Description of fast matrix multiplication algorithm: ⟨8×10×12:624⟩

Algorithm type

20 X^{4} Y^{4} Z^{4} + 13 X^{4} Y^{3} Z^{4} + 2 X^{2} Y^{3} Z^{6} + 8 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 10 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 4 X^{6} Y Z^{2} + 3 X^{4} Y Z^{4} + 28 X^{2} Y^{5} Z^{2} + 9 X^{2} Y^{3} Z^{4} + 2 X^{2} Y Z^{6} + 3 X Y^{7} Z + 3 X^{4} Y^{2} Z^{2} + 76 X^{2} Y^{4} Z^{2} + 30 X^{2} Y^{2} Z^{4} + 7 X Y^{6} Z + 2 X Y^{5} Z^{2} + X^{4} Y Z^{2} + 5 X^{3} Y^{3} Z + 34 X^{2} Y^{3} Z^{2} + 9 X^{2} Y Z^{4} + 3 X Y^{5} Z + 4 X Y^{4} Z^{2} + 8 X Y^{3} Z^{3} + 4 X^{3} Y^{2} Z + 2 X^{2} Y^{3} Z + 21 X^{2} Y^{2} Z^{2} + 8 X Y^{4} Z + 37 X Y^{3} Z^{2} + 5 X Y^{2} Z^{3} + 9 X^{3} Y Z + X^{2} Y^{2} Z + 7 X^{2} Y Z^{2} + 147 X Y^{3} Z + 18 X Y^{2} Z^{2} + 3 X Y Z^{3} + 3 X^{2} Y Z + 11 X Y^{2} Z + 33 X Y Z^{2} + 11 X Y Z

Algorithm definition

The algorithm ⟨8×10×12:624⟩ 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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