Description of fast matrix multiplication algorithm: ⟨13×13×13:1421⟩

Algorithm type

8 X^{5} Y^{4} Z^{4} + 8 X^{4} Y^{4} Z^{5} + 3 X^{6} Y^{4} Z^{2} + 5 X^{6} Y^{2} Z^{4} + 4 X^{5} Y^{4} Z^{3} + 46 X^{4} Y^{4} Z^{4} + 2 X^{3} Y^{4} Z^{5} + 4 X^{7} Y^{2} Z^{2} + X^{5} Y^{4} Z^{2} + X^{5} Y^{2} Z^{4} + 8 X^{4} Y^{4} Z^{3} + 7 X^{4} Y^{3} Z^{4} + 14 X^{3} Y^{4} Z^{4} + 6 X^{2} Y^{6} Z^{3} + 3 X^{2} Y^{2} Z^{7} + 7 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 4 X^{4} Y^{3} Z^{3} + 45 X^{3} Y^{4} Z^{3} + 2 X^{3} Y^{3} Z^{4} + 27 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 14 X^{2} Y^{2} Z^{6} + 21 X^{5} Y^{2} Z^{2} + 4 X^{4} Y^{3} Z^{2} + 7 X^{3} Y^{4} Z^{2} + 6 X^{3} Y^{3} Z^{3} + 4 X^{2} Y^{6} Z + 4 X^{2} Y^{3} Z^{4} + 16 X^{2} Y^{2} Z^{5} + X Y^{2} Z^{6} + 2 X^{5} Y^{2} Z + 16 X^{4} Y^{2} Z^{2} + 14 X^{3} Y^{4} Z + 80 X^{3} Y^{2} Z^{3} + 83 X^{2} Y^{4} Z^{2} + 22 X^{2} Y^{2} Z^{4} + 2 X Y^{4} Z^{3} + 2 X Y^{3} Z^{4} + 2 X Y^{2} Z^{5} + 2 X^{4} Y^{2} Z + 2 X^{4} Y Z^{2} + 30 X^{3} Y^{2} Z^{2} + 48 X^{3} Y Z^{3} + 2 X^{2} Y^{4} Z + 15 X^{2} Y^{3} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 4 X Y^{4} Z^{2} + 12 X Y^{3} Z^{3} + 4 X Y^{2} Z^{4} + X^{4} Y Z + 48 X^{3} Y^{2} Z + 26 X^{3} Y Z^{2} + 16 X^{2} Y^{3} Z + 176 X^{2} Y^{2} Z^{2} + 30 X Y^{3} Z^{2} + 33 X Y^{2} Z^{3} + 2 X Y Z^{4} + 24 X^{3} Y Z + 59 X^{2} Y^{2} Z + 2 X^{2} Y Z^{2} + 10 X Y^{3} Z + 49 X Y^{2} Z^{2} + 52 X Y Z^{3} + 54 X^{2} Y Z + 41 X Y^{2} Z + 80 X Y Z^{2} + 64 X Y Z

Algorithm definition

The algorithm ⟨13×13×13:1421⟩ 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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