Description of fast matrix multiplication algorithm: ⟨8×11×12:676⟩

Algorithm type

6 X^{4} Y^{5} Z^{4} + 30 X^{4} Y^{4} Z^{4} + 2 X^{6} Y^{3} Z^{2} + X^{4} Y^{3} Z^{4} + 4 X^{2} Y^{5} Z^{4} + 5 X^{2} Y^{3} Z^{6} + 7 X^{6} Y^{2} Z^{2} + 7 X^{4} Y^{2} Z^{4} + 19 X^{2} Y^{6} Z^{2} + 7 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + X^{4} Y^{3} Z^{2} + 55 X^{2} Y^{5} Z^{2} + 7 X^{2} Y^{3} Z^{4} + 4 X^{4} Y^{2} Z^{2} + 65 X^{2} Y^{4} Z^{2} + 14 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + 7 X Y^{5} Z^{2} + 6 X^{3} Y^{3} Z + 47 X^{2} Y^{3} Z^{2} + 6 X Y^{5} Z + 2 X Y^{4} Z^{2} + 5 X Y^{3} Z^{3} + 5 X^{3} Y^{2} Z + 2 X^{2} Y^{3} Z + 27 X^{2} Y^{2} Z^{2} + 4 X Y^{4} Z + 12 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + X^{3} Y Z + 2 X^{2} Y^{2} Z + 120 X Y^{3} Z + 14 X Y^{2} Z^{2} + 2 X Y Z^{3} + 100 X Y^{2} Z + 4 X Y Z^{2} + 50 X Y Z

Algorithm definition

The algorithm ⟨8×11×12:676⟩ 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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