Description of fast matrix multiplication algorithm: ⟨9×16×30:2532⟩

Algorithm type

240 X^{4} Y^{4} Z^{4} + 54 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{4} Z^{2} + 36 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 72 X^{2} Y^{2} Z^{6} + 42 X^{4} Y^{2} Z^{2} + 378 X^{2} Y^{4} Z^{2} + 354 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 72 X Y Z^{6} + 18 X^{2} Y^{4} Z + 36 X Y^{4} Z^{2} + 36 X Y^{2} Z^{4} + 54 X^{3} Y^{2} Z + 54 X^{3} Y Z^{2} + 96 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 36 X Y^{3} Z^{2} + 72 X Y^{2} Z^{3} + 108 X Y Z^{4} + 36 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 252 X Y^{2} Z^{2} + 12 X^{2} Y Z + 36 X Y^{2} Z + 96 X Y Z^{2} + 60 X Y Z

Algorithm definition

The algorithm ⟨9×16×30:2532⟩ is serendipitous tensor product (⟨3×4×5:47⟩ - 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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