Description of fast matrix multiplication algorithm: ⟨18×26×27:7020⟩

Algorithm type

15 X^{8} Y^{10} Z^{8} + 36 X^{8} Y^{8} Z^{8} + 72 X^{6} Y^{14} Z^{4} + 3 X^{8} Y^{10} Z^{4} + 12 X^{8} Y^{6} Z^{8} + 48 X^{6} Y^{14} Z^{2} + 24 X^{6} Y^{12} Z^{4} + 9 X^{12} Y^{4} Z^{4} + 12 X^{8} Y^{8} Z^{4} + 3 X^{8} Y^{4} Z^{8} + 60 X^{6} Y^{12} Z^{2} + 96 X^{6} Y^{10} Z^{4} + 21 X^{4} Y^{12} Z^{4} + 15 X^{8} Y^{6} Z^{4} + 180 X^{6} Y^{10} Z^{2} + 6 X^{4} Y^{12} Z^{2} + 39 X^{4} Y^{10} Z^{4} + 3 X^{4} Y^{6} Z^{8} + 3 X^{2} Y^{14} Z^{2} + 30 X^{4} Y^{5} Z^{8} + 21 X^{8} Y^{4} Z^{4} + 3 X^{4} Y^{10} Z^{2} + 66 X^{4} Y^{8} Z^{4} + 81 X^{4} Y^{4} Z^{8} + 18 X^{2} Y^{12} Z^{2} + 24 X^{4} Y^{3} Z^{8} + 3 X^{8} Y^{2} Z^{4} + 9 X^{6} Y^{6} Z^{2} + 6 X^{4} Y^{8} Z^{2} + 66 X^{4} Y^{6} Z^{4} + 18 X^{4} Y^{2} Z^{8} + 144 X^{3} Y^{7} Z^{4} + 6 X^{2} Y^{10} Z^{2} + 36 X^{4} Y^{5} Z^{4} + 48 X^{3} Y^{6} Z^{4} + 6 X^{2} Y^{3} Z^{8} + 18 X^{6} Y^{2} Z^{4} + 39 X^{4} Y^{6} Z^{2} + 186 X^{4} Y^{4} Z^{4} + 240 X^{3} Y^{7} Z^{2} + 192 X^{3} Y^{5} Z^{4} + 18 X^{2} Y^{8} Z^{2} + 63 X^{2} Y^{6} Z^{4} + 18 X^{2} Y^{2} Z^{8} + 6 X^{4} Y^{5} Z^{2} + 54 X^{4} Y^{3} Z^{4} + 96 X^{3} Y^{7} Z + 168 X^{3} Y^{6} Z^{2} + 78 X^{2} Y^{5} Z^{4} + 24 X^{2} Y Z^{8} + 30 X^{6} Y^{2} Z^{2} + 54 X^{4} Y^{4} Z^{2} + 69 X^{4} Y^{2} Z^{4} + 120 X^{3} Y^{6} Z + 552 X^{3} Y^{5} Z^{2} + 174 X^{2} Y^{6} Z^{2} + 147 X^{2} Y^{4} Z^{4} + 6 X Y^{7} Z^{2} + 30 X^{4} Y^{3} Z^{2} + 6 X^{4} Y Z^{4} + 360 X^{3} Y^{5} Z + 12 X^{2} Y^{6} Z + 84 X^{2} Y^{5} Z^{2} + 138 X^{2} Y^{3} Z^{4} + 6 X Y^{7} Z + 36 X Y^{6} Z^{2} + 78 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{3} Z^{2} + 6 X^{2} Y^{5} Z + 204 X^{2} Y^{4} Z^{2} + 216 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 12 X Y^{5} Z^{2} + 42 X Y^{3} Z^{4} + 6 X^{4} Y Z^{2} + 18 X^{3} Y^{3} Z + 12 X^{2} Y^{4} Z + 210 X^{2} Y^{3} Z^{2} + 66 X^{2} Y Z^{4} + 12 X Y^{5} Z + 36 X Y^{4} Z^{2} + 30 X Y^{2} Z^{4} + 24 X^{3} Y Z^{2} + 78 X^{2} Y^{3} Z + 288 X^{2} Y^{2} Z^{2} + 36 X Y^{4} Z + 282 X Y^{3} Z^{2} + 36 X Y Z^{4} + 24 X^{3} Y Z + 60 X^{2} Y^{2} Z + 114 X^{2} Y Z^{2} + 240 X Y^{3} Z + 150 X Y^{2} Z^{2} + 72 X^{2} Y Z + 120 X Y^{2} Z + 132 X Y Z^{2} + 96 X Y Z

Algorithm definition

The algorithm ⟨18×26×27:7020⟩ is the (Kronecker) tensor product of ⟨3×2×3:15⟩ with ⟨6×13×9:468⟩.

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