Description of fast matrix multiplication algorithm: ⟨9×13×13:981⟩

Algorithm type

8 X^{4} Y^{6} Z^{4} + 54 X^{4} Y^{4} Z^{4} + 2 X^{3} Y^{5} Z^{4} + 5 X^{2} Y^{8} Z^{2} + 4 X^{4} Y^{4} Z^{3} + 2 X^{4} Y^{3} Z^{4} + X^{2} Y^{7} Z^{2} + 8 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 7 X^{4} Y^{2} Z^{4} + 3 X^{3} Y^{3} Z^{4} + 16 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{2} Z^{6} + 3 X^{2} Y^{5} Z^{2} + 16 X^{2} Y^{3} Z^{4} + 4 X^{2} Y^{2} Z^{5} + 26 X^{4} Y^{2} Z^{2} + 2 X^{3} Y Z^{4} + 40 X^{2} Y^{4} Z^{2} + 107 X^{2} Y^{2} Z^{4} + 2 X^{2} Y Z^{5} + X Y^{5} Z^{2} + 6 X Y Z^{6} + 2 X^{3} Y^{2} Z^{2} + X^{3} Y Z^{3} + 23 X^{2} Y^{3} Z^{2} + 7 X^{2} Y^{2} Z^{3} + 13 X^{2} Y Z^{4} + 8 X Y^{4} Z^{2} + 4 X Y^{2} Z^{4} + 3 X Y Z^{5} + 7 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 118 X^{2} Y^{2} Z^{2} + 4 X^{2} Y Z^{3} + 10 X Y^{4} Z + 34 X Y^{3} Z^{2} + 10 X Y Z^{4} + 8 X^{3} Y Z + 67 X^{2} Y Z^{2} + 46 X Y^{3} Z + 90 X Y^{2} Z^{2} + 13 X Y Z^{3} + 18 X^{2} Y Z + 71 X Y^{2} Z + 43 X Y Z^{2} + 38 X Y Z

Algorithm definition

The algorithm ⟨9×13×13:981⟩ 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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