Description of fast matrix multiplication algorithm: ⟨18×28×28:7707⟩

Algorithm type

2 X^{12} Y^{12} Z^{8} + 8 X^{10} Y^{12} Z^{8} + 4 X^{12} Y^{8} Z^{8} + 6 X^{8} Y^{12} Z^{8} + 16 X^{16} Y^{6} Z^{4} + 17 X^{10} Y^{8} Z^{8} + 8 X^{6} Y^{12} Z^{8} + 16 X^{16} Y^{6} Z^{2} + 17 X^{8} Y^{8} Z^{8} + 4 X^{4} Y^{16} Z^{4} + 8 X^{14} Y^{6} Z^{2} + 44 X^{12} Y^{6} Z^{4} + 2 X^{10} Y^{4} Z^{8} + 16 X^{6} Y^{12} Z^{4} + 20 X^{6} Y^{8} Z^{8} + 4 X^{2} Y^{16} Z^{4} + 40 X^{12} Y^{6} Z^{2} + 29 X^{12} Y^{4} Z^{4} + 8 X^{10} Y^{6} Z^{4} + 10 X^{8} Y^{4} Z^{8} + 28 X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{8} Z^{8} + 6 X^{12} Y^{2} Z^{4} + 8 X^{10} Y^{6} Z^{2} + 27 X^{10} Y^{4} Z^{4} + 14 X^{8} Y^{6} Z^{4} + 16 X^{6} Y^{8} Z^{4} + 8 X^{6} Y^{4} Z^{8} + 4 X^{2} Y^{12} Z^{4} + 4 X^{12} Y^{2} Z^{2} + 8 X^{10} Y^{2} Z^{4} + 49 X^{8} Y^{4} Z^{4} + 4 X^{6} Y^{8} Z^{2} + 32 X^{6} Y^{6} Z^{4} + 24 X^{4} Y^{8} Z^{4} + 4 X^{4} Y^{4} Z^{8} + 48 X^{5} Y^{6} Z^{4} + 8 X^{10} Y^{2} Z^{2} + 16 X^{8} Y^{2} Z^{4} + 40 X^{6} Y^{6} Z^{2} + 103 X^{6} Y^{4} Z^{4} + 10 X^{4} Y^{8} Z^{2} + 36 X^{4} Y^{6} Z^{4} + 8 X^{2} Y^{8} Z^{4} + 96 X^{8} Y^{3} Z^{2} + 102 X^{5} Y^{4} Z^{4} + 48 X^{3} Y^{6} Z^{4} + 96 X^{8} Y^{3} Z + 20 X^{8} Y^{2} Z^{2} + 54 X^{6} Y^{4} Z^{2} + 14 X^{6} Y^{2} Z^{4} + 48 X^{4} Y^{6} Z^{2} + 141 X^{4} Y^{4} Z^{4} + 28 X^{2} Y^{8} Z^{2} + 48 X^{7} Y^{3} Z + 264 X^{6} Y^{3} Z^{2} + 12 X^{5} Y^{2} Z^{4} + 96 X^{3} Y^{6} Z^{2} + 120 X^{3} Y^{4} Z^{4} + 24 X Y^{8} Z^{2} + 240 X^{6} Y^{3} Z + 216 X^{6} Y^{2} Z^{2} + 48 X^{5} Y^{3} Z^{2} + 80 X^{4} Y^{4} Z^{2} + 70 X^{4} Y^{2} Z^{4} + 188 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 36 X^{6} Y Z^{2} + 48 X^{5} Y^{3} Z + 162 X^{5} Y^{2} Z^{2} + 84 X^{4} Y^{3} Z^{2} + 96 X^{3} Y^{4} Z^{2} + 48 X^{3} Y^{2} Z^{4} + 24 X Y^{6} Z^{2} + 24 X^{6} Y Z + 48 X^{5} Y Z^{2} + 350 X^{4} Y^{2} Z^{2} + 24 X^{3} Y^{4} Z + 120 X^{3} Y^{3} Z^{2} + 172 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{2} Z^{4} + 48 X^{5} Y Z + 96 X^{4} Y Z^{2} + 240 X^{3} Y^{3} Z + 474 X^{3} Y^{2} Z^{2} + 60 X^{2} Y^{4} Z + 48 X Y^{4} Z^{2} + 120 X^{4} Y Z + 324 X^{3} Y^{2} Z + 84 X^{3} Y Z^{2} + 288 X^{2} Y^{3} Z + 248 X^{2} Y^{2} Z^{2} + 24 X Y^{4} Z + 252 X^{3} Y Z + 480 X^{2} Y^{2} Z + 60 X^{2} Y Z^{2} + 120 X Y^{3} Z + 36 X Y^{2} Z^{2} + 336 X^{2} Y Z + 168 X Y^{2} Z + 84 X Y Z

Algorithm definition

The algorithm ⟨18×28×28:7707⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×14×14:1101⟩.

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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