Description of fast matrix multiplication algorithm: ⟨18×22×28:6174⟩

Algorithm type

12 X^{10} Y^{12} Z^{4} + 16 X^{10} Y^{8} Z^{8} + 11 X^{6} Y^{12} Z^{8} + 4 X^{8} Y^{12} Z^{4} + 24 X^{8} Y^{8} Z^{8} + 13 X^{4} Y^{12} Z^{8} + 5 X^{12} Y^{6} Z^{4} + 10 X^{6} Y^{12} Z^{4} + 8 X^{6} Y^{8} Z^{8} + 25 X^{6} Y^{4} Z^{12} + 14 X^{12} Y^{4} Z^{4} + 22 X^{10} Y^{6} Z^{4} + 6 X^{4} Y^{12} Z^{4} + 15 X^{4} Y^{4} Z^{12} + 8 X^{10} Y^{6} Z^{2} + 65 X^{10} Y^{4} Z^{4} + 11 X^{8} Y^{6} Z^{4} + 10 X^{6} Y^{4} Z^{8} + 8 X^{2} Y^{12} Z^{4} + 10 X^{10} Y^{2} Z^{4} + 2 X^{8} Y^{6} Z^{2} + 60 X^{8} Y^{4} Z^{4} + 6 X^{6} Y^{8} Z^{2} + 18 X^{6} Y^{6} Z^{4} + 6 X^{4} Y^{4} Z^{8} + 16 X^{8} Y^{2} Z^{4} + 86 X^{6} Y^{6} Z^{2} + 31 X^{6} Y^{4} Z^{4} + 30 X^{6} Y^{2} Z^{6} + 4 X^{4} Y^{8} Z^{2} + 10 X^{4} Y^{6} Z^{4} + 72 X^{5} Y^{6} Z^{2} + 96 X^{5} Y^{4} Z^{4} + 66 X^{3} Y^{6} Z^{4} + 76 X^{6} Y^{4} Z^{2} + 24 X^{6} Y^{2} Z^{4} + 52 X^{4} Y^{6} Z^{2} + 163 X^{4} Y^{4} Z^{4} + 10 X^{4} Y^{2} Z^{6} + 4 X^{2} Y^{8} Z^{2} + 84 X^{2} Y^{6} Z^{4} + 30 X^{6} Y^{3} Z^{2} + 60 X^{3} Y^{6} Z^{2} + 48 X^{3} Y^{4} Z^{4} + 150 X^{3} Y^{2} Z^{6} + 154 X^{6} Y^{2} Z^{2} + 132 X^{5} Y^{3} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 8 X^{4} Y^{2} Z^{4} + 46 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 100 X^{2} Y^{2} Z^{6} + 48 X^{5} Y^{3} Z + 390 X^{5} Y^{2} Z^{2} + 66 X^{4} Y^{3} Z^{2} + 60 X^{3} Y^{2} Z^{4} + 48 X Y^{6} Z^{2} + 60 X^{5} Y Z^{2} + 12 X^{4} Y^{3} Z + 384 X^{4} Y^{2} Z^{2} + 36 X^{3} Y^{4} Z + 108 X^{3} Y^{3} Z^{2} + 40 X^{2} Y^{2} Z^{4} + 96 X^{4} Y Z^{2} + 516 X^{3} Y^{3} Z + 186 X^{3} Y^{2} Z^{2} + 180 X^{3} Y Z^{3} + 24 X^{2} Y^{4} Z + 60 X^{2} Y^{3} Z^{2} + 456 X^{3} Y^{2} Z + 144 X^{3} Y Z^{2} + 168 X^{2} Y^{3} Z + 125 X^{2} Y^{2} Z^{2} + 60 X^{2} Y Z^{3} + 24 X Y^{4} Z + 36 X Y^{3} Z^{2} + 420 X^{3} Y Z + 48 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 60 X Y^{3} Z + 24 X Y^{2} Z^{2} + 60 X Y Z^{3} + 144 X^{2} Y Z + 24 X Y Z^{2} + 66 X Y Z

Algorithm definition

The algorithm ⟨18×22×28:6174⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×11×14:882⟩.

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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