Description of fast matrix multiplication algorithm: ⟨20×26×26:7574⟩

Algorithm type

X^{12} Y^{6} Z^{8} + 9 X^{8} Y^{10} Z^{8} + X^{8} Y^{10} Z^{6} + 39 X^{8} Y^{8} Z^{8} + X^{4} Y^{2} Z^{18} + 3 X^{8} Y^{8} Z^{6} + 11 X^{8} Y^{6} Z^{8} + 2 X^{4} Y^{2} Z^{16} + 3 X^{12} Y^{4} Z^{4} + 5 X^{8} Y^{6} Z^{6} + 2 X^{4} Y^{8} Z^{8} + X^{4} Y^{4} Z^{12} + X^{4} Y^{2} Z^{14} + X^{12} Y^{2} Z^{4} + X^{8} Y^{6} Z^{4} + 6 X^{4} Y^{10} Z^{4} + 4 X^{4} Y^{6} Z^{8} + 11 X^{8} Y^{4} Z^{4} + 18 X^{4} Y^{8} Z^{4} + X^{4} Y^{6} Z^{6} + 9 X^{4} Y^{4} Z^{8} + 3 X^{8} Y^{4} Z^{2} + 5 X^{8} Y^{2} Z^{4} + 3 X^{6} Y^{4} Z^{4} + 18 X^{4} Y^{6} Z^{4} + 3 X^{4} Y^{4} Z^{6} + 4 X^{4} Y^{2} Z^{8} + X^{2} Y^{2} Z^{10} + 6 X^{6} Y^{3} Z^{4} + 54 X^{4} Y^{5} Z^{4} + X^{4} Y^{6} Z^{2} + 6 X^{4} Y^{5} Z^{3} + 595 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 3 X^{2} Y^{2} Z^{8} + 6 X^{2} Y Z^{9} + 18 X^{4} Y^{4} Z^{3} + 66 X^{4} Y^{3} Z^{4} + 12 X^{2} Y Z^{8} + 29 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 30 X^{4} Y^{3} Z^{3} + 9 X^{4} Y^{2} Z^{4} + 10 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 13 X^{2} Y^{2} Z^{6} + 6 X^{2} Y Z^{7} + 6 X^{6} Y Z^{2} + 6 X^{4} Y^{3} Z^{2} + 36 X^{2} Y^{5} Z^{2} + 24 X^{2} Y^{3} Z^{4} + 174 X^{4} Y^{2} Z^{2} + 259 X^{2} Y^{4} Z^{2} + 6 X^{2} Y^{3} Z^{3} + 157 X^{2} Y^{2} Z^{4} + 18 X^{4} Y^{2} Z + 30 X^{4} Y Z^{2} + 18 X^{3} Y^{2} Z^{2} + 108 X^{2} Y^{3} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 24 X^{2} Y Z^{4} + 6 X Y Z^{5} + 6 X^{2} Y^{3} Z + 2298 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 18 X Y Z^{4} + 66 X^{3} Y Z + 36 X^{2} Y^{2} Z + 54 X^{2} Y Z^{2} + 60 X Y^{3} Z + 72 X Y^{2} Z^{2} + 42 X Y Z^{3} + 648 X^{2} Y Z + 906 X Y^{2} Z + 618 X Y Z^{2} + 792 X Y Z

Algorithm definition

The algorithm ⟨20×26×26:7574⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×13×13:1082⟩.

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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