Description of fast matrix multiplication algorithm: ⟨12×16×16:1815⟩

Algorithm type

19 X^{4} Y^{6} Z^{4} + 38 X^{4} Y^{5} Z^{4} + 108 X^{4} Y^{4} Z^{4} + 48 X^{6} Y^{2} Z^{2} + 67 X^{2} Y^{6} Z^{2} + 58 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 21 X^{4} Y^{3} Z^{2} + 30 X^{2} Y^{5} Z^{2} + 82 X^{2} Y^{3} Z^{4} + 6 X^{4} Y^{2} Z^{2} + 97 X^{2} Y^{4} Z^{2} + 16 X^{2} Y^{2} Z^{4} + 23 X Y^{6} Z + 70 X^{2} Y^{3} Z^{2} + 5 X Y^{5} Z + 31 X Y^{4} Z^{2} + 26 X Y^{2} Z^{4} + 47 X^{2} Y^{3} Z + 264 X^{2} Y^{2} Z^{2} + 18 X Y^{4} Z + 45 X Y^{3} Z^{2} + 10 X Y Z^{4} + 96 X^{3} Y Z + 2 X^{2} Y^{2} Z + 9 X^{2} Y Z^{2} + 121 X Y^{3} Z + 125 X Y^{2} Z^{2} + 96 X Y Z^{3} + 5 X^{2} Y Z + 114 X Y^{2} Z + 45 X Y Z^{2} + 25 X Y Z

Algorithm definition

The algorithm ⟨12×16×16:1815⟩ 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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