Description of fast matrix multiplication algorithm: ⟨20×21×30:7170⟩

Algorithm type

3 X^{8} Y^{8} Z^{12} + 33 X^{8} Y^{8} Z^{8} + 9 X^{14} Y^{4} Z^{4} + 9 X^{4} Y^{14} Z^{4} + 3 X^{14} Y^{2} Z^{4} + 36 X^{6} Y^{6} Z^{8} + 12 X^{4} Y^{8} Z^{8} + 30 X^{4} Y^{4} Z^{12} + 3 X^{2} Y^{14} Z^{4} + 6 X^{4} Y^{8} Z^{6} + 6 X^{4} Y^{6} Z^{8} + 9 X^{4} Y^{2} Z^{12} + 18 X^{2} Y^{14} Z^{2} + 6 X Y^{14} Z^{2} + 72 X^{4} Y^{8} Z^{4} + 9 X^{4} Y^{4} Z^{8} + 6 X^{2} Y^{6} Z^{8} + 3 X^{4} Y^{6} Z^{4} + 15 X^{4} Y^{4} Z^{6} + 24 X^{2} Y^{8} Z^{4} + 18 X^{7} Y^{4} Z^{2} + 72 X^{3} Y^{6} Z^{4} + 36 X^{8} Y^{2} Z^{2} + 9 X^{6} Y^{2} Z^{4} + 459 X^{4} Y^{4} Z^{4} + 48 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{6} Z^{4} + 60 X^{2} Y^{4} Z^{6} + 21 X^{2} Y^{2} Z^{8} + 24 X^{7} Y^{2} Z^{2} + 18 X^{2} Y^{7} Z^{2} + 12 X Y^{6} Z^{4} + 6 X^{7} Y Z^{2} + 45 X^{6} Y^{2} Z^{2} + 27 X^{4} Y^{2} Z^{4} + 72 X^{3} Y^{3} Z^{4} + 51 X^{2} Y^{6} Z^{2} + 135 X^{2} Y^{4} Z^{4} + 204 X^{2} Y^{2} Z^{6} + 72 X Y^{8} Z + 6 X Y^{7} Z^{2} + 18 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{3} Z^{4} + 18 X^{2} Y Z^{6} + 24 X Y^{6} Z^{2} + 9 X^{4} Y^{2} Z^{2} + 843 X^{2} Y^{4} Z^{2} + 171 X^{2} Y^{2} Z^{4} + 90 X Y^{6} Z + 12 X Y^{3} Z^{4} + 72 X^{4} Y^{2} Z + 18 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{3} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 186 X Y^{4} Z^{2} + 42 X Y^{2} Z^{4} + 72 X^{4} Y Z + 90 X^{3} Y^{2} Z + 18 X^{3} Y Z^{2} + 1038 X^{2} Y^{2} Z^{2} + 162 X Y^{4} Z + 24 X Y^{3} Z^{2} + 252 X Y^{2} Z^{3} + 42 X Y Z^{4} + 90 X^{3} Y Z + 18 X^{2} Y^{2} Z + 54 X^{2} Y Z^{2} + 90 X Y^{3} Z + 492 X Y^{2} Z^{2} + 252 X Y Z^{3} + 18 X^{2} Y Z + 486 X Y^{2} Z + 306 X Y Z^{2} + 396 X Y Z

Algorithm definition

The algorithm ⟨20×21×30:7170⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨10×7×10:478⟩.

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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