Description of fast matrix multiplication algorithm: ⟨18×22×32:6972⟩

Algorithm type

4 X^{8} Y^{12} Z^{8} + 13 X^{8} Y^{10} Z^{8} + X^{8} Y^{12} Z^{4} + 47 X^{8} Y^{8} Z^{8} + 2 X^{4} Y^{16} Z^{4} + X^{18} Y^{2} Z^{2} + 3 X^{12} Y^{6} Z^{4} + 4 X^{8} Y^{10} Z^{4} + 5 X^{6} Y^{8} Z^{8} + 2 X^{4} Y^{14} Z^{4} + 3 X^{4} Y^{10} Z^{8} + 4 X^{4} Y^{6} Z^{12} + 8 X^{2} Y^{2} Z^{18} + 26 X^{12} Y^{4} Z^{4} + 2 X^{8} Y^{8} Z^{4} + 36 X^{4} Y^{12} Z^{4} + 32 X^{4} Y^{8} Z^{8} + 36 X^{4} Y^{4} Z^{12} + 5 X^{2} Y^{16} Z^{2} + X^{14} Y^{2} Z^{2} + 3 X^{10} Y^{4} Z^{4} + 2 X^{8} Y^{6} Z^{4} + 7 X^{4} Y^{12} Z^{2} + 30 X^{4} Y^{10} Z^{4} + 38 X^{4} Y^{6} Z^{8} + 4 X^{2} Y^{14} Z^{2} + 3 X^{2} Y^{12} Z^{4} + 9 X^{2} Y^{8} Z^{8} + 20 X^{2} Y^{4} Z^{12} + X^{12} Y^{2} Z^{2} + 4 X^{8} Y^{4} Z^{4} + 3 X^{4} Y^{10} Z^{2} + 71 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{4} Z^{8} + 27 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{10} Z^{4} + 4 X^{2} Y^{6} Z^{8} + 10 X^{2} Y^{2} Z^{12} + 24 X^{6} Y^{6} Z^{2} + 15 X^{6} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{6} + 4 X^{4} Y^{8} Z^{2} + 49 X^{4} Y^{6} Z^{4} + 14 X^{2} Y^{10} Z^{2} + 37 X^{2} Y^{8} Z^{4} + 16 X^{2} Y^{6} Z^{6} + 7 X^{2} Y^{4} Z^{8} + 78 X^{4} Y^{5} Z^{4} + 13 X^{6} Y^{4} Z^{2} + 21 X^{6} Y^{2} Z^{4} + 15 X^{4} Y^{6} Z^{2} + 343 X^{4} Y^{4} Z^{4} + 37 X^{2} Y^{8} Z^{2} + 43 X^{2} Y^{6} Z^{4} + 15 X^{2} Y^{4} Z^{6} + 6 X^{9} Y Z + 18 X^{6} Y^{3} Z^{2} + 24 X^{4} Y^{5} Z^{2} + 30 X^{3} Y^{4} Z^{4} + 12 X^{2} Y^{7} Z^{2} + 18 X^{2} Y^{5} Z^{4} + 24 X^{2} Y^{3} Z^{6} + 48 X Y Z^{9} + 175 X^{6} Y^{2} Z^{2} + 15 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 241 X^{2} Y^{6} Z^{2} + 222 X^{2} Y^{4} Z^{4} + 246 X^{2} Y^{2} Z^{6} + 30 X Y^{8} Z + 6 X^{7} Y Z + 18 X^{5} Y^{2} Z^{2} + 12 X^{4} Y^{3} Z^{2} + 42 X^{2} Y^{6} Z + 180 X^{2} Y^{5} Z^{2} + 228 X^{2} Y^{3} Z^{4} + 24 X Y^{7} Z + 18 X Y^{6} Z^{2} + 54 X Y^{4} Z^{4} + 120 X Y^{2} Z^{6} + 6 X^{6} Y Z + 31 X^{4} Y^{2} Z^{2} + 18 X^{2} Y^{5} Z + 455 X^{2} Y^{4} Z^{2} + 152 X^{2} Y^{2} Z^{4} + 162 X Y^{6} Z + 48 X Y^{5} Z^{2} + 24 X Y^{3} Z^{4} + 60 X Y Z^{6} + 144 X^{3} Y^{3} Z + 90 X^{3} Y^{2} Z^{2} + 36 X^{3} Y Z^{3} + 24 X^{2} Y^{4} Z + 150 X^{2} Y^{3} Z^{2} + 84 X Y^{5} Z + 222 X Y^{4} Z^{2} + 96 X Y^{3} Z^{3} + 42 X Y^{2} Z^{4} + 78 X^{3} Y^{2} Z + 126 X^{3} Y Z^{2} + 54 X^{2} Y^{3} Z + 371 X^{2} Y^{2} Z^{2} + 150 X Y^{4} Z + 258 X Y^{3} Z^{2} + 90 X Y^{2} Z^{3} + 114 X^{3} Y Z + 18 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 150 X Y^{3} Z + 180 X Y^{2} Z^{2} + 180 X Y Z^{3} + 42 X^{2} Y Z + 174 X Y^{2} Z + 48 X Y Z^{2} + 30 X Y Z

Algorithm definition

The algorithm ⟨18×22×32:6972⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×11×16:996⟩.

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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