Description of fast matrix multiplication algorithm: ⟨5×7×8:204⟩

Algorithm type

3 X^{4} Y^{4} Z^{4} + 3 X^{3} Y^{4} Z^{3} + 2 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 2 X^{3} Y^{4} Z^{2} + 2 X^{2} Y^{2} Z^{5} + X Y^{6} Z^{2} + 2 X^{4} Y^{2} Z^{2} + 2 X^{2} Y^{4} Z^{2} + 4 X^{2} Y^{3} Z^{3} + X Y^{5} Z^{2} + X^{5} Y Z + X^{3} Y^{2} Z^{2} + 2 X^{2} Y^{4} Z + X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + X Y^{4} Z^{2} + 41 X^{2} Y^{2} Z^{2} + X Y^{4} Z + 4 X Y^{3} Z^{2} + 7 X^{3} Y Z + 7 X^{2} Y^{2} Z + 18 X Y^{3} Z + 10 X Y^{2} Z^{2} + 10 X Y Z^{3} + 5 X^{2} Y Z + 28 X Y^{2} Z + 5 X Y Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨5×7×8:204⟩ 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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