Description of fast matrix multiplication algorithm: ⟨20×21×32:7708⟩

Algorithm type

39 X^{8} Y^{8} Z^{8} + 13 X^{8} Y^{6} Z^{8} + 12 X^{12} Y^{4} Z^{4} + 6 X^{8} Y^{4} Z^{8} + 26 X^{6} Y^{6} Z^{8} + 9 X^{4} Y^{12} Z^{4} + 3 X^{4} Y^{8} Z^{8} + 6 X^{4} Y^{4} Z^{12} + 4 X^{12} Y^{3} Z^{4} + 2 X^{8} Y^{3} Z^{8} + 2 X^{4} Y^{3} Z^{12} + 6 X^{2} Y^{15} Z^{2} + 26 X^{4} Y^{10} Z^{4} + X^{4} Y^{6} Z^{8} + 4 X^{3} Y^{3} Z^{12} + 4 X^{6} Y^{3} Z^{8} + 3 X^{4} Y^{9} Z^{4} + 2 X^{3} Y^{6} Z^{8} + 8 X^{9} Y^{3} Z^{4} + 18 X^{8} Y^{4} Z^{4} + 61 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{4} Z^{8} + 6 X^{3} Y^{9} Z^{4} + 12 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{10} Z^{4} + 6 X^{8} Y^{3} Z^{4} + 8 X^{4} Y^{3} Z^{8} + 29 X^{4} Y^{6} Z^{4} + 16 X^{3} Y^{3} Z^{8} + 6 X^{2} Y^{10} Z^{2} + 4 X^{2} Y^{8} Z^{4} + 8 X^{6} Y^{5} Z^{2} + 12 X^{6} Y^{3} Z^{4} + 4 X^{4} Y^{5} Z^{4} + 6 X^{3} Y^{6} Z^{4} + 6 X^{2} Y^{9} Z^{2} + 4 X^{2} Y^{5} Z^{6} + 16 X^{6} Y^{4} Z^{2} + 517 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z^{2} + 28 X^{2} Y^{6} Z^{4} + 8 X^{2} Y^{4} Z^{6} + 6 X Y^{9} Z^{2} + 8 X^{6} Y^{3} Z^{2} + 12 X^{4} Y^{5} Z^{2} + 9 X^{4} Y^{3} Z^{4} + 16 X^{2} Y^{5} Z^{4} + 4 X^{2} Y^{3} Z^{6} + 54 X Y^{9} Z + 2 X Y^{6} Z^{4} + 152 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{4} Z^{2} + 102 X^{4} Y^{2} Z^{4} + 10 X^{3} Y^{3} Z^{4} + 354 X^{2} Y^{6} Z^{2} + 70 X^{2} Y^{4} Z^{4} + 76 X^{2} Y^{2} Z^{6} + 4 X Y^{3} Z^{6} + 8 X^{6} Y Z^{2} + 12 X^{4} Y^{3} Z^{2} + 4 X^{4} Y Z^{4} + 10 X^{2} Y^{5} Z^{2} + 20 X^{2} Y^{3} Z^{4} + 4 X^{2} Y Z^{6} + 24 X Y^{6} Z^{2} + 228 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{3} Z^{2} + 446 X^{2} Y^{4} Z^{2} + 306 X^{2} Y^{2} Z^{4} + 126 X Y^{6} Z + 16 X Y^{3} Z^{4} + 12 X^{4} Y Z^{2} + 72 X^{3} Y^{3} Z + 64 X^{2} Y^{3} Z^{2} + 16 X^{2} Y Z^{4} + 24 X Y^{4} Z^{2} + 36 X Y^{3} Z^{3} + 96 X^{3} Y^{2} Z + 108 X^{2} Y^{3} Z + 1102 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 154 X Y^{3} Z^{2} + 48 X Y^{2} Z^{3} + 264 X^{3} Y Z + 144 X^{2} Y^{2} Z + 142 X^{2} Y Z^{2} + 288 X Y^{3} Z + 258 X Y^{2} Z^{2} + 132 X Y Z^{3} + 396 X^{2} Y Z + 318 X Y^{2} Z + 528 X Y Z^{2} + 330 X Y Z

Algorithm definition

The algorithm ⟨20×21×32:7708⟩ is the (Kronecker) tensor product of ⟨4×7×8:164⟩ with ⟨5×3×4:47⟩.

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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