Description of fast matrix multiplication algorithm: ⟨8×9×13:615⟩

Algorithm type

31 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{3} Z^{5} + 2 X Y^{9} Z + 2 X Y^{7} Z^{3} + 10 X^{6} Y^{2} Z^{2} + X^{4} Y^{3} Z^{3} + 3 X^{4} Y^{2} Z^{4} + 9 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{5} Z^{3} + 3 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 19 X^{4} Y^{2} Z^{3} + 4 X^{2} Y^{5} Z^{2} + X^{2} Y^{4} Z^{3} + 3 X^{2} Y^{2} Z^{5} + 4 X Y^{7} Z + 8 X^{4} Y^{2} Z^{2} + 36 X^{2} Y^{4} Z^{2} + 23 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + 4 X^{3} Y^{3} Z + 32 X^{2} Y^{2} Z^{3} + 7 X Y^{3} Z^{3} + 12 X^{3} Y^{2} Z + 76 X^{2} Y^{2} Z^{2} + 5 X^{2} Y Z^{3} + 3 X Y^{3} Z^{2} + 5 X Y^{2} Z^{3} + 24 X^{3} Y Z + 13 X^{2} Y^{2} Z + 66 X^{2} Y Z^{2} + 22 X Y^{3} Z + 22 X Y^{2} Z^{2} + 64 X Y Z^{3} + 31 X^{2} Y Z + 7 X Y^{2} Z + 33 X Y Z^{2} + 15 X Y Z

Algorithm definition

The algorithm ⟨8×9×13:615⟩ 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