Description of fast matrix multiplication algorithm: ⟨18×20×22:4557⟩

Algorithm type

16 X^{8} Y^{12} Z^{12} + 24 X^{4} Y^{12} Z^{12} + 18 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{6} + 6 X^{6} Y^{8} Z^{8} + 38 X^{8} Y^{6} Z^{6} + 2 X^{6} Y^{6} Z^{8} + 2 X^{6} Y^{6} Z^{6} + 37 X^{8} Y^{4} Z^{4} + 22 X^{4} Y^{8} Z^{4} + 192 X^{4} Y^{6} Z^{6} + 24 X^{4} Y^{4} Z^{8} + 3 X^{10} Y^{2} Z^{2} + X^{8} Y^{4} Z^{2} + 12 X^{6} Y^{4} Z^{4} + 2 X^{4} Y^{8} Z^{2} + 6 X^{4} Y^{6} Z^{4} + 6 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{8} Z^{4} + 216 X^{2} Y^{6} Z^{6} + 2 X^{2} Y^{4} Z^{8} + X^{8} Y^{2} Z^{2} + 3 X^{4} Y^{6} Z^{2} + 144 X^{4} Y^{4} Z^{4} + 10 X^{4} Y^{2} Z^{6} + 2 X^{2} Y^{2} Z^{8} + 12 X^{4} Y^{4} Z^{3} + 36 X^{3} Y^{4} Z^{4} + 8 X^{6} Y^{2} Z^{2} + 37 X^{4} Y^{4} Z^{2} + 228 X^{4} Y^{3} Z^{3} + 33 X^{4} Y^{2} Z^{4} + 12 X^{3} Y^{3} Z^{4} + 5 X^{2} Y^{6} Z^{2} + 5 X^{2} Y^{4} Z^{4} + 10 X^{2} Y^{2} Z^{6} + 12 X^{3} Y^{3} Z^{3} + 259 X^{4} Y^{2} Z^{2} + 157 X^{2} Y^{4} Z^{2} + 576 X^{2} Y^{3} Z^{3} + 165 X^{2} Y^{2} Z^{4} + 18 X^{5} Y Z + 6 X^{4} Y^{2} Z + 72 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{4} Z + 36 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 24 X Y^{4} Z^{2} + 432 X Y^{3} Z^{3} + 12 X Y^{2} Z^{4} + 6 X^{4} Y Z + 18 X^{2} Y^{3} Z + 239 X^{2} Y^{2} Z^{2} + 60 X^{2} Y Z^{3} + 12 X Y Z^{4} + 48 X^{3} Y Z + 222 X^{2} Y^{2} Z + 198 X^{2} Y Z^{2} + 30 X Y^{3} Z + 30 X Y^{2} Z^{2} + 60 X Y Z^{3} + 222 X^{2} Y Z + 150 X Y^{2} Z + 126 X Y Z^{2} + 138 X Y Z

Algorithm definition

The algorithm ⟨18×20×22:4557⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×10×11:651⟩.

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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