Description of fast matrix multiplication algorithm: ⟨8×12×13:784⟩

Algorithm type

4 X^{4} Y^{6} Z^{4} + 16 X^{4} Y^{5} Z^{4} + 29 X^{4} Y^{4} Z^{4} + X^{2} Y^{8} Z^{2} + X Y^{9} Z^{2} + X^{6} Y^{3} Z^{2} + 10 X^{4} Y^{3} Z^{4} + X^{3} Y^{6} Z^{2} + X^{6} Y^{2} Z^{2} + X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 4 X^{3} Y^{5} Z^{2} + 2 X^{2} Y^{7} Z + 9 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{2} Z^{6} + 2 X Y^{7} Z^{2} + 2 X^{6} Y Z^{2} + 2 X^{4} Y^{3} Z^{2} + 5 X^{3} Y^{4} Z^{2} + 73 X^{2} Y^{5} Z^{2} + 2 X Y^{6} Z^{2} + 3 X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{3} Z^{2} + 4 X^{2} Y^{5} Z + 56 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + X Y^{5} Z^{2} + 10 X^{3} Y^{3} Z + 3 X^{3} Y^{2} Z^{2} + 4 X^{2} Y^{4} Z + 83 X^{2} Y^{3} Z^{2} + 5 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 4 X^{3} Y^{2} Z + 13 X^{2} Y^{3} Z + 55 X^{2} Y^{2} Z^{2} + 2 X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 2 X^{3} Y Z + 2 X^{2} Y^{2} Z + 9 X^{2} Y Z^{2} + 186 X Y^{3} Z + 3 X Y^{2} Z^{2} + 5 X^{2} Y Z + 102 X Y^{2} Z + 52 X Y Z

Algorithm definition

The algorithm ⟨8×12×13:784⟩ 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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