Description of fast matrix multiplication algorithm: ⟨12×13×16:1509⟩

Algorithm type

6 X^{4} Y^{6} Z^{6} + 4 X^{4} Y^{5} Z^{6} + 3 X^{8} Y^{4} Z^{2} + 3 X^{6} Y^{4} Z^{4} + 2 X^{4} Y^{6} Z^{4} + 8 X^{4} Y^{4} Z^{6} + 32 X^{4} Y^{5} Z^{4} + 4 X^{2} Y^{5} Z^{6} + 27 X^{6} Y^{4} Z^{2} + 6 X^{6} Y^{2} Z^{4} + 2 X^{4} Y^{6} Z^{2} + 61 X^{4} Y^{4} Z^{4} + 4 X^{3} Y^{5} Z^{4} + 2 X^{2} Y^{8} Z^{2} + 20 X^{2} Y^{4} Z^{6} + 3 X^{9} Y Z + X^{4} Y^{6} Z + 4 X^{4} Y^{5} Z^{2} + 4 X^{4} Y^{3} Z^{4} + 4 X^{2} Y^{7} Z^{2} + 7 X^{2} Y^{6} Z^{3} + 27 X^{2} Y^{3} Z^{6} + 2 X Y^{9} Z + 4 X Y^{4} Z^{6} + 4 X Y Z^{9} + 26 X^{6} Y^{2} Z^{2} + X^{4} Y^{5} Z + 10 X^{4} Y^{4} Z^{2} + 16 X^{4} Y^{2} Z^{4} + X^{3} Y^{6} Z + 3 X^{3} Y^{3} Z^{4} + 40 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{5} Z^{3} + 25 X^{2} Y^{4} Z^{4} + 59 X^{2} Y^{2} Z^{6} + X Y^{8} Z + X Y^{6} Z^{3} + 5 X Y^{3} Z^{6} + 2 X^{6} Y Z^{2} + X^{4} Y^{4} Z + 4 X^{4} Y^{3} Z^{2} + X^{3} Y^{5} Z + 3 X^{3} Y^{4} Z^{2} + 10 X^{3} Y^{2} Z^{4} + 5 X^{2} Y^{6} Z + 20 X^{2} Y^{5} Z^{2} + 9 X^{2} Y^{4} Z^{3} + 35 X^{2} Y^{3} Z^{4} + 4 X^{2} Y Z^{6} + 2 X Y^{7} Z + 2 X Y^{6} Z^{2} + X Y^{5} Z^{3} + 45 X Y^{2} Z^{6} + X^{6} Y Z + X^{4} Y^{3} Z + 6 X^{4} Y^{2} Z^{2} + X^{3} Y^{4} Z + 6 X^{3} Y^{3} Z^{2} + 5 X^{3} Y Z^{4} + 4 X^{2} Y^{5} Z + 61 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{3} Z^{3} + 87 X^{2} Y^{2} Z^{4} + 15 X Y^{6} Z + 6 X Y^{5} Z^{2} + 5 X Y^{4} Z^{3} + 32 X Y Z^{6} + 32 X^{3} Y^{3} Z + 7 X^{3} Y^{2} Z^{2} + 8 X^{3} Y Z^{3} + 6 X^{2} Y^{4} Z + 61 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 10 X^{2} Y Z^{4} + 2 X Y^{5} Z + 13 X Y^{4} Z^{2} + 27 X Y^{3} Z^{3} + 36 X Y^{2} Z^{4} + 10 X^{3} Y^{2} Z + 15 X^{3} Y Z^{2} + 81 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 5 X Y^{4} Z + 31 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 18 X Y Z^{4} + 35 X^{3} Y Z + 4 X^{2} Y^{2} Z + 5 X^{2} Y Z^{2} + 81 X Y^{3} Z + 74 X Y^{2} Z^{2} + 46 X Y Z^{3} + 25 X Y^{2} Z + 37 X Y Z^{2} + 12 X Y Z

Algorithm definition

The algorithm ⟨12×13×16:1509⟩ 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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