Description of fast matrix multiplication algorithm: ⟨13×13×16:1704⟩

Algorithm type

72 X^{4} Y^{4} Z^{8} + 33 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{2} Z^{8} + 3 X^{3} Y^{4} Z^{4} + 54 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{4} Z^{3} + 39 X^{3} Y^{3} Z^{4} + 43 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 18 X^{5} Y^{2} Z^{2} + 6 X^{3} Y^{3} Z^{3} + 6 X^{2} Y^{5} Z^{2} + 3 X^{2} Y^{2} Z^{5} + 3 X Y^{2} Z^{6} + 3 X^{5} Y Z^{2} + 63 X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{2} Z^{3} + 3 X^{3} Y Z^{4} + 71 X^{2} Y^{4} Z^{2} + 60 X^{2} Y^{2} Z^{4} + 9 X Y^{5} Z^{2} + 3 X Y^{3} Z^{4} + 9 X^{5} Y Z + 3 X^{4} Y Z^{2} + 30 X^{3} Y^{2} Z^{2} + 25 X^{2} Y^{3} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 51 X^{2} Y Z^{4} + 8 X Y^{5} Z + 2 X Y^{4} Z^{2} + 40 X Y^{2} Z^{4} + 11 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 6 X^{2} Y^{3} Z + 160 X^{2} Y^{2} Z^{2} + 21 X^{2} Y Z^{3} + 5 X Y^{3} Z^{2} + 29 X Y^{2} Z^{3} + 9 X Y Z^{4} + 5 X^{3} Y Z + 46 X^{2} Y^{2} Z + 113 X^{2} Y Z^{2} + 10 X Y^{3} Z + 113 X Y^{2} Z^{2} + 3 X Y Z^{3} + 199 X^{2} Y Z + 190 X Y^{2} Z + 9 X Y Z^{2} + 4 X Y Z

Algorithm definition

The algorithm ⟨13×13×16:1704⟩ 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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