Description of fast matrix multiplication algorithm: ⟨5×12×16:655⟩

Algorithm type

12 X^{4} Y^{4} Z^{4} + 16 X^{2} Y^{8} Z^{2} + 3 X^{4} Y^{4} Z^{3} + X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{3} Z^{3} + 24 X^{3} Y^{4} Z^{3} + 3 X^{2} Y^{6} Z^{2} + 17 X Y^{8} Z + 3 X^{5} Y^{2} Z^{2} + 5 X^{3} Y^{3} Z^{3} + X^{2} Y^{6} Z + X^{2} Y^{5} Z^{2} + X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{2} Z^{5} + X Y^{7} Z + 2 X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{3} Z^{2} + 83 X^{2} Y^{4} Z^{2} + 13 X^{2} Y^{2} Z^{4} + 8 X Y^{6} Z + X Y^{4} Z^{3} + 2 X Y^{2} Z^{5} + X^{3} Y^{2} Z^{2} + 13 X^{2} Y^{4} Z + 13 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 2 X Y^{5} Z + 4 X Y^{4} Z^{2} + 6 X^{3} Y^{2} Z + 3 X^{2} Y^{3} Z + 56 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 55 X Y^{4} Z + 18 X Y^{2} Z^{3} + 6 X^{3} Y Z + 9 X^{2} Y^{2} Z + 17 X Y^{3} Z + 33 X Y^{2} Z^{2} + 9 X Y Z^{3} + 6 X^{2} Y Z + 98 X Y^{2} Z + 32 X Y Z^{2} + 56 X Y Z

Algorithm definition

The algorithm ⟨5×12×16:655⟩ 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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