Description of fast matrix multiplication algorithm: ⟨16×21×30:5592⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 3 X^{4} Y^{6} Z^{4} + 666 X^{4} Y^{4} Z^{4} + 18 X^{4} Y^{4} Z^{2} + 12 X^{2} Y^{6} Z^{2} + 6 X^{3} Y^{4} Z^{2} + 276 X^{4} Y^{2} Z^{2} + 996 X^{2} Y^{4} Z^{2} + 792 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + 6 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 360 X^{2} Y^{2} Z^{2} + 354 X Y^{4} Z + 144 X Y Z^{4} + 354 X^{2} Y^{2} Z + 234 X^{2} Y Z^{2} + 12 X Y^{3} Z + 414 X Y^{2} Z^{2} + 84 X^{2} Y Z + 444 X Y^{2} Z + 288 X Y Z^{2} + 72 X Y Z

Algorithm definition

The algorithm ⟨16×21×30:5592⟩ is serendipitous tensor product (⟨4×7×5:104⟩ - 17) ⊗ ⟨4×3×6:54⟩ +⟨4×9×6:159⟩ +7⟨4×6×6:105⟩.

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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