Description of fast matrix multiplication algorithm: ⟨4×16×16:666⟩

Algorithm type

3 X^{4} Y^{8} Z^{4} + 9 X^{4} Y^{6} Z^{4} + 27 X^{4} Y^{4} Z^{4} + 20 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{7} Z^{2} + 6 X Y^{9} Z + 9 X^{4} Y^{2} Z^{4} + 57 X^{2} Y^{6} Z^{2} + 15 X Y^{8} Z + 7 X^{2} Y^{5} Z^{2} + 23 X Y^{7} Z + 64 X^{2} Y^{4} Z^{2} + 14 X Y^{6} Z + 8 X^{2} Y^{3} Z^{2} + 23 X Y^{5} Z + 77 X^{2} Y^{2} Z^{2} + 59 X Y^{4} Z + 27 X^{2} Y Z^{2} + 75 X Y^{3} Z + 54 X Y^{2} Z + 87 X Y Z

Algorithm definition

The algorithm ⟨4×16×16:666⟩ 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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