Description of fast matrix multiplication algorithm: ⟨11×12×15:1234⟩

Algorithm type

5 X^{6} Y^{4} Z^{4} + 21 X^{5} Y^{4} Z^{4} + X^{8} Y^{2} Z^{2} + 57 X^{4} Y^{4} Z^{4} + 3 X^{7} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{3} + 9 X^{3} Y^{6} Z^{2} + 2 X^{3} Y^{4} Z^{4} + 2 X^{3} Y^{2} Z^{6} + X Y^{9} Z + 5 X^{8} Y Z + 36 X^{6} Y^{2} Z^{2} + 31 X^{4} Y^{4} Z^{2} + 27 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 24 X^{2} Y^{2} Z^{6} + 4 X^{7} Y Z + 2 X^{6} Y^{2} Z + X^{6} Y Z^{2} + 16 X^{5} Y^{2} Z^{2} + 2 X^{4} Y^{2} Z^{3} + 54 X^{3} Y^{4} Z^{2} + 11 X^{3} Y^{2} Z^{4} + 22 X^{2} Y^{6} Z + 6 X^{2} Y^{2} Z^{5} + 9 X^{6} Y Z + 4 X^{5} Y^{2} Z + 2 X^{5} Y Z^{2} + 51 X^{4} Y^{2} Z^{2} + 39 X^{2} Y^{4} Z^{2} + 55 X^{2} Y^{2} Z^{4} + 11 X Y^{6} Z + 20 X Y Z^{6} + 3 X^{5} Y Z + 12 X^{4} Y^{2} Z + 2 X^{4} Y Z^{2} + 22 X^{3} Y^{3} Z + 41 X^{3} Y^{2} Z^{2} + 13 X^{3} Y Z^{3} + 28 X^{2} Y^{4} Z + 16 X^{2} Y^{2} Z^{3} + 3 X Y^{4} Z^{2} + 7 X Y Z^{5} + 3 X^{4} Y Z + 34 X^{3} Y^{2} Z + 34 X^{3} Y Z^{2} + 124 X^{2} Y^{2} Z^{2} + 8 X Y^{4} Z + 20 X Y^{3} Z^{2} + 9 X Y^{2} Z^{3} + 3 X Y Z^{4} + 34 X^{3} Y Z + 51 X^{2} Y^{2} Z + 35 X^{2} Y Z^{2} + 48 X Y^{3} Z + 12 X Y^{2} Z^{2} + 41 X Y Z^{3} + 54 X^{2} Y Z + 13 X Y^{2} Z + 18 X Y Z^{2} + 3 X Y Z

Algorithm definition

The algorithm ⟨11×12×15:1234⟩ 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