Description of fast matrix multiplication algorithm: ⟨20×21×21:4967⟩

Algorithm type

X^{4} Y^{10} Z^{4} + X^{4} Y^{9} Z^{4} + 12 X^{6} Y^{4} Z^{6} + 3 X^{4} Y^{8} Z^{4} + X^{4} Y^{7} Z^{4} + 3 X^{2} Y^{11} Z^{2} + 30 X^{6} Y^{4} Z^{4} + 144 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{10} Z^{2} + 4 X Y Z^{12} + 12 X^{8} Y^{2} Z^{3} + 4 X^{3} Y^{2} Z^{8} + X^{2} Y^{9} Z^{2} + 12 X^{2} Y^{2} Z^{9} + 30 X^{8} Y^{2} Z^{2} + 12 X^{6} Y^{4} Z^{2} + 360 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z^{2} + 48 X^{2} Y^{2} Z^{8} + 2 X Y^{10} Z + 12 X^{8} Y^{2} Z + 24 X^{6} Y^{2} Z^{3} + 36 X^{4} Y^{4} Z^{3} + 24 X^{3} Y^{2} Z^{6} + 9 X^{2} Y^{7} Z^{2} + 30 X^{2} Y^{6} Z^{3} + X Y^{9} Z + 24 X Y Z^{9} + 60 X^{6} Y^{2} Z^{2} + 234 X^{4} Y^{4} Z^{2} + 93 X^{2} Y^{6} Z^{2} + 330 X^{2} Y^{2} Z^{6} + 9 X Y^{8} Z + 4 X Y Z^{8} + 24 X^{6} Y^{2} Z + 36 X^{4} Y^{4} Z + 84 X^{4} Y^{2} Z^{3} + 4 X^{4} Y Z^{4} + 24 X^{3} Y^{2} Z^{4} + 30 X^{2} Y^{6} Z + 10 X^{2} Y^{5} Z^{2} + 72 X^{2} Y^{4} Z^{3} + 32 X Y^{7} Z + 210 X^{4} Y^{2} Z^{2} + 24 X^{4} Y Z^{3} + 8 X^{3} Y Z^{4} + 208 X^{2} Y^{4} Z^{2} + 330 X^{2} Y^{2} Z^{4} + 14 X Y^{6} Z + 10 X Y^{3} Z^{4} + 48 X Y Z^{6} + 84 X^{4} Y^{2} Z + 24 X^{4} Y Z^{2} + 20 X^{3} Y^{2} Z^{2} + 48 X^{3} Y Z^{3} + 72 X^{2} Y^{4} Z + 96 X^{2} Y^{2} Z^{3} + 28 X^{2} Y Z^{4} + 16 X Y^{5} Z + 60 X Y^{3} Z^{3} + 24 X Y^{2} Z^{4} + 20 X^{4} Y Z + 48 X^{3} Y Z^{2} + 355 X^{2} Y^{2} Z^{2} + 168 X^{2} Y Z^{3} + 34 X Y^{4} Z + 60 X Y^{3} Z^{2} + 144 X Y^{2} Z^{3} + 28 X Y Z^{4} + 40 X^{3} Y Z + 72 X^{2} Y^{2} Z + 168 X^{2} Y Z^{2} + 86 X Y^{3} Z + 144 X Y^{2} Z^{2} + 44 X Y Z^{3} + 140 X^{2} Y Z + 120 X Y^{2} Z + 44 X Y Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨20×21×21:4967⟩ is serendipitous tensor product (⟨5×7×3:79⟩ - 5) ⊗ ⟨4×3×7:63⟩ +⟨4×15×7:305⟩.

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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