Description of fast matrix multiplication algorithm: ⟨9×20×30:3126⟩

Algorithm type

18 X^{6} Y^{4} Z^{2} + 312 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{8} Z^{2} + 18 X^{2} Y^{4} Z^{6} + 90 X^{6} Y^{2} Z^{2} + 36 X^{4} Y^{4} Z^{2} + 18 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 90 X^{2} Y^{2} Z^{6} + 36 X Y^{8} Z + 18 X Y^{2} Z^{6} + 30 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{4} Z + 540 X^{2} Y^{4} Z^{2} + 348 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 18 X Y^{4} Z^{3} + 90 X Y Z^{6} + 18 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{4} Z + 72 X Y^{4} Z^{2} + 36 X Y^{2} Z^{4} + 90 X^{3} Y^{2} Z + 90 X^{3} Y Z^{2} + 114 X^{2} Y^{2} Z^{2} + 234 X Y^{4} Z + 18 X Y^{3} Z^{2} + 90 X Y^{2} Z^{3} + 42 X Y Z^{4} + 18 X^{2} Y^{2} Z + 42 X^{2} Y Z^{2} + 252 X Y^{2} Z^{2} + 24 X^{2} Y Z + 54 X Y^{2} Z + 102 X Y Z^{2} + 24 X Y Z

Algorithm definition

The algorithm ⟨9×20×30:3126⟩ is serendipitous tensor product (⟨3×5×5:58⟩ - 4) ⊗ ⟨3×4×6:54⟩ +2⟨6×4×6:105⟩.

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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