Description of fast matrix multiplication algorithm: ⟨13×15×15:1797⟩

Algorithm type

10 X^{4} Y^{4} Z^{6} + X^{2} Y Z^{11} + 4 X^{9} Y^{2} Z^{2} + 2 X^{8} Y^{2} Z^{3} + 16 X^{5} Y^{2} Z^{6} + 7 X Y Z^{11} + 8 X^{10} Y Z + 2 X^{8} Y Z^{3} + 2 X^{7} Y^{2} Z^{3} + 5 X^{6} Y^{2} Z^{4} + 20 X^{5} Y^{4} Z^{3} + 10 X^{5} Y^{2} Z^{5} + 2 X^{5} Y Z^{6} + 90 X^{4} Y^{4} Z^{4} + 25 X^{4} Y^{2} Z^{6} + 3 X^{3} Y^{6} Z^{3} + 20 X^{2} Y^{4} Z^{6} + 8 X^{9} Y Z + 2 X^{8} Y^{2} Z + 2 X^{7} Y Z^{3} + 23 X^{6} Y^{2} Z^{3} + 16 X^{5} Y^{2} Z^{4} + 10 X^{4} Y^{4} Z^{3} + 5 X^{3} Y^{6} Z^{2} + 6 X^{3} Y Z^{7} + 10 X^{2} Y^{4} Z^{5} + 6 X^{8} Y Z + 2 X^{7} Y^{2} Z + 25 X^{6} Y^{2} Z^{2} + 4 X^{6} Y Z^{3} + X^{5} Y^{2} Z^{3} + 2 X^{5} Y Z^{4} + 2 X^{3} Y^{6} Z + 6 X^{3} Y^{4} Z^{3} + 8 X^{3} Y^{2} Z^{5} + X^{3} Y Z^{6} + 40 X^{2} Y^{6} Z^{2} + 35 X^{2} Y^{2} Z^{6} + 6 X^{2} Y Z^{7} + 12 X Y^{6} Z^{3} + 6 X^{7} Y Z + 3 X^{6} Y^{2} Z + 53 X^{5} Y^{2} Z^{2} + X^{5} Y Z^{3} + X^{4} Y^{2} Z^{3} + 5 X^{3} Y^{4} Z^{2} + 9 X^{3} Y^{3} Z^{3} + 2 X^{3} Y^{2} Z^{4} + X^{2} Y^{6} Z + 28 X^{2} Y^{2} Z^{5} + X Y^{6} Z^{2} + 8 X Y^{2} Z^{6} + 2 X^{6} Y Z + 4 X^{5} Y^{2} Z + 2 X^{5} Y Z^{2} + 14 X^{4} Y^{2} Z^{2} + 6 X^{4} Y Z^{3} + 11 X^{3} Y^{4} Z + 5 X^{3} Y^{3} Z^{2} + 28 X^{3} Y^{2} Z^{3} + 16 X^{3} Y Z^{4} + 103 X^{2} Y^{4} Z^{2} + 23 X^{2} Y^{3} Z^{3} + X^{2} Y^{2} Z^{4} + X^{2} Y Z^{5} + 30 X Y^{4} Z^{3} + 6 X Y^{2} Z^{5} + 4 X Y Z^{6} + 2 X^{5} Y Z + 4 X^{4} Y Z^{2} + 25 X^{3} Y^{3} Z + 44 X^{3} Y^{2} Z^{2} + 27 X^{3} Y Z^{3} + X^{2} Y^{4} Z + 5 X^{2} Y^{3} Z^{2} + 40 X^{2} Y^{2} Z^{3} + 5 X^{2} Y Z^{4} + 4 X Y^{4} Z^{2} + 13 X Y^{3} Z^{3} + 3 X Y Z^{5} + X^{4} Y Z + 58 X^{3} Y^{2} Z + 17 X^{3} Y Z^{2} + 7 X^{2} Y^{3} Z + 234 X^{2} Y^{2} Z^{2} + 65 X^{2} Y Z^{3} + 3 X Y^{3} Z^{2} + 70 X Y^{2} Z^{3} + 39 X^{3} Y Z + 16 X^{2} Y^{2} Z + 13 X^{2} Y Z^{2} + 24 X Y^{3} Z + 10 X Y^{2} Z^{2} + 40 X Y Z^{3} + 6 X^{2} Y Z + 60 X Y^{2} Z + 7 X Y Z^{2} + 121 X Y Z

Algorithm definition

The algorithm ⟨13×15×15:1797⟩ 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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