Description of fast matrix multiplication algorithm: ⟨20×21×25:5940⟩

Algorithm type

13 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{2} Z^{9} + 611 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 2 X^{2} Y^{4} Z^{6} + X^{6} Y^{3} Z^{2} + 3 X^{6} Y^{2} Z^{3} + 4 X^{2} Y^{6} Z^{3} + 6 X Y Z^{9} + 148 X^{6} Y^{2} Z^{2} + 4 X^{5} Y^{3} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 60 X^{4} Y^{2} Z^{4} + 188 X^{2} Y^{6} Z^{2} + 94 X^{2} Y^{4} Z^{4} + 141 X^{2} Y^{2} Z^{6} + 2 X^{6} Y^{2} Z + 3 X^{6} Y Z^{2} + 2 X^{5} Y^{2} Z^{2} + 14 X^{4} Y^{3} Z^{2} + 3 X^{4} Y^{2} Z^{3} + X^{4} Y Z^{4} + 8 X^{3} Y^{4} Z^{2} + 6 X^{2} Y^{4} Z^{3} + 5 X^{2} Y Z^{6} + 6 X Y^{2} Z^{6} + 50 X^{6} Y Z + 3 X^{5} Y^{2} Z + X^{4} Y^{3} Z + 377 X^{4} Y^{2} Z^{2} + 2 X^{3} Y^{4} Z + 28 X^{3} Y^{3} Z^{2} + 514 X^{2} Y^{4} Z^{2} + 495 X^{2} Y^{2} Z^{4} + 68 X Y^{6} Z + 42 X Y Z^{6} + 2 X^{5} Y Z + 7 X^{4} Y^{2} Z + 19 X^{4} Y Z^{2} + 9 X^{3} Y^{3} Z + 38 X^{3} Y^{2} Z^{2} + 9 X^{3} Y Z^{3} + 6 X^{2} Y^{4} Z + 13 X^{2} Y^{3} Z^{2} + 5 X^{2} Y^{2} Z^{3} + 17 X^{2} Y Z^{4} + 36 X Y^{4} Z^{2} + 12 X Y^{3} Z^{3} + 18 X Y^{2} Z^{4} + 59 X^{4} Y Z + 86 X^{3} Y^{2} Z + 29 X^{3} Y Z^{2} + 90 X^{2} Y^{3} Z + 600 X^{2} Y^{2} Z^{2} + 44 X^{2} Y Z^{3} + 109 X Y^{4} Z + 40 X Y^{3} Z^{2} + 52 X Y^{2} Z^{3} + 72 X Y Z^{4} + 91 X^{3} Y Z + 191 X^{2} Y^{2} Z + 188 X^{2} Y Z^{2} + 92 X Y^{3} Z + 255 X Y^{2} Z^{2} + 57 X Y Z^{3} + 187 X^{2} Y Z + 248 X Y^{2} Z + 220 X Y Z^{2} + 125 X Y Z

Algorithm definition

The algorithm ⟨20×21×25:5940⟩ is serendipitous tensor product (⟨5×7×5:127⟩ - 13) ⊗ ⟨4×3×5:47⟩ +⟨4×9×5:132⟩ +5⟨4×6×5:90⟩.

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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