Description of fast matrix multiplication algorithm: ⟨20×22×30:7476⟩

Algorithm type

3 X^{8} Y^{8} Z^{12} + 4 X^{16} Y^{4} Z^{4} + 45 X^{8} Y^{8} Z^{8} + 4 X^{4} Y^{16} Z^{4} + 6 X^{14} Y^{4} Z^{4} + 6 X^{4} Y^{14} Z^{4} + 2 X^{14} Y^{2} Z^{4} + 24 X^{6} Y^{6} Z^{8} + 16 X^{4} Y^{8} Z^{8} + 33 X^{4} Y^{4} Z^{12} + 8 X^{2} Y^{16} Z^{2} + 2 X^{2} Y^{14} Z^{4} + 4 X^{4} Y^{8} Z^{6} + 4 X^{4} Y^{6} Z^{8} + 6 X^{4} Y^{2} Z^{12} + 8 X^{2} Y^{14} Z^{2} + 2 X^{2} Y^{12} Z^{4} + 110 X^{4} Y^{8} Z^{4} + 10 X^{4} Y^{4} Z^{8} + 10 X^{2} Y^{12} Z^{2} + 4 X^{2} Y^{6} Z^{8} + 14 X^{8} Y^{4} Z^{2} + 2 X^{6} Y^{4} Z^{4} + 26 X^{4} Y^{6} Z^{4} + 22 X^{4} Y^{4} Z^{6} + 28 X^{2} Y^{8} Z^{4} + 4 X^{2} Y^{4} Z^{8} + 42 X^{8} Y^{2} Z^{2} + 10 X^{6} Y^{4} Z^{2} + 2 X^{6} Y^{2} Z^{4} + 437 X^{4} Y^{4} Z^{4} + 54 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{4} + 48 X^{2} Y^{4} Z^{6} + 6 X^{2} Y^{2} Z^{8} + 36 X^{7} Y^{2} Z^{2} + 36 X^{2} Y^{7} Z^{2} + 12 X^{7} Y Z^{2} + 10 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 10 X^{4} Y^{2} Z^{4} + 144 X^{3} Y^{3} Z^{4} + 14 X^{2} Y^{6} Z^{2} + 174 X^{2} Y^{4} Z^{4} + 258 X^{2} Y^{2} Z^{6} + 48 X Y^{8} Z + 12 X Y^{7} Z^{2} + 24 X^{2} Y^{4} Z^{3} + 24 X^{2} Y^{3} Z^{4} + 36 X^{2} Y Z^{6} + 48 X Y^{7} Z + 12 X Y^{6} Z^{2} + 2 X^{4} Y^{2} Z^{2} + 746 X^{2} Y^{4} Z^{2} + 104 X^{2} Y^{2} Z^{4} + 60 X Y^{6} Z + 24 X Y^{3} Z^{4} + 84 X^{4} Y^{2} Z + 12 X^{3} Y^{2} Z^{2} + 156 X^{2} Y^{3} Z^{2} + 24 X^{2} Y^{2} Z^{3} + 168 X Y^{4} Z^{2} + 24 X Y^{2} Z^{4} + 108 X^{4} Y Z + 60 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 1082 X^{2} Y^{2} Z^{2} + 180 X Y^{4} Z + 72 X Y^{3} Z^{2} + 288 X Y^{2} Z^{3} + 36 X Y Z^{4} + 60 X^{3} Y Z + 12 X^{2} Y^{2} Z + 60 X^{2} Y Z^{2} + 84 X Y^{3} Z + 468 X Y^{2} Z^{2} + 360 X Y Z^{3} + 12 X^{2} Y Z + 516 X Y^{2} Z + 264 X Y Z^{2} + 480 X Y Z

Algorithm definition

The algorithm ⟨20×22×30:7476⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×11×15:1068⟩.

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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