Description of fast matrix multiplication algorithm: ⟨7×8×12:452⟩

Algorithm type

12 X^{4} Y^{4} Z^{4} + 12 X^{4} Y^{4} Z^{3} + X^{2} Y^{6} Z^{3} + 5 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{6} Z + 6 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{2} Z^{5} + 22 X^{2} Y^{4} Z^{2} + 22 X^{2} Y^{2} Z^{4} + X^{3} Y Z^{3} + 4 X^{2} Y^{4} Z + 29 X^{2} Y^{2} Z^{3} + 6 X Y^{3} Z^{3} + 3 X Y^{2} Z^{4} + 3 X Y Z^{5} + 4 X^{3} Y Z^{2} + 59 X^{2} Y^{2} Z^{2} + 7 X Y^{3} Z^{2} + 30 X Y^{2} Z^{3} + 4 X Y Z^{4} + 4 X^{3} Y Z + 10 X^{2} Y^{2} Z + X^{2} Y Z^{2} + 12 X Y^{3} Z + 36 X Y^{2} Z^{2} + 30 X Y Z^{3} + 2 X^{2} Y Z + 38 X Y^{2} Z + 31 X Y Z^{2} + 44 X Y Z

Algorithm definition

The algorithm ⟨7×8×12:452⟩ 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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