Description of fast matrix multiplication algorithm: ⟨16×30×30:7830⟩

Algorithm type

3 X^{10} Y^{4} Z^{4} + 3 X^{8} Y^{4} Z^{4} + 3 X^{6} Y^{6} Z^{4} + 6 X^{4} Y^{8} Z^{4} + 3 X^{6} Y^{4} Z^{4} + 6 X^{4} Y^{6} Z^{4} + 15 X^{6} Y^{4} Z^{2} + 1002 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z^{2} + 6 X^{5} Y^{4} Z^{2} + 6 X^{3} Y^{6} Z^{2} + 9 X^{6} Y^{2} Z^{2} + 81 X^{4} Y^{4} Z^{2} + 48 X^{2} Y^{6} Z^{2} + 6 X^{5} Y^{2} Z^{2} + 6 X^{3} Y^{4} Z^{2} + 339 X^{4} Y^{2} Z^{2} + 30 X^{3} Y^{4} Z + 6 X^{3} Y^{3} Z^{2} + 1452 X^{2} Y^{4} Z^{2} + 1116 X^{2} Y^{2} Z^{4} + 54 X Y^{6} Z + 6 X^{3} Y^{2} Z^{2} + 132 X^{2} Y^{4} Z + 12 X^{2} Y^{3} Z^{2} + 48 X^{3} Y^{2} Z + 390 X^{2} Y^{2} Z^{2} + 474 X Y^{4} Z + 18 X Y^{3} Z^{2} + 144 X Y Z^{4} + 18 X^{3} Y Z + 510 X^{2} Y^{2} Z + 270 X^{2} Y Z^{2} + 36 X Y^{3} Z + 486 X Y^{2} Z^{2} + 126 X^{2} Y Z + 540 X Y^{2} Z + 216 X Y Z^{2} + 192 X Y Z

Algorithm definition

The algorithm ⟨16×30×30:7830⟩ is serendipitous tensor product (⟨4×10×5:146⟩ - 37) ⊗ ⟨4×3×6:54⟩ +⟨4×12×6:210⟩ +⟨4×9×6:159⟩ +15⟨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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