Description of fast matrix multiplication algorithm: ⟨7×12×16:878⟩

Algorithm type

6 X^{4} Y^{4} Z^{5} + 34 X^{4} Y^{4} Z^{4} + 3 X^{3} Y^{4} Z^{5} + 5 X^{4} Y^{4} Z^{3} + 3 X^{2} Y^{6} Z^{3} + 3 X^{2} Y^{4} Z^{5} + 4 X Y^{9} Z + 6 X^{6} Y^{2} Z^{2} + 3 X^{5} Y^{2} Z^{3} + X^{4} Y^{4} Z^{2} + 17 X^{3} Y^{4} Z^{3} + 25 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 10 X^{2} Y^{2} Z^{6} + X Y^{4} Z^{5} + 14 X^{5} Y^{2} Z^{2} + X^{4} Y^{4} Z + X^{3} Y^{4} Z^{2} + X^{2} Y^{6} Z + 40 X^{2} Y^{4} Z^{3} + 13 X^{2} Y^{2} Z^{5} + 6 X Y^{6} Z^{2} + X Y^{4} Z^{4} + X^{5} Y^{2} Z + 69 X^{2} Y^{4} Z^{2} + 22 X^{2} Y^{2} Z^{4} + 24 X Y^{6} Z + 3 X Y^{4} Z^{3} + 2 X Y^{2} Z^{5} + 7 X Y Z^{6} + X^{4} Y^{2} Z + 5 X^{3} Y^{3} Z + 5 X^{3} Y^{2} Z^{2} + 3 X^{3} Y Z^{3} + 9 X^{2} Y^{4} Z + 35 X^{2} Y^{2} Z^{3} + 43 X Y^{4} Z^{2} + 8 X Y^{3} Z^{3} + 7 X Y^{2} Z^{4} + X Y Z^{5} + 27 X^{3} Y^{2} Z + 4 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 69 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 23 X Y^{4} Z + 9 X Y^{3} Z^{2} + 33 X Y^{2} Z^{3} + 6 X Y Z^{4} + 31 X^{3} Y Z + 14 X^{2} Y^{2} Z + 38 X Y^{3} Z + 60 X Y^{2} Z^{2} + 24 X Y Z^{3} + 6 X^{2} Y Z + 44 X Y^{2} Z + 28 X Y Z^{2} + 13 X Y Z

Algorithm definition

The algorithm ⟨7×12×16:878⟩ 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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