Description of fast matrix multiplication algorithm: ⟨20×30×30:9573⟩

Algorithm type

3 X^{4} Y^{10} Z^{4} + 3 X^{6} Y^{4} Z^{4} + 9 X^{4} Y^{8} Z^{2} + 3 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z^{2} + 18 X^{8} Y^{2} Z^{2} + 36 X^{6} Y^{2} Z^{4} + 3 X^{4} Y^{6} Z^{2} + 1326 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + 18 X^{2} Y^{6} Z^{4} + 18 X^{2} Y^{8} Z + 6 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 15 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 6 X Y^{8} Z + 6 X^{3} Y^{4} Z^{2} + 6 X^{2} Y^{6} Z + 6 X^{2} Y^{5} Z^{2} + 18 X Y^{6} Z^{2} + 534 X^{4} Y^{2} Z^{2} + 36 X^{3} Y Z^{4} + 1908 X^{2} Y^{4} Z^{2} + 1458 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 18 X Y^{3} Z^{4} + 18 X^{4} Y^{2} Z + 18 X^{4} Y Z^{2} + 42 X^{3} Y^{2} Z^{2} + 54 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 18 X^{2} Y Z^{4} + 18 X Y^{4} Z^{2} + 18 X Y^{2} Z^{4} + 12 X^{3} Y^{2} Z + 6 X^{2} Y^{3} Z + 348 X^{2} Y^{2} Z^{2} + 624 X Y^{4} Z + 162 X Y Z^{4} + 12 X^{3} Y Z + 636 X^{2} Y^{2} Z + 468 X^{2} Y Z^{2} + 18 X Y^{3} Z + 648 X Y^{2} Z^{2} + 132 X^{2} Y Z + 456 X Y^{2} Z + 216 X Y Z^{2} + 108 X Y Z

Algorithm definition

The algorithm ⟨20×30×30:9573⟩ is serendipitous tensor product (⟨5×10×5:178⟩ - 27) ⊗ ⟨4×3×6:54⟩ +⟨4×9×6:159⟩ +12⟨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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