Description of fast matrix multiplication algorithm: ⟨20×21×24:5592⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 3 X^{4} Y^{6} Z^{4} + 666 X^{4} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 6 X^{2} Y^{6} Z^{2} + 6 X^{3} Y^{4} Z^{2} + 312 X^{4} Y^{2} Z^{2} + 960 X^{2} Y^{4} Z^{2} + 792 X^{2} Y^{2} Z^{4} + 6 X^{3} Y^{2} Z^{2} + 24 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 12 X^{3} Y^{2} Z + 366 X^{2} Y^{2} Z^{2} + 318 X Y^{4} Z + 144 X Y Z^{4} + 12 X^{3} Y Z + 378 X^{2} Y^{2} Z + 270 X^{2} Y Z^{2} + 378 X Y^{2} Z^{2} + 84 X^{2} Y Z + 456 X Y^{2} Z + 288 X Y Z^{2} + 84 X Y Z

Algorithm definition

The algorithm ⟨20×21×24:5592⟩ is serendipitous tensor product (⟨5×7×4:104⟩ - 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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