Description of fast matrix multiplication algorithm: ⟨20×21×30:6840⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 18 X^{4} Y^{4} Z^{6} + 6 X^{6} Y^{4} Z^{2} + 861 X^{4} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 72 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{4} Z^{2} + 18 X^{2} Y^{4} Z^{3} + 312 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{4} Z + 1206 X^{2} Y^{4} Z^{2} + 1008 X^{2} Y^{2} Z^{4} + 54 X Y Z^{6} + 6 X^{3} Y^{2} Z^{2} + 24 X^{2} Y^{4} Z + 18 X^{2} Y Z^{4} + 24 X^{3} Y^{2} Z + 462 X^{2} Y^{2} Z^{2} + 354 X Y^{4} Z + 54 X Y^{2} Z^{3} + 162 X Y Z^{4} + 12 X^{3} Y Z + 360 X^{2} Y^{2} Z + 288 X^{2} Y Z^{2} + 468 X Y^{2} Z^{2} + 48 X^{2} Y Z + 498 X Y^{2} Z + 378 X Y Z^{2} + 72 X Y Z

Algorithm definition

The algorithm ⟨20×21×30:6840⟩ is serendipitous tensor product (⟨5×7×5:127⟩ - 13) ⊗ ⟨4×3×6:54⟩ +⟨4×9×6:159⟩ +5⟨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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