Description of fast matrix multiplication algorithm: ⟨20×24×30:7746⟩

Algorithm type

3 X^{8} Y^{4} Z^{4} + 3 X^{6} Y^{4} Z^{4} + 9 X^{4} Y^{6} Z^{4} + 6 X^{6} Y^{4} Z^{2} + 1023 X^{4} Y^{4} Z^{4} + 12 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{4} Z^{2} + 36 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{4} Z^{2} + 396 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{4} Z + 1422 X^{2} Y^{4} Z^{2} + 1242 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 18 X Y Z^{6} + 6 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{4} Z + 18 X^{2} Y^{3} Z^{2} + 36 X^{3} Y^{2} Z + 354 X^{2} Y^{2} Z^{2} + 444 X Y^{4} Z + 18 X Y^{2} Z^{3} + 234 X Y Z^{4} + 24 X^{3} Y Z + 456 X^{2} Y^{2} Z + 360 X^{2} Y Z^{2} + 36 X Y^{3} Z + 558 X Y^{2} Z^{2} + 60 X^{2} Y Z + 480 X Y^{2} Z + 288 X Y Z^{2} + 72 X Y Z

Algorithm definition

The algorithm ⟨20×24×30:7746⟩ is serendipitous tensor product (⟨5×8×5:144⟩ - 20) ⊗ ⟨4×3×6:54⟩ +10⟨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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