Description of fast matrix multiplication algorithm: ⟨12×26×32:5586⟩

Algorithm type

24 X^{8} Y^{20} Z^{8} + 36 X^{4} Y^{20} Z^{4} + 20 X^{4} Y^{18} Z^{4} + 28 X^{4} Y^{14} Z^{8} + 22 X^{8} Y^{8} Z^{8} + 6 X^{6} Y^{10} Z^{8} + 20 X^{4} Y^{12} Z^{8} + 16 X^{2} Y^{20} Z^{2} + 16 X^{2} Y^{18} Z^{2} + 10 X^{12} Y^{4} Z^{4} + 6 X^{8} Y^{8} Z^{4} + 21 X^{4} Y^{12} Z^{4} + 14 X^{4} Y^{4} Z^{12} + 2 X^{2} Y^{16} Z^{2} + 22 X^{2} Y^{14} Z^{4} + X^{6} Y^{10} Z^{2} + 153 X^{4} Y^{10} Z^{4} + 5 X^{2} Y^{14} Z^{2} + 24 X^{2} Y^{12} Z^{4} + 6 X^{6} Y^{8} Z^{2} + 25 X^{4} Y^{8} Z^{4} + 13 X^{2} Y^{12} Z^{2} + 6 X^{2} Y^{10} Z^{4} + 10 X^{6} Y^{6} Z^{2} + 18 X^{4} Y^{6} Z^{4} + 221 X^{2} Y^{10} Z^{2} + 10 X^{2} Y^{6} Z^{6} + 120 X^{2} Y^{9} Z^{2} + 168 X^{2} Y^{7} Z^{4} + 8 X^{6} Y^{4} Z^{2} + 231 X^{4} Y^{4} Z^{4} + 36 X^{3} Y^{5} Z^{4} + 8 X^{2} Y^{8} Z^{2} + 120 X^{2} Y^{6} Z^{4} + 8 X^{2} Y^{4} Z^{6} + 96 X Y^{10} Z + 96 X Y^{9} Z + 87 X^{6} Y^{2} Z^{2} + 36 X^{4} Y^{4} Z^{2} + 170 X^{2} Y^{6} Z^{2} + 60 X^{2} Y^{4} Z^{4} + 118 X^{2} Y^{2} Z^{6} + 12 X Y^{8} Z + 132 X Y^{7} Z^{2} + 6 X^{3} Y^{5} Z + 54 X^{2} Y^{5} Z^{2} + 30 X Y^{7} Z + 144 X Y^{6} Z^{2} + 36 X^{3} Y^{4} Z + 202 X^{2} Y^{4} Z^{2} + 36 X^{2} Y^{2} Z^{4} + 78 X Y^{6} Z + 36 X Y^{5} Z^{2} + 60 X^{3} Y^{3} Z + 108 X^{2} Y^{3} Z^{2} + 30 X Y^{5} Z + 60 X Y^{3} Z^{3} + 48 X^{3} Y^{2} Z + 621 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 48 X Y^{2} Z^{3} + 162 X^{3} Y Z + 264 X Y^{3} Z + 360 X Y^{2} Z^{2} + 204 X Y Z^{3} + 312 X Y^{2} Z + 216 X Y Z^{2} + 162 X Y Z

Algorithm definition

The algorithm ⟨12×26×32:5586⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×13×16:798⟩.

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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