Description of fast matrix multiplication algorithm: ⟨20×26×30:8610⟩

Algorithm type

X^{16} Y^{6} Z^{4} + X^{12} Y^{6} Z^{8} + 15 X^{8} Y^{10} Z^{8} + X^{4} Y^{6} Z^{16} + 7 X^{16} Y^{4} Z^{4} + 60 X^{8} Y^{8} Z^{8} + 8 X^{4} Y^{16} Z^{4} + X^{4} Y^{12} Z^{8} + X^{4} Y^{4} Z^{16} + X^{12} Y^{6} Z^{4} + 3 X^{8} Y^{6} Z^{8} + 18 X^{4} Y^{6} Z^{12} + 4 X^{2} Y^{18} Z^{2} + 4 X^{12} Y^{4} Z^{4} + 15 X^{8} Y^{4} Z^{8} + 22 X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{8} Z^{8} + 11 X^{4} Y^{4} Z^{12} + 4 X^{2} Y^{16} Z^{2} + 2 X^{8} Y^{6} Z^{4} + 36 X^{4} Y^{10} Z^{4} + 9 X^{4} Y^{6} Z^{8} + 8 X^{2} Y^{14} Z^{2} + 9 X^{8} Y^{6} Z^{2} + 7 X^{8} Y^{4} Z^{4} + 99 X^{4} Y^{8} Z^{4} + 22 X^{4} Y^{4} Z^{8} + 12 X^{2} Y^{12} Z^{2} + 8 X^{8} Y^{4} Z^{2} + 157 X^{4} Y^{6} Z^{4} + 8 X^{2} Y^{10} Z^{2} + 50 X^{2} Y^{6} Z^{6} + 6 X^{8} Y^{3} Z^{2} + 6 X^{6} Y^{3} Z^{4} + 90 X^{4} Y^{5} Z^{4} + 6 X^{2} Y^{3} Z^{8} + 57 X^{8} Y^{2} Z^{2} + 24 X^{4} Y^{6} Z^{2} + 461 X^{4} Y^{4} Z^{4} + 65 X^{2} Y^{8} Z^{2} + 26 X^{2} Y^{6} Z^{4} + 36 X^{2} Y^{4} Z^{6} + 6 X^{2} Y^{2} Z^{8} + 6 X^{6} Y^{3} Z^{2} + 18 X^{4} Y^{3} Z^{4} + 108 X^{2} Y^{3} Z^{6} + 24 X Y^{9} Z + 24 X^{6} Y^{2} Z^{2} + 26 X^{4} Y^{4} Z^{2} + 120 X^{4} Y^{2} Z^{4} + 255 X^{2} Y^{6} Z^{2} + 27 X^{2} Y^{4} Z^{4} + 76 X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 12 X^{4} Y^{3} Z^{2} + 216 X^{2} Y^{5} Z^{2} + 54 X^{2} Y^{3} Z^{4} + 48 X Y^{7} Z + 54 X^{4} Y^{3} Z + 67 X^{4} Y^{2} Z^{2} + 676 X^{2} Y^{4} Z^{2} + 172 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 48 X^{4} Y^{2} Z + 942 X^{2} Y^{3} Z^{2} + 48 X Y^{5} Z + 300 X Y^{3} Z^{3} + 90 X^{4} Y Z + 144 X^{2} Y^{3} Z + 666 X^{2} Y^{2} Z^{2} + 102 X Y^{4} Z + 120 X Y^{3} Z^{2} + 216 X Y^{2} Z^{3} + 156 X^{2} Y^{2} Z + 180 X^{2} Y Z^{2} + 738 X Y^{3} Z + 90 X Y^{2} Z^{2} + 60 X Y Z^{3} + 150 X^{2} Y Z + 492 X Y^{2} Z + 240 X Y Z^{2} + 360 X Y Z

Algorithm definition

The algorithm ⟨20×26×30:8610⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×13×15:1230⟩.

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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