Description of fast matrix multiplication algorithm: ⟨18×20×32:6580⟩

Algorithm type

52 X^{8} Y^{8} Z^{8} + 12 X^{2} Y^{2} Z^{18} + 16 X^{12} Y^{4} Z^{4} + 8 X^{8} Y^{8} Z^{4} + 8 X^{4} Y^{12} Z^{4} + 4 X^{4} Y^{8} Z^{8} + 64 X^{4} Y^{4} Z^{12} + 4 X^{2} Y^{4} Z^{12} + 24 X^{8} Y^{4} Z^{4} + 32 X^{4} Y^{8} Z^{4} + 12 X^{4} Y^{4} Z^{8} + 12 X^{2} Y^{2} Z^{12} + 16 X^{6} Y^{2} Z^{6} + 8 X^{4} Y^{4} Z^{6} + 8 X^{2} Y^{6} Z^{6} + 488 X^{4} Y^{4} Z^{4} + 24 X^{4} Y^{2} Z^{6} + 32 X^{2} Y^{4} Z^{6} + 72 X Y Z^{9} + 144 X^{6} Y^{2} Z^{2} + 72 X^{4} Y^{4} Z^{2} + 72 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 440 X^{2} Y^{2} Z^{6} + 24 X Y^{2} Z^{6} + 216 X^{4} Y^{2} Z^{2} + 288 X^{2} Y^{4} Z^{2} + 108 X^{2} Y^{2} Z^{4} + 72 X Y Z^{6} + 96 X^{3} Y Z^{3} + 48 X^{2} Y^{2} Z^{3} + 48 X Y^{3} Z^{3} + 1116 X^{2} Y^{2} Z^{2} + 144 X^{2} Y Z^{3} + 192 X Y^{2} Z^{3} + 288 X^{3} Y Z + 144 X^{2} Y^{2} Z + 144 X Y^{3} Z + 72 X Y^{2} Z^{2} + 336 X Y Z^{3} + 432 X^{2} Y Z + 576 X Y^{2} Z + 216 X Y Z^{2} + 360 X Y Z

Algorithm definition

The algorithm ⟨18×20×32:6580⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×10×16:940⟩.

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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