Description of fast matrix multiplication algorithm: ⟨18×27×32:8280⟩

Algorithm type

192 X^{4} Y^{16} Z^{6} + 84 X^{8} Y^{8} Z^{8} + 288 X^{2} Y^{16} Z^{6} + 12 X^{12} Y^{6} Z^{4} + 192 X^{4} Y^{12} Z^{6} + 36 X^{4} Y^{12} Z^{4} + 24 X^{4} Y^{8} Z^{8} + 24 X^{4} Y^{4} Z^{12} + 288 X^{2} Y^{12} Z^{6} + 9 X^{4} Y^{10} Z^{4} + 12 X^{2} Y^{14} Z^{2} + 6 X^{2} Y^{12} Z^{4} + 24 X^{12} Y^{3} Z^{2} + 168 X^{8} Y^{4} Z^{4} + 102 X^{4} Y^{8} Z^{4} + 48 X^{4} Y^{4} Z^{8} + 9 X^{2} Y^{12} Z^{2} + 384 X^{4} Y^{8} Z^{3} + 12 X^{6} Y^{6} Z^{2} + 12 X^{4} Y^{6} Z^{4} + 15 X^{2} Y^{10} Z^{2} + 15 X^{2} Y^{8} Z^{4} + 12 X^{2} Y^{6} Z^{6} + 384 X^{4} Y^{6} Z^{3} + 960 X^{2} Y^{8} Z^{3} + 72 X^{4} Y^{6} Z^{2} + 297 X^{4} Y^{4} Z^{4} + 48 X^{4} Y^{2} Z^{6} + 33 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{6} Z^{4} + 6 X^{2} Y^{4} Z^{6} + 576 X Y^{8} Z^{3} + 24 X^{6} Y^{3} Z^{2} + 18 X^{4} Y^{5} Z^{2} + 960 X^{2} Y^{6} Z^{3} + 24 X^{6} Y^{3} Z + 204 X^{4} Y^{4} Z^{2} + 96 X^{4} Y^{2} Z^{4} + 24 X^{2} Y^{7} Z + 129 X^{2} Y^{6} Z^{2} + 54 X^{2} Y^{4} Z^{4} + 54 X^{2} Y^{2} Z^{6} + 576 X Y^{6} Z^{3} + 24 X^{4} Y^{3} Z^{2} + 18 X^{2} Y^{6} Z + 18 X^{2} Y^{5} Z^{2} + 24 X Y^{7} Z + 12 X Y^{6} Z^{2} + 162 X^{4} Y^{2} Z^{2} + 30 X^{2} Y^{5} Z + 246 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{3} Z^{3} + 117 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 24 X^{3} Y^{3} Z + 66 X^{2} Y^{4} Z + 72 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 30 X Y^{5} Z + 30 X Y^{4} Z^{2} + 24 X Y^{3} Z^{3} + 90 X^{2} Y^{3} Z + 204 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 66 X Y^{4} Z + 48 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 24 X^{2} Y^{2} Z + 42 X^{2} Y Z^{2} + 90 X Y^{3} Z + 12 X Y^{2} Z^{2} + 12 X Y Z^{3} + 60 X^{2} Y Z + 24 X Y^{2} Z + 42 X Y Z^{2} + 60 X Y Z

Algorithm definition

The algorithm ⟨18×27×32:8280⟩ is the (Kronecker) tensor product of ⟨3×3×2:15⟩ with ⟨6×9×16:552⟩.

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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