Description of fast matrix multiplication algorithm: ⟨18×24×28:6580⟩

Algorithm type

24 X^{12} Y^{12} Z^{10} + 8 X^{12} Y^{12} Z^{8} + 36 X^{12} Y^{12} Z^{6} + 12 X^{12} Y^{12} Z^{4} + 23 X^{8} Y^{8} Z^{10} + 13 X^{8} Y^{8} Z^{8} + 48 X^{4} Y^{6} Z^{14} + 80 X^{4} Y^{6} Z^{12} + 68 X^{2} Y^{6} Z^{14} + 34 X^{4} Y^{4} Z^{12} + 88 X^{2} Y^{6} Z^{12} + 18 X^{8} Y^{4} Z^{6} + 18 X^{4} Y^{8} Z^{6} + 18 X^{4} Y^{4} Z^{10} + 20 X^{2} Y^{6} Z^{10} + 144 X^{6} Y^{6} Z^{5} + 18 X^{8} Y^{4} Z^{4} + 48 X^{6} Y^{6} Z^{4} + 18 X^{4} Y^{8} Z^{4} + 56 X^{4} Y^{4} Z^{8} + 16 X^{2} Y^{6} Z^{8} + 216 X^{6} Y^{6} Z^{3} + 72 X^{6} Y^{6} Z^{2} + 25 X^{4} Y^{4} Z^{6} + 138 X^{4} Y^{4} Z^{5} + 89 X^{4} Y^{4} Z^{4} + 78 X^{4} Y^{2} Z^{6} + 78 X^{2} Y^{4} Z^{6} + 288 X^{2} Y^{3} Z^{7} + 480 X^{2} Y^{3} Z^{6} + 408 X Y^{3} Z^{7} + 38 X^{4} Y^{2} Z^{4} + 38 X^{2} Y^{4} Z^{4} + 204 X^{2} Y^{2} Z^{6} + 528 X Y^{3} Z^{6} + 108 X^{4} Y^{2} Z^{3} + 108 X^{2} Y^{4} Z^{3} + 108 X^{2} Y^{2} Z^{5} + 120 X Y^{3} Z^{5} + 136 X^{4} Y^{2} Z^{2} + 136 X^{2} Y^{4} Z^{2} + 336 X^{2} Y^{2} Z^{4} + 96 X Y^{3} Z^{4} + 150 X^{2} Y^{2} Z^{3} + 66 X^{2} Y^{2} Z^{2} + 468 X^{2} Y Z^{3} + 468 X Y^{2} Z^{3} + 228 X^{2} Y Z^{2} + 228 X Y^{2} Z^{2} + 168 X^{2} Y Z + 168 X Y^{2} Z

Algorithm definition

The algorithm ⟨18×24×28:6580⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×12×14:940⟩.

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