Description of fast matrix multiplication algorithm: ⟨14×16×16:2128⟩

Algorithm type

6 X^{6} Y^{4} Z^{6} + 8 X^{6} Y^{4} Z^{5} + 8 X^{5} Y^{4} Z^{6} + 16 X^{6} Y^{4} Z^{4} + 42 X^{6} Y^{2} Z^{6} + 18 X^{5} Y^{4} Z^{5} + 18 X^{4} Y^{4} Z^{6} + 8 X^{6} Y^{2} Z^{5} + 14 X^{5} Y^{4} Z^{4} + 6 X^{5} Y^{2} Z^{6} + 16 X^{4} Y^{4} Z^{5} + 8 X^{8} Y^{2} Z^{2} + 6 X^{6} Y^{2} Z^{4} + 124 X^{4} Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{6} + 10 X^{2} Y^{2} Z^{8} + 10 X^{7} Y^{2} Z^{2} + 34 X^{4} Y^{4} Z^{3} + 8 X^{4} Y^{2} Z^{5} + 13 X^{3} Y^{4} Z^{4} + 10 X^{2} Y^{2} Z^{7} + 12 X Y^{9} Z + 23 X^{6} Y^{2} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 10 X^{4} Y^{2} Z^{4} + 21 X^{3} Y^{4} Z^{3} + 82 X^{2} Y^{6} Z^{2} + 7 X^{2} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{6} + X^{5} Y^{2} Z^{2} + 3 X^{2} Y^{4} Z^{3} + X^{2} Y^{2} Z^{5} + X^{6} Y Z + 31 X^{4} Y^{2} Z^{2} + 3 X^{4} Y Z^{3} + 57 X^{3} Y^{2} Z^{3} + 3 X^{3} Y Z^{4} + 56 X^{2} Y^{4} Z^{2} + 45 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 2 X Y^{3} Z^{4} + X Y Z^{6} + 68 X^{3} Y^{2} Z^{2} + 130 X^{3} Y Z^{3} + 80 X^{2} Y^{2} Z^{3} + 8 X Y^{2} Z^{4} + 49 X^{4} Y Z + 2 X^{3} Y^{2} Z + 17 X^{3} Y Z^{2} + 6 X^{2} Y^{3} Z + 374 X^{2} Y^{2} Z^{2} + 9 X^{2} Y Z^{3} + 4 X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 35 X Y Z^{4} + 47 X^{3} Y Z + 68 X^{2} Y^{2} Z + 2 X^{2} Y Z^{2} + 124 X Y^{3} Z + 48 X Y^{2} Z^{2} + 51 X Y Z^{3} + 50 X^{2} Y Z + 7 X Y^{2} Z + 84 X Y Z^{2} + 50 X Y Z

Algorithm definition

The algorithm ⟨14×16×16:2128⟩ 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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