Description of fast matrix multiplication algorithm: ⟨18×30×32:9166⟩

Algorithm type

32 X^{2} Y^{6} Z^{7} + 32 X^{2} Y^{5} Z^{7} + 48 X Y^{6} Z^{7} + 32 X Y^{5} Z^{7} + 1272 X^{4} Y^{4} Z^{4} + 16 X Y^{5} Z^{6} + 6 X^{4} Y^{2} Z^{4} + 18 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{6} + 1536 X^{4} Y^{2} Z^{2} + 1674 X^{2} Y^{4} Z^{2} + 498 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 12 X^{4} Y Z^{2} + 36 X Y^{4} Z^{2} + 270 X^{4} Y Z + 18 X^{2} Y^{3} Z + 474 X^{2} Y^{2} Z^{2} + 36 X^{2} Y Z^{3} + 414 X Y^{4} Z + 36 X Y^{2} Z^{3} + 648 X^{2} Y^{2} Z + 540 X^{2} Y Z^{2} + 468 X Y^{2} Z^{2} + 468 X^{2} Y Z + 396 X Y^{2} Z + 60 X Y Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨18×30×32:9166⟩ is serendipitous tensor product (⟨6×5×8:170⟩ - 11) ⊗ ⟨3×6×4:54⟩ +⟨3×6×12:160⟩ +4⟨6×6×4:105⟩.

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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