Description of fast matrix multiplication algorithm: ⟨18×20×24:4788⟩

Algorithm type

16 X^{8} Y^{12} Z^{12} + 24 X^{4} Y^{12} Z^{12} + 26 X^{8} Y^{8} Z^{8} + 8 X^{6} Y^{8} Z^{8} + 64 X^{8} Y^{6} Z^{6} + 2 X^{6} Y^{6} Z^{8} + 26 X^{8} Y^{4} Z^{4} + 32 X^{4} Y^{8} Z^{4} + 256 X^{4} Y^{6} Z^{6} + 32 X^{4} Y^{4} Z^{8} + 10 X^{6} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z^{4} + 240 X^{2} Y^{6} Z^{6} + 4 X^{2} Y^{4} Z^{8} + 192 X^{4} Y^{4} Z^{4} + 48 X^{3} Y^{4} Z^{4} + 32 X^{4} Y^{4} Z^{2} + 384 X^{4} Y^{3} Z^{3} + 32 X^{4} Y^{2} Z^{4} + 12 X^{3} Y^{3} Z^{4} + 156 X^{4} Y^{2} Z^{2} + 232 X^{2} Y^{4} Z^{2} + 960 X^{2} Y^{3} Z^{3} + 232 X^{2} Y^{2} Z^{4} + 60 X^{3} Y^{2} Z^{2} + 24 X Y^{4} Z^{2} + 576 X Y^{3} Z^{3} + 24 X Y^{2} Z^{4} + 216 X^{2} Y^{2} Z^{2} + 192 X^{2} Y^{2} Z + 192 X^{2} Y Z^{2} + 240 X Y^{2} Z + 240 X Y Z^{2}

Algorithm definition

The algorithm ⟨18×20×24:4788⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×10×12:684⟩.

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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