Description of fast matrix multiplication algorithm: ⟨20×27×30:8658⟩

Algorithm type

18 X^{6} Y^{2} Z^{4} + 1188 X^{4} Y^{4} Z^{4} + 18 X^{4} Y^{2} Z^{6} + 6 X^{4} Y^{4} Z^{2} + 18 X^{2} Y Z^{6} + 462 X^{4} Y^{2} Z^{2} + 18 X^{3} Y Z^{4} + 1764 X^{2} Y^{4} Z^{2} + 1332 X^{2} Y^{2} Z^{4} + 18 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{4} Z + 18 X^{2} Y^{2} Z^{3} + 378 X^{2} Y^{2} Z^{2} + 612 X Y^{4} Z + 180 X Y Z^{4} + 540 X^{2} Y^{2} Z + 396 X^{2} Y Z^{2} + 648 X Y^{2} Z^{2} + 132 X^{2} Y Z + 522 X Y^{2} Z + 234 X Y Z^{2} + 144 X Y Z

Algorithm definition

The algorithm ⟨20×27×30:8658⟩ is serendipitous tensor product (⟨5×9×5:161⟩ - 24) ⊗ ⟨4×3×6:54⟩ +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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