Description of fast matrix multiplication algorithm: ⟨20×32×32:10920⟩

Algorithm type

8 X^{16} Y^{16} Z^{8} + 25 X^{8} Y^{16} Z^{8} + 5 X^{8} Y^{12} Z^{12} + 4 X^{8} Y^{8} Z^{16} + 8 X^{16} Y^{8} Z^{4} + 21 X^{8} Y^{16} Z^{4} + 26 X^{8} Y^{12} Z^{8} + 2 X^{8} Y^{8} Z^{12} + 2 X^{8} Y^{4} Z^{16} + 5 X^{4} Y^{16} Z^{8} + 12 X^{4} Y^{18} Z^{4} + 5 X^{12} Y^{8} Z^{4} + 7 X^{8} Y^{12} Z^{4} + 49 X^{8} Y^{8} Z^{8} + 5 X^{8} Y^{4} Z^{12} + 4 X^{4} Y^{18} Z^{2} + 60 X^{4} Y^{16} Z^{4} + 2 X^{4} Y^{14} Z^{6} + 10 X^{4} Y^{12} Z^{8} + 12 X^{4} Y^{8} Z^{12} + 5 X^{4} Y^{16} Z^{2} + 17 X^{4} Y^{14} Z^{4} + 2 X^{4} Y^{12} Z^{6} + 16 X^{2} Y^{18} Z^{2} + 5 X^{2} Y^{16} Z^{4} + 7 X^{12} Y^{4} Z^{4} + 50 X^{8} Y^{8} Z^{4} + 14 X^{8} Y^{4} Z^{8} + 5 X^{4} Y^{14} Z^{2} + 71 X^{4} Y^{12} Z^{4} + 3 X^{4} Y^{10} Z^{6} + 10 X^{4} Y^{8} Z^{8} + 35 X^{2} Y^{16} Z^{2} + 4 X^{2} Y^{14} Z^{4} + 4 X^{2} Y^{12} Z^{6} + 16 X^{8} Y^{8} Z^{2} + 21 X^{4} Y^{10} Z^{4} + 7 X^{4} Y^{8} Z^{6} + 5 X^{4} Y^{6} Z^{8} + 26 X^{2} Y^{14} Z^{2} + 13 X^{2} Y^{12} Z^{4} + 10 X^{8} Y^{4} Z^{4} + 5 X^{6} Y^{8} Z^{2} + 6 X^{4} Y^{10} Z^{2} + 260 X^{4} Y^{8} Z^{4} + 34 X^{4} Y^{6} Z^{6} + 24 X^{4} Y^{4} Z^{8} + 33 X^{2} Y^{12} Z^{2} + 6 X^{2} Y^{10} Z^{4} + 16 X^{2} Y^{8} Z^{6} + 48 X^{8} Y^{4} Z^{2} + 9 X^{6} Y^{6} Z^{2} + 134 X^{4} Y^{8} Z^{2} + 222 X^{4} Y^{6} Z^{4} + 20 X^{4} Y^{4} Z^{6} + 24 X^{4} Y^{2} Z^{8} + 33 X^{2} Y^{10} Z^{2} + 36 X^{2} Y^{8} Z^{4} + 72 X^{2} Y^{9} Z^{2} + 30 X^{6} Y^{4} Z^{2} + 66 X^{4} Y^{6} Z^{2} + 413 X^{4} Y^{4} Z^{4} + 40 X^{4} Y^{2} Z^{6} + 24 X^{2} Y^{9} Z + 426 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{7} Z^{3} + 60 X^{2} Y^{6} Z^{4} + 88 X^{2} Y^{4} Z^{6} + 30 X^{2} Y^{8} Z + 102 X^{2} Y^{7} Z^{2} + 12 X^{2} Y^{6} Z^{3} + 96 X Y^{9} Z + 30 X Y^{8} Z^{2} + 64 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 128 X^{4} Y^{2} Z^{4} + 30 X^{2} Y^{7} Z + 535 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{5} Z^{3} + 98 X^{2} Y^{4} Z^{4} + 210 X Y^{8} Z + 24 X Y^{7} Z^{2} + 24 X Y^{6} Z^{3} + 96 X^{4} Y^{4} Z + 126 X^{2} Y^{5} Z^{2} + 42 X^{2} Y^{4} Z^{3} + 30 X^{2} Y^{3} Z^{4} + 156 X Y^{7} Z + 78 X Y^{6} Z^{2} + 80 X^{4} Y^{2} Z^{2} + 30 X^{3} Y^{4} Z + 36 X^{2} Y^{5} Z + 750 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{3} Z^{3} + 198 X Y^{6} Z + 36 X Y^{5} Z^{2} + 96 X Y^{4} Z^{3} + 54 X^{3} Y^{3} Z + 48 X^{2} Y^{4} Z + 396 X^{2} Y^{3} Z^{2} + 48 X^{2} Y^{2} Z^{3} + 72 X^{2} Y Z^{4} + 198 X Y^{5} Z + 36 X Y^{4} Z^{2} + 144 X^{2} Y^{3} Z + 824 X^{2} Y^{2} Z^{2} + 60 X^{2} Y Z^{3} + 396 X Y^{4} Z + 96 X Y^{2} Z^{3} + 132 X^{3} Y Z + 264 X^{2} Y Z^{2} + 654 X Y^{3} Z + 228 X Y^{2} Z^{2} + 120 X^{2} Y Z + 540 X Y^{2} Z + 660 X Y Z

Algorithm definition

The algorithm ⟨20×32×32:10920⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×16×16:1560⟩.

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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