Description of fast matrix multiplication algorithm: ⟨18×27×28:7410⟩

Algorithm type

3 X^{8} Y^{12} Z^{8} + 9 X^{8} Y^{10} Z^{8} + 60 X^{8} Y^{8} Z^{8} + 96 X^{4} Y^{14} Z^{6} + 3 X^{4} Y^{12} Z^{8} + 6 X^{12} Y^{6} Z^{4} + 3 X^{4} Y^{14} Z^{4} + 6 X^{4} Y^{6} Z^{12} + 120 X^{2} Y^{14} Z^{6} + 3 X^{12} Y^{4} Z^{4} + 30 X^{4} Y^{12} Z^{4} + 96 X^{4} Y^{10} Z^{6} + 15 X^{4} Y^{8} Z^{8} + 12 X^{4} Y^{4} Z^{12} + 6 X^{2} Y^{16} Z^{2} + 24 X^{2} Y^{12} Z^{6} + 6 X^{8} Y^{6} Z^{4} + 36 X^{4} Y^{10} Z^{4} + 3 X^{4} Y^{6} Z^{8} + 12 X^{2} Y^{14} Z^{2} + 6 X^{2} Y^{12} Z^{4} + 138 X^{2} Y^{10} Z^{6} + 12 X^{12} Y^{3} Z^{2} + 18 X^{8} Y^{5} Z^{4} + 6 X^{12} Y^{2} Z^{2} + 138 X^{8} Y^{4} Z^{4} + 75 X^{4} Y^{8} Z^{4} + 33 X^{4} Y^{4} Z^{8} + 6 X^{2} Y^{12} Z^{2} + 6 X^{2} Y^{10} Z^{4} + 6 X^{2} Y^{8} Z^{6} + 12 X^{6} Y^{6} Z^{2} + 192 X^{4} Y^{7} Z^{3} + 69 X^{4} Y^{6} Z^{4} + 30 X^{2} Y^{10} Z^{2} + 18 X^{2} Y^{8} Z^{4} + 12 X^{2} Y^{6} Z^{6} + 6 X^{4} Y^{7} Z^{2} + 18 X^{4} Y^{5} Z^{4} + 12 X^{4} Y^{3} Z^{6} + 36 X^{8} Y^{2} Z^{2} + 12 X^{6} Y^{4} Z^{2} + 60 X^{4} Y^{6} Z^{2} + 192 X^{4} Y^{5} Z^{3} + 252 X^{4} Y^{4} Z^{4} + 24 X^{4} Y^{2} Z^{6} + 42 X^{2} Y^{8} Z^{2} + 432 X^{2} Y^{7} Z^{3} + 36 X^{2} Y^{6} Z^{4} + 24 X^{2} Y^{4} Z^{6} + 12 X^{6} Y^{3} Z^{2} + 72 X^{4} Y^{5} Z^{2} + 6 X^{4} Y^{3} Z^{4} + 12 X^{2} Y^{8} Z + 6 X^{2} Y^{7} Z^{2} + 48 X^{2} Y^{6} Z^{3} + 12 X^{2} Y^{3} Z^{6} + 240 X Y^{7} Z^{3} + 24 X^{6} Y^{3} Z + 6 X^{6} Y^{2} Z^{2} + 150 X^{4} Y^{4} Z^{2} + 66 X^{4} Y^{2} Z^{4} + 24 X^{2} Y^{7} Z + 156 X^{2} Y^{6} Z^{2} + 468 X^{2} Y^{5} Z^{3} + 72 X^{2} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{6} + 12 X Y^{8} Z + 48 X Y^{6} Z^{3} + 24 X^{6} Y^{2} Z + 114 X^{4} Y^{3} Z^{2} + 12 X^{2} Y^{6} Z + 84 X^{2} Y^{5} Z^{2} + 12 X^{2} Y^{4} Z^{3} + 6 X^{2} Y^{3} Z^{4} + 24 X Y^{7} Z + 12 X Y^{6} Z^{2} + 276 X Y^{5} Z^{3} + 240 X^{4} Y^{2} Z^{2} + 60 X^{2} Y^{5} Z + 252 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{3} Z^{3} + 108 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + 12 X Y^{5} Z^{2} + 12 X Y^{4} Z^{3} + 24 X^{3} Y^{3} Z + 84 X^{2} Y^{4} Z + 174 X^{2} Y^{3} Z^{2} + 48 X^{2} Y^{2} Z^{3} + 60 X Y^{5} Z + 36 X Y^{4} Z^{2} + 24 X Y^{3} Z^{3} + 24 X^{3} Y^{2} Z + 168 X^{2} Y^{3} Z + 354 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 84 X Y^{4} Z + 60 X Y^{3} Z^{2} + 48 X Y^{2} Z^{3} + 132 X^{2} Y^{2} Z + 84 X^{2} Y Z^{2} + 168 X Y^{3} Z + 84 X Y^{2} Z^{2} + 24 X Y Z^{3} + 132 X^{2} Y Z + 132 X Y^{2} Z + 84 X Y Z^{2} + 132 X Y Z

Algorithm definition

The algorithm ⟨18×27×28:7410⟩ is the (Kronecker) tensor product of ⟨3×3×2:15⟩ with ⟨6×9×14:494⟩.

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.

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