Description of fast matrix multiplication algorithm: ⟨16×18×28:4578⟩

Algorithm type

2 X^{8} Y^{12} Z^{8} + 3 X^{8} Y^{10} Z^{8} + 29 X^{8} Y^{8} Z^{8} + 4 X^{12} Y^{6} Z^{4} + 2 X^{4} Y^{14} Z^{4} + 9 X^{12} Y^{4} Z^{4} + 6 X^{8} Y^{4} Z^{8} + 15 X^{4} Y^{12} Z^{4} + 6 X^{4} Y^{8} Z^{8} + 6 X^{4} Y^{4} Z^{12} + 3 X^{2} Y^{16} Z^{2} + 2 X^{8} Y^{6} Z^{4} + 30 X^{4} Y^{10} Z^{4} + 7 X^{4} Y^{6} Z^{8} + 6 X^{2} Y^{14} Z^{2} + X^{8} Y^{4} Z^{4} + 40 X^{4} Y^{8} Z^{4} + 26 X^{4} Y^{4} Z^{8} + 4 X^{2} Y^{10} Z^{4} + 10 X^{6} Y^{6} Z^{2} + 57 X^{4} Y^{6} Z^{4} + 24 X^{2} Y^{10} Z^{2} + 4 X^{2} Y^{8} Z^{4} + 4 X^{2} Y^{6} Z^{6} + 18 X^{4} Y^{5} Z^{4} + 10 X^{6} Y^{4} Z^{2} + 4 X^{4} Y^{6} Z^{2} + 235 X^{4} Y^{4} Z^{4} + 25 X^{2} Y^{8} Z^{2} + 42 X^{2} Y^{6} Z^{4} + 4 X^{2} Y^{4} Z^{6} + 24 X^{6} Y^{3} Z^{2} + 12 X^{2} Y^{7} Z^{2} + 58 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{4} Z^{2} + 44 X^{4} Y^{2} Z^{4} + 126 X^{2} Y^{6} Z^{2} + 110 X^{2} Y^{4} Z^{4} + 44 X^{2} Y^{2} Z^{6} + 18 X Y^{8} Z + 12 X^{4} Y^{3} Z^{2} + 180 X^{2} Y^{5} Z^{2} + 42 X^{2} Y^{3} Z^{4} + 36 X Y^{7} Z + 6 X^{4} Y^{2} Z^{2} + 268 X^{2} Y^{4} Z^{2} + 208 X^{2} Y^{2} Z^{4} + 24 X Y^{5} Z^{2} + 60 X^{3} Y^{3} Z + 270 X^{2} Y^{3} Z^{2} + 144 X Y^{5} Z + 24 X Y^{4} Z^{2} + 24 X Y^{3} Z^{3} + 60 X^{3} Y^{2} Z + 24 X^{2} Y^{3} Z + 372 X^{2} Y^{2} Z^{2} + 150 X Y^{4} Z + 252 X Y^{3} Z^{2} + 24 X Y^{2} Z^{3} + 24 X^{3} Y Z + 24 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 216 X Y^{3} Z + 444 X Y^{2} Z^{2} + 48 X Y Z^{3} + 168 X Y^{2} Z + 312 X Y Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨16×18×28:4578⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×9×14:654⟩.

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