Description of fast matrix multiplication algorithm: ⟨9×12×13:878⟩

Algorithm type

16 X^{6} Y^{6} Z^{4} + 8 X^{6} Y^{6} Z^{3} + 16 X^{6} Y^{6} Z^{2} + 6 X^{4} Y^{4} Z^{6} + 31 X^{4} Y^{4} Z^{5} + 15 X^{4} Y^{4} Z^{4} + X^{4} Y^{4} Z^{3} + 16 X^{3} Y^{3} Z^{5} + X^{4} Y^{4} Z^{2} + 16 X^{3} Y^{3} Z^{4} + 16 X^{2} Y^{2} Z^{6} + 32 X^{4} Y^{2} Z^{3} + 32 X^{3} Y^{3} Z^{3} + X^{3} Y Z^{5} + 32 X^{2} Y^{4} Z^{3} + 3 X^{2} Y^{3} Z^{4} + 49 X^{2} Y^{2} Z^{5} + 3 X^{2} Y Z^{6} + X Y^{2} Z^{6} + X Y Z^{7} + 20 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{3} Z^{2} + 2 X^{3} Y^{2} Z^{3} + X^{3} Y Z^{4} + 20 X^{2} Y^{4} Z^{2} + 5 X^{2} Y^{3} Z^{3} + 56 X^{2} Y^{2} Z^{4} + 3 X^{2} Y Z^{5} + 4 X Y^{4} Z^{3} + 4 X Y^{2} Z^{5} + 4 X Y Z^{6} + 2 X^{4} Y^{2} Z + 4 X^{3} Y^{3} Z + 8 X^{3} Y^{2} Z^{2} + 14 X^{3} Y Z^{3} + 2 X^{2} Y^{4} Z + 47 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + 4 X Y^{4} Z^{2} + 5 X Y^{3} Z^{3} + 4 X Y^{2} Z^{4} + 16 X Y Z^{5} + 2 X^{3} Y^{2} Z + 2 X^{3} Y Z^{2} + 12 X^{2} Y^{2} Z^{2} + 62 X^{2} Y Z^{3} + 9 X Y^{3} Z^{2} + 72 X Y^{2} Z^{3} + 17 X Y Z^{4} + 6 X^{3} Y Z + 28 X^{2} Y Z^{2} + 6 X Y^{3} Z + 48 X Y^{2} Z^{2} + 14 X Y Z^{3} + 18 X^{2} Y Z + 27 X Y^{2} Z + 13 X Y Z^{2} + 7 X Y Z

Algorithm definition

The algorithm ⟨9×12×13:878⟩ 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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