^{2} Y^{4} Z^{3} + 31 X^{2} Y^{2} Z^{5} + 8 X^{2} Y Z^{6} + 13 X Y^{6} Z^{2} + 6 X Y^{4} Z^{4} + 6 X Y^{2} Z^{6} + 9 X Y Z^{7} + 15 X^{6} Y Z + 2 X^{5} Y^{2} Z + 32 X^{4} Y^{2} Z^{2} + 2 X^{3} Y^{4} Z + 11 X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 59 X^{2} Y^{4} Z^{2} + 73 X^{2} Y^{2} Z^{4} + 6 X^{2} Y Z^{5} + 16 X Y^{6} Z + 4 X Y^{4} Z^{3} + 22 X Y^{2} Z^{5} + 38 X Y Z^{6} + 3 X^{5} Y Z + 2 X^{4} Y^{2} Z + 13 X^{3} Y^{3} Z + 7 X^{3} Y^{2} Z^{2} + 15 X^{3} Y Z^{3} + 5 X^{2} Y^{4} Z + 64 X^{2} Y^{2} Z^{3} + 3 X^{2} Y Z^{4} + 12 X Y^{4} Z^{2} + 11 X Y^{3} Z^{3} + 35 X Y^{2} Z^{4} + 18 X Y Z^{5} + 21 X^{3} Y^{2} Z + 18 X^{3} Y Z^{2} + 13 X^{2} Y^{3} Z + 85 X^{2} Y^{2} Z^{2} + 9 X^{2} Y Z^{3} + 4 X Y^{4} Z + 11 X Y^{3} Z^{2} + 50 X Y^{2} Z^{3} + 12 X Y Z^{4} + 24 X^{3} Y Z + 10 X^{2} Y^{2} Z + 17 X^{2} Y Z^{2} + 34 X Y^{3} Z + 80 X Y^{2} Z^{2} + 55 X Y Z^{3} + 2 X^{2} Y Z + 14 X Y^{2} Z + 33 X Y Z^{2} + 7 X Y Z

Algorithm definition

The algorithm ⟨11×15×16:1605⟩ 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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