Description of fast matrix multiplication algorithm: ⟨20×24×32:8554⟩

Algorithm type

78 X^{8} Y^{8} Z^{8} + 6 X^{2} Y^{18} Z^{2} + 24 X^{12} Y^{4} Z^{4} + 12 X^{8} Y^{4} Z^{8} + 44 X^{4} Y^{12} Z^{4} + 6 X^{4} Y^{8} Z^{8} + 12 X^{4} Y^{4} Z^{12} + 2 X^{2} Y^{12} Z^{4} + 36 X^{8} Y^{4} Z^{4} + 122 X^{4} Y^{8} Z^{4} + 48 X^{4} Y^{4} Z^{8} + 30 X^{2} Y^{12} Z^{2} + 8 X^{6} Y^{6} Z^{2} + 4 X^{4} Y^{6} Z^{4} + 8 X^{2} Y^{8} Z^{4} + 4 X^{2} Y^{6} Z^{6} + 32 X^{6} Y^{4} Z^{2} + 12 X^{4} Y^{6} Z^{2} + 644 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{6} Z^{4} + 16 X^{2} Y^{4} Z^{6} + 36 X Y^{9} Z + 184 X^{6} Y^{2} Z^{2} + 48 X^{4} Y^{4} Z^{2} + 92 X^{4} Y^{2} Z^{4} + 304 X^{2} Y^{6} Z^{2} + 110 X^{2} Y^{4} Z^{4} + 92 X^{2} Y^{2} Z^{6} + 12 X Y^{6} Z^{2} + 276 X^{4} Y^{2} Z^{2} + 802 X^{2} Y^{4} Z^{2} + 368 X^{2} Y^{2} Z^{4} + 180 X Y^{6} Z + 48 X^{3} Y^{3} Z + 24 X^{2} Y^{3} Z^{2} + 48 X Y^{4} Z^{2} + 24 X Y^{3} Z^{3} + 192 X^{3} Y^{2} Z + 72 X^{2} Y^{3} Z + 1106 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 96 X Y^{3} Z^{2} + 96 X Y^{2} Z^{3} + 240 X^{3} Y Z + 288 X^{2} Y^{2} Z + 120 X^{2} Y Z^{2} + 240 X Y^{3} Z + 444 X Y^{2} Z^{2} + 120 X Y Z^{3} + 360 X^{2} Y Z + 420 X Y^{2} Z + 480 X Y Z^{2} + 300 X Y Z

Algorithm definition

The algorithm ⟨20×24×32:8554⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×12×16:1222⟩.

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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