Description of fast matrix multiplication algorithm: ⟨12×14×16:1617⟩

Algorithm type

10 X^{4} Y^{6} Z^{8} + 24 X^{4} Y^{6} Z^{6} + 31 X^{4} Y^{4} Z^{8} + 2 X^{4} Y^{6} Z^{4} + 53 X^{4} Y^{4} Z^{6} + 8 X^{4} Y^{2} Z^{8} + 8 X^{2} Y^{8} Z^{4} + 10 X^{2} Y^{3} Z^{8} + 4 X^{6} Y^{2} Z^{4} + 13 X^{4} Y^{4} Z^{4} + 10 X^{4} Y^{2} Z^{6} + 4 X^{2} Y^{8} Z^{2} + 48 X^{2} Y^{6} Z^{4} + 14 X^{2} Y^{3} Z^{7} + 35 X^{2} Y^{2} Z^{8} + 12 X^{2} Y^{3} Z^{6} + 30 X^{2} Y^{2} Z^{7} + 2 X^{2} Y Z^{8} + 24 X^{4} Y^{2} Z^{4} + 24 X^{2} Y^{6} Z^{2} + 64 X^{2} Y^{4} Z^{4} + 16 X^{2} Y^{3} Z^{5} + 33 X^{2} Y^{2} Z^{6} + 4 X^{2} Y Z^{7} + 8 X^{2} Y^{3} Z^{4} + 35 X^{2} Y^{2} Z^{5} + 18 X^{2} Y Z^{6} + 2 X Y^{4} Z^{4} + 8 X^{3} Y Z^{4} + 8 X^{2} Y^{4} Z^{2} + 89 X^{2} Y^{2} Z^{4} + 6 X^{2} Y Z^{5} + 10 X Y^{4} Z^{3} + 64 X Y^{3} Z^{4} + 48 X^{2} Y^{3} Z^{2} + 34 X^{2} Y Z^{4} + 40 X Y^{3} Z^{3} + 68 X Y^{2} Z^{4} + 140 X^{2} Y^{2} Z^{2} + 24 X Y^{4} Z + 36 X Y^{2} Z^{3} + 86 X Y Z^{4} + 56 X^{2} Y Z^{2} + 112 X Y^{3} Z + 34 X Y Z^{3} + 112 X Y^{2} Z + 96 X Y Z

Algorithm definition

The algorithm ⟨12×14×16:1617⟩ 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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