Description of fast matrix multiplication algorithm: ⟨13×15×16:1885⟩

Algorithm type

X^{4} Y^{6} Z^{5} + 3 X^{4} Y^{4} Z^{7} + X^{2} Y^{12} Z + 7 X^{4} Y^{4} Z^{6} + X^{3} Y^{8} Z^{3} + X^{3} Y^{4} Z^{7} + X^{9} Y Z^{3} + 2 X^{6} Y^{2} Z^{5} + X^{4} Y^{8} Z + 32 X^{4} Y^{4} Z^{5} + X^{4} Y^{2} Z^{7} + X^{2} Y^{9} Z^{2} + X^{2} Y^{6} Z^{5} + 14 X^{6} Y^{2} Z^{4} + 3 X^{6} Y Z^{5} + X^{4} Y^{6} Z^{2} + 99 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + X^{3} Y^{6} Z^{3} + 7 X^{3} Y^{4} Z^{5} + X^{3} Y^{2} Z^{7} + X^{2} Y^{9} Z + X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{2} Z^{8} + 2 X^{2} Y Z^{9} + 2 X Y^{9} Z^{2} + 5 X^{9} Y Z + X^{7} Y Z^{3} + X^{6} Y^{4} Z + 2 X^{6} Y^{3} Z^{2} + 10 X^{6} Y^{2} Z^{3} + 6 X^{4} Y^{4} Z^{3} + 8 X^{2} Y^{6} Z^{3} + 3 X^{2} Y^{4} Z^{5} + X^{2} Y^{3} Z^{6} + 9 X^{2} Y^{2} Z^{7} + 4 X Y^{9} Z + 3 X Y Z^{9} + X^{6} Y^{3} Z + 33 X^{6} Y^{2} Z^{2} + X^{6} Y Z^{3} + 11 X^{4} Y^{4} Z^{2} + X^{4} Y^{3} Z^{3} + 4 X^{4} Y^{2} Z^{4} + X^{4} Y Z^{5} + X^{3} Y^{6} Z + 3 X^{3} Y^{4} Z^{3} + X^{3} Y^{3} Z^{4} + 43 X^{2} Y^{6} Z^{2} + 30 X^{2} Y^{4} Z^{4} + 52 X^{2} Y^{2} Z^{6} + 2 X^{2} Y Z^{7} + X Y^{3} Z^{6} + X Y^{2} Z^{7} + 3 X Y Z^{8} + X^{7} Y Z + 6 X^{6} Y^{2} Z + 3 X^{5} Y^{2} Z^{2} + X^{4} Y^{4} Z + 20 X^{4} Y^{2} Z^{3} + X^{3} Y^{4} Z^{2} + 2 X^{3} Y^{3} Z^{3} + X^{3} Y^{2} Z^{4} + 5 X^{3} Y Z^{5} + 8 X^{2} Y^{6} Z + 105 X^{2} Y^{4} Z^{3} + X^{2} Y^{3} Z^{4} + 50 X^{2} Y^{2} Z^{5} + 7 X Y^{6} Z^{2} + 3 X Y^{2} Z^{6} + 6 X Y Z^{7} + 7 X^{6} Y Z + 46 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + X^{3} Y^{4} Z + X^{3} Y^{3} Z^{2} + 5 X^{3} Y^{2} Z^{3} + 16 X^{3} Y Z^{4} + 81 X^{2} Y^{4} Z^{2} + 4 X^{2} Y^{3} Z^{3} + 101 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 2 X Y^{4} Z^{3} + X Y^{3} Z^{4} + 2 X Y^{2} Z^{5} + 27 X Y Z^{6} + 12 X^{3} Y^{3} Z + 4 X^{3} Y^{2} Z^{2} + 22 X^{3} Y Z^{3} + X^{2} Y^{4} Z + 68 X^{2} Y^{2} Z^{3} + 4 X^{2} Y Z^{4} + 27 X Y^{4} Z^{2} + 20 X Y^{3} Z^{3} + 19 X Y^{2} Z^{4} + 11 X Y Z^{5} + X^{4} Y Z + 8 X^{3} Y^{2} Z + 20 X^{3} Y Z^{2} + 14 X^{2} Y^{3} Z + 121 X^{2} Y^{2} Z^{2} + 32 X^{2} Y Z^{3} + 25 X Y^{4} Z + 17 X Y^{3} Z^{2} + 56 X Y^{2} Z^{3} + 27 X Y Z^{4} + 17 X^{3} Y Z + 18 X^{2} Y^{2} Z + 26 X^{2} Y Z^{2} + 24 X Y^{3} Z + 128 X Y^{2} Z^{2} + 81 X Y Z^{3} + 11 X^{2} Y Z + 60 X Y^{2} Z + 29 X Y Z^{2} + 18 X Y Z

Algorithm definition

The algorithm ⟨13×15×16:1885⟩ 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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