Description of fast matrix multiplication algorithm: ⟨20×21×27:6390⟩

Algorithm type

8 X^{4} Y^{6} Z^{7} + 12 X^{6} Y^{4} Z^{6} + 2 X^{4} Y^{5} Z^{7} + 8 X^{4} Y^{6} Z^{5} + 3 X^{4} Y^{5} Z^{6} + 174 X^{6} Y^{4} Z^{4} + 4 X^{4} Y^{6} Z^{4} + 12 X^{4} Y^{5} Z^{5} + 36 X^{4} Y^{4} Z^{6} + X^{2} Y^{8} Z^{4} + 4 X^{8} Y^{2} Z^{3} + 2 X^{4} Y^{2} Z^{7} + X^{2} Y^{2} Z^{9} + 58 X^{8} Y^{2} Z^{2} + X^{4} Y^{5} Z^{3} + 438 X^{4} Y^{4} Z^{4} + 14 X^{2} Y^{6} Z^{4} + 21 X^{2} Y^{4} Z^{6} + 4 X^{2} Y^{3} Z^{7} + 24 X^{6} Y^{2} Z^{3} + X^{4} Y^{5} Z^{2} + 48 X^{3} Y^{6} Z^{2} + 24 X^{3} Y^{4} Z^{4} + 24 X^{3} Y^{2} Z^{6} + 10 X^{2} Y^{6} Z^{3} + 27 X^{2} Y^{5} Z^{4} + 9 X^{2} Y^{4} Z^{5} + 18 X^{2} Y^{3} Z^{6} + 4 X^{8} Y Z + 360 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{3} Z^{3} + 4 X^{4} Y^{2} Z^{4} + 125 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{5} Z^{3} + 267 X^{2} Y^{4} Z^{4} + 19 X^{2} Y^{3} Z^{5} + 65 X^{2} Y^{2} Z^{6} + 2 X Y^{7} Z^{2} + X Y Z^{8} + 4 X^{4} Y^{3} Z^{2} + 24 X^{4} Y^{2} Z^{3} + 60 X^{3} Y^{4} Z^{2} + 78 X^{3} Y^{2} Z^{4} + 7 X^{2} Y^{5} Z^{2} + 52 X^{2} Y^{4} Z^{3} + 36 X^{2} Y^{3} Z^{4} + 24 X^{2} Y^{2} Z^{5} + 4 X^{2} Y Z^{6} + 55 X Y^{6} Z^{2} + 24 X Y^{4} Z^{4} + 36 X Y^{2} Z^{6} + 24 X^{6} Y Z + 16 X^{4} Y^{3} Z + 386 X^{4} Y^{2} Z^{2} + 8 X^{4} Y Z^{3} + 2 X^{2} Y^{5} Z + 167 X^{2} Y^{4} Z^{2} + 41 X^{2} Y^{3} Z^{3} + 293 X^{2} Y^{2} Z^{4} + X Y^{6} Z + 24 X Y^{5} Z^{2} + 9 X Y^{4} Z^{3} + 11 X Y^{3} Z^{4} + 7 X Y^{2} Z^{5} + 5 X Y Z^{6} + 20 X^{4} Y^{2} Z + 26 X^{4} Y Z^{2} + 96 X^{3} Y^{3} Z + 84 X^{3} Y^{2} Z^{2} + 48 X^{3} Y Z^{3} + 42 X^{2} Y^{3} Z^{2} + 107 X^{2} Y^{2} Z^{3} + 14 X^{2} Y Z^{4} + 4 X Y^{5} Z + 95 X Y^{4} Z^{2} + 27 X Y^{3} Z^{3} + 92 X Y^{2} Z^{4} + 2 X Y Z^{5} + 36 X^{4} Y Z + 120 X^{3} Y^{2} Z + 156 X^{3} Y Z^{2} + 107 X^{2} Y^{3} Z + 482 X^{2} Y^{2} Z^{2} + 61 X^{2} Y Z^{3} + 14 X Y^{4} Z + 67 X Y^{3} Z^{2} + 55 X Y^{2} Z^{3} + 24 X Y Z^{4} + 72 X^{3} Y Z + 141 X^{2} Y^{2} Z + 207 X^{2} Y Z^{2} + 106 X Y^{3} Z + 226 X Y^{2} Z^{2} + 69 X Y Z^{3} + 100 X^{2} Y Z + 147 X Y^{2} Z + 210 X Y Z^{2} + 78 X Y Z

Algorithm definition

The algorithm ⟨20×21×27:6390⟩ is serendipitous tensor product (⟨5×3×9:102⟩ - 26) ⊗ ⟨4×7×3:63⟩ +2⟨4×7×9:186⟩ +10⟨4×7×6:123⟩.

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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