Description of fast matrix multiplication algorithm: ⟨16×27×30:7080⟩

Algorithm type

6 X^{8} Y^{4} Z^{4} + 3 X^{4} Y^{8} Z^{4} + 3 X^{6} Y^{4} Z^{4} + 9 X^{4} Y^{6} Z^{4} + 891 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{8} Z^{2} + 30 X^{6} Y^{2} Z^{2} + 54 X^{4} Y^{4} Z^{2} + 42 X^{2} Y^{6} Z^{2} + 6 X^{3} Y^{4} Z^{2} + 306 X^{4} Y^{2} Z^{2} + 1284 X^{2} Y^{4} Z^{2} + 1026 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 6 X^{3} Y^{2} Z^{2} + 66 X^{2} Y^{4} Z + 18 X^{2} Y^{3} Z^{2} + 60 X^{3} Y^{2} Z + 384 X^{2} Y^{2} Z^{2} + 414 X Y^{4} Z + 162 X Y Z^{4} + 60 X^{3} Y Z + 402 X^{2} Y^{2} Z + 234 X^{2} Y Z^{2} + 48 X Y^{3} Z + 468 X Y^{2} Z^{2} + 120 X^{2} Y Z + 516 X Y^{2} Z + 216 X Y Z^{2} + 192 X Y Z

Algorithm definition

The algorithm ⟨16×27×30:7080⟩ is serendipitous tensor product (⟨4×9×5:132⟩ - 33) ⊗ ⟨4×3×6:54⟩ +⟨4×12×6:210⟩ +⟨4×9×6:159⟩ +13⟨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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