Description of fast matrix multiplication algorithm: ⟨20×24×32:8157⟩

Algorithm type

1120 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{6} Z^{4} + 5 X^{2} Y^{6} Z^{3} + 36 X^{2} Y^{6} Z^{2} + 40 X^{2} Y^{4} Z^{4} + 16 X^{2} Y^{2} Z^{6} + 9 X^{2} Y^{4} Z^{3} + 8 X Y^{6} Z^{2} + 240 X^{4} Y^{2} Z^{2} + 470 X^{2} Y^{4} Z^{2} + 374 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + 7 X Y^{3} Z^{4} + 11 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 2649 X^{2} Y^{2} Z^{2} + 7 X Y^{4} Z + 8 X Y^{3} Z^{2} + 6 X Y Z^{4} + 2 X^{3} Y Z + 65 X Y^{3} Z + 66 X Y^{2} Z^{2} + 34 X Y Z^{3} + 488 X^{2} Y Z + 928 X Y^{2} Z + 741 X Y Z^{2} + 811 X Y Z

Algorithm definition

The algorithm ⟨20×24×32:8157⟩ is serendipitous tensor product (⟨5×6×8:170⟩ - 27) ⊗ ⟨4×4×4:48⟩ +⟨4×4×12:141⟩ +12⟨4×4×8:96⟩.

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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