Description of fast matrix multiplication algorithm: ⟨12×20×20:2842⟩

Algorithm type

X^{12} Y^{8} Z^{4} + 17 X^{8} Y^{8} Z^{8} + 2 X^{4} Y^{16} Z^{4} + X^{4} Y^{8} Z^{12} + 5 X^{12} Y^{4} Z^{4} + 2 X^{8} Y^{8} Z^{4} + X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{8} Z^{8} + 5 X^{4} Y^{4} Z^{12} + X^{8} Y^{4} Z^{4} + 13 X^{4} Y^{8} Z^{4} + X^{4} Y^{4} Z^{8} + 12 X^{6} Y^{4} Z^{2} + 211 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{4} Z^{6} + 60 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{4} Z^{2} + 12 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 60 X^{2} Y^{2} Z^{6} + 12 X^{4} Y^{2} Z^{2} + 156 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{2} Z^{4} + 36 X^{3} Y^{2} Z + 696 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 36 X Y^{2} Z^{3} + 180 X^{3} Y Z + 72 X^{2} Y^{2} Z + 36 X Y^{3} Z + 72 X Y^{2} Z^{2} + 180 X Y Z^{3} + 36 X^{2} Y Z + 468 X Y^{2} Z + 36 X Y Z^{2} + 252 X Y Z

Algorithm definition

The algorithm ⟨12×20×20:2842⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×10×10:406⟩.

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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