Description of fast matrix multiplication algorithm: ⟨13×14×15:1681⟩

Algorithm type

7 X^{4} Y^{4} Z^{6} + 2 X^{4} Y^{6} Z^{3} + 40 X^{4} Y^{4} Z^{5} + 49 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + 22 X^{4} Y^{4} Z^{3} + 2 X^{2} Y^{6} Z^{3} + 2 X^{6} Y^{2} Z^{2} + 16 X^{4} Y^{4} Z^{2} + 2 X^{2} Y^{6} Z^{2} + 25 X^{2} Y^{2} Z^{6} + 2 X^{6} Y^{2} Z + 4 X^{4} Y^{4} Z + 14 X^{4} Y^{2} Z^{3} + 27 X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{3} Z^{4} + 101 X^{2} Y^{2} Z^{5} + 21 X^{4} Y^{2} Z^{2} + 28 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 143 X^{2} Y^{2} Z^{4} + 4 X Y^{4} Z^{3} + 10 X Y Z^{6} + 10 X^{4} Y^{2} Z + X^{3} Y Z^{3} + 5 X^{2} Y^{4} Z + X^{2} Y^{3} Z^{2} + 212 X^{2} Y^{2} Z^{3} + 4 X Y^{3} Z^{3} + 15 X Y Z^{5} + 4 X^{3} Y Z^{2} + 108 X^{2} Y^{2} Z^{2} + 61 X^{2} Y Z^{3} + 2 X Y^{3} Z^{2} + 72 X Y^{2} Z^{3} + 34 X Y Z^{4} + 3 X^{3} Y Z + 15 X^{2} Y^{2} Z + 57 X^{2} Y Z^{2} + 2 X Y^{3} Z + 65 X Y^{2} Z^{2} + 178 X Y Z^{3} + 36 X^{2} Y Z + 47 X Y^{2} Z + 141 X Y Z^{2} + 82 X Y Z

Algorithm definition

The algorithm ⟨13×14×15:1681⟩ 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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