Description of fast matrix multiplication algorithm: ⟨12×16×18:2072⟩

Algorithm type

12 X^{8} Y^{8} Z^{8} + 12 X^{4} Y^{12} Z^{4} + 24 X^{4} Y^{4} Z^{8} + 136 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{6} Z^{4} + 4 X^{2} Y^{4} Z^{6} + 8 X^{6} Y^{2} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 104 X^{2} Y^{6} Z^{2} + 16 X^{4} Y^{2} Z^{2} + 20 X^{2} Y^{4} Z^{2} + 168 X^{2} Y^{2} Z^{4} + 432 X^{2} Y^{2} Z^{2} + 144 X Y^{3} Z^{2} + 24 X Y^{2} Z^{3} + 48 X^{3} Y Z + 48 X^{2} Y^{2} Z + 192 X Y^{3} Z + 96 X^{2} Y Z + 120 X Y^{2} Z + 144 X Y Z^{2} + 288 X Y Z

Algorithm definition

The algorithm ⟨12×16×18:2072⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×8×9:296⟩.

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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