Description of fast matrix multiplication algorithm: ⟨18×24×26:6146⟩

Algorithm type

16 X^{12} Y^{12} Z^{8} + 8 X^{12} Y^{12} Z^{6} + 16 X^{12} Y^{12} Z^{4} + 6 X^{8} Y^{8} Z^{12} + 31 X^{8} Y^{8} Z^{10} + 15 X^{8} Y^{8} Z^{8} + X^{8} Y^{8} Z^{6} + 16 X^{6} Y^{6} Z^{10} + X^{8} Y^{8} Z^{4} + 16 X^{6} Y^{6} Z^{8} + 16 X^{4} Y^{4} Z^{12} + 32 X^{8} Y^{4} Z^{6} + 32 X^{6} Y^{6} Z^{6} + X^{6} Y^{2} Z^{10} + 32 X^{4} Y^{8} Z^{6} + 3 X^{4} Y^{6} Z^{8} + 49 X^{4} Y^{4} Z^{10} + 3 X^{4} Y^{2} Z^{12} + X^{2} Y^{4} Z^{12} + X^{2} Y^{2} Z^{14} + 20 X^{8} Y^{4} Z^{4} + 108 X^{6} Y^{6} Z^{4} + 2 X^{6} Y^{4} Z^{6} + X^{6} Y^{2} Z^{8} + 20 X^{4} Y^{8} Z^{4} + 5 X^{4} Y^{6} Z^{6} + 56 X^{4} Y^{4} Z^{8} + 3 X^{4} Y^{2} Z^{10} + 4 X^{2} Y^{8} Z^{6} + 4 X^{2} Y^{4} Z^{10} + 4 X^{2} Y^{2} Z^{12} + 48 X^{6} Y^{6} Z^{3} + 2 X^{8} Y^{4} Z^{2} + 100 X^{6} Y^{6} Z^{2} + 8 X^{6} Y^{4} Z^{4} + 14 X^{6} Y^{2} Z^{6} + 2 X^{4} Y^{8} Z^{2} + 83 X^{4} Y^{4} Z^{6} + 2 X^{4} Y^{2} Z^{8} + 4 X^{2} Y^{8} Z^{4} + 5 X^{2} Y^{6} Z^{6} + 4 X^{2} Y^{4} Z^{8} + 16 X^{2} Y^{2} Z^{10} + 186 X^{4} Y^{4} Z^{5} + 2 X^{6} Y^{4} Z^{2} + 2 X^{6} Y^{2} Z^{4} + 102 X^{4} Y^{4} Z^{4} + 62 X^{4} Y^{2} Z^{6} + 9 X^{2} Y^{6} Z^{4} + 72 X^{2} Y^{4} Z^{6} + 17 X^{2} Y^{2} Z^{8} + 6 X^{4} Y^{4} Z^{3} + 96 X^{3} Y^{3} Z^{5} + 6 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 28 X^{4} Y^{2} Z^{4} + 96 X^{3} Y^{3} Z^{4} + 6 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{4} Z^{4} + 110 X^{2} Y^{2} Z^{6} + 192 X^{4} Y^{2} Z^{3} + 192 X^{3} Y^{3} Z^{3} + 6 X^{3} Y Z^{5} + 192 X^{2} Y^{4} Z^{3} + 18 X^{2} Y^{3} Z^{4} + 294 X^{2} Y^{2} Z^{5} + 18 X^{2} Y Z^{6} + 6 X Y^{2} Z^{6} + 6 X Y Z^{7} + 138 X^{4} Y^{2} Z^{2} + 72 X^{3} Y^{3} Z^{2} + 12 X^{3} Y^{2} Z^{3} + 6 X^{3} Y Z^{4} + 147 X^{2} Y^{4} Z^{2} + 30 X^{2} Y^{3} Z^{3} + 349 X^{2} Y^{2} Z^{4} + 18 X^{2} Y Z^{5} + 24 X Y^{4} Z^{3} + 24 X Y^{2} Z^{5} + 24 X Y Z^{6} + 12 X^{4} Y^{2} Z + 24 X^{3} Y^{3} Z + 48 X^{3} Y^{2} Z^{2} + 84 X^{3} Y Z^{3} + 12 X^{2} Y^{4} Z + 282 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + 24 X Y^{4} Z^{2} + 30 X Y^{3} Z^{3} + 24 X Y^{2} Z^{4} + 96 X Y Z^{5} + 12 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 79 X^{2} Y^{2} Z^{2} + 372 X^{2} Y Z^{3} + 54 X Y^{3} Z^{2} + 432 X Y^{2} Z^{3} + 102 X Y Z^{4} + 36 X^{3} Y Z + 168 X^{2} Y Z^{2} + 36 X Y^{3} Z + 288 X Y^{2} Z^{2} + 84 X Y Z^{3} + 108 X^{2} Y Z + 162 X Y^{2} Z + 78 X Y Z^{2} + 42 X Y Z

Algorithm definition

The algorithm ⟨18×24×26:6146⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×12×13:878⟩.

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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