Description of fast matrix multiplication algorithm: ⟨7×10×12:557⟩

Algorithm type

16 X^{4} Y^{8} Z^{4} + 16 X^{4} Y^{8} Z^{3} + 4 X^{2} Y^{8} Z^{3} + 20 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z + 16 X^{2} Y^{4} Z^{5} + 16 X^{2} Y^{4} Z^{4} + 16 X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{2} Z^{5} + 24 X^{2} Y^{4} Z^{2} + 9 X^{2} Y^{2} Z^{4} + 24 X Y^{4} Z^{3} + 31 X^{2} Y^{2} Z^{3} + 20 X Y^{4} Z^{2} + 3 X Y^{3} Z^{3} + 4 X Y Z^{5} + 4 X^{3} Y Z^{2} + 55 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 28 X Y^{4} Z + 2 X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 2 X Y Z^{4} + 8 X^{3} Y Z + 12 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + X Y^{3} Z + 12 X Y^{2} Z^{2} + 62 X Y Z^{3} + 6 X^{2} Y Z + 10 X Y^{2} Z + 67 X Y Z^{2} + 45 X Y Z

Algorithm definition

The algorithm ⟨7×10×12:557⟩ 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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