Description of fast matrix multiplication algorithm: ⟨6×16×16:972⟩

Algorithm type

6 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{6} Z^{4} + X^{2} Y^{8} Z^{4} + 9 X^{6} Y^{4} Z^{2} + 4 X^{4} Y^{6} Z^{2} + 34 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{4} Z^{6} + 6 X^{2} Y^{7} Z^{2} + 4 X Y^{9} Z + 4 X Y^{8} Z^{2} + 13 X^{6} Y^{2} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 54 X^{2} Y^{6} Z^{2} + 17 X^{2} Y^{4} Z^{4} + 15 X^{2} Y^{2} Z^{6} + 13 X Y^{8} Z + 6 X^{2} Y^{6} Z + 15 X^{2} Y^{5} Z^{2} + 12 X Y^{7} Z + 7 X Y^{6} Z^{2} + 6 X^{4} Y^{2} Z^{2} + 14 X^{3} Y^{4} Z + 3 X^{2} Y^{5} Z + 102 X^{2} Y^{4} Z^{2} + 5 X^{2} Y^{2} Z^{4} + 28 X Y^{6} Z + X Y^{5} Z^{2} + 12 X Y^{4} Z^{3} + 15 X^{3} Y^{3} Z + 11 X^{2} Y^{4} Z + 18 X Y^{5} Z + 16 X Y^{4} Z^{2} + 12 X Y^{3} Z^{3} + 6 X^{2} Y^{3} Z + 90 X^{2} Y^{2} Z^{2} + 76 X Y^{4} Z + 4 X Y^{3} Z^{2} + 33 X^{3} Y Z + 17 X^{2} Y^{2} Z + 29 X Y^{3} Z + 26 X Y^{2} Z^{2} + 30 X Y Z^{3} + 11 X^{2} Y Z + 78 X Y^{2} Z + 10 X Y Z^{2} + 40 X Y Z

Algorithm definition

The algorithm ⟨6×16×16:972⟩ 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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