Description of fast matrix multiplication algorithm: ⟨9×13×16:1167⟩

Algorithm type

X^{4} Y^{6} Z^{4} + 18 X^{4} Y^{5} Z^{4} + 58 X^{4} Y^{4} Z^{4} + 8 X^{3} Y^{5} Z^{4} + 3 X^{9} Y Z + 2 X^{4} Y^{5} Z^{2} + 2 X^{2} Y^{7} Z^{2} + X^{2} Y^{5} Z^{4} + X^{2} Y^{3} Z^{6} + 7 X Y Z^{9} + 22 X^{6} Y^{2} Z^{2} + 3 X^{5} Y^{3} Z^{2} + 9 X^{4} Y^{4} Z^{2} + X^{3} Y^{5} Z^{2} + 2 X^{3} Y^{3} Z^{4} + 27 X^{2} Y^{6} Z^{2} + 33 X^{2} Y^{4} Z^{4} + 37 X^{2} Y^{2} Z^{6} + X Y^{5} Z^{4} + 4 X^{7} Y Z + 2 X^{5} Y^{2} Z^{2} + 3 X^{4} Y^{4} Z + 18 X^{4} Y^{3} Z^{2} + 3 X^{3} Y^{4} Z^{2} + 2 X^{3} Y^{3} Z^{3} + X^{2} Y^{6} Z + 29 X^{2} Y^{5} Z^{2} + 47 X^{2} Y^{3} Z^{4} + 2 X Y^{7} Z + 3 X Y^{6} Z^{2} + 9 X Y^{2} Z^{6} + 3 X^{6} Y Z + X^{4} Y^{3} Z + 32 X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{4} Z + 3 X^{3} Y^{3} Z^{2} + 90 X^{2} Y^{4} Z^{2} + 33 X^{2} Y^{2} Z^{4} + 19 X Y^{6} Z + 7 X Y^{5} Z^{2} + 9 X Y Z^{6} + 2 X^{4} Y^{2} Z + 7 X^{3} Y^{3} Z + 6 X^{3} Y^{2} Z^{2} + 11 X^{3} Y Z^{3} + 3 X^{2} Y^{4} Z + 36 X^{2} Y^{3} Z^{2} + 3 X^{2} Y^{2} Z^{3} + 11 X Y^{5} Z + 20 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 5 X Y^{2} Z^{4} + 15 X^{3} Y^{2} Z + 8 X^{3} Y Z^{2} + 34 X^{2} Y^{3} Z + 83 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 38 X Y^{4} Z + 48 X Y^{3} Z^{2} + 25 X Y^{2} Z^{3} + 2 X Y Z^{4} + 17 X^{3} Y Z + 11 X^{2} Y^{2} Z + 28 X^{2} Y Z^{2} + 49 X Y^{3} Z + 65 X Y^{2} Z^{2} + 15 X Y Z^{3} + 18 X^{2} Y Z + 26 X Y^{2} Z + 9 X Y Z^{2}

Algorithm definition

The algorithm ⟨9×13×16:1167⟩ 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.

Back to main table