Description of fast matrix multiplication algorithm: ⟨14×22×22:4039⟩

Algorithm type

X^{14} Y^{16} Z^{14} + 2 X^{12} Y^{12} Z^{14} + 2 X^{8} Y^{14} Z^{8} + X^{6} Y^{14} Z^{8} + X^{6} Y^{14} Z^{6} + 4 X^{8} Y^{8} Z^{8} + 2 X^{6} Y^{12} Z^{6} + 4 X^{8} Y^{8} Z^{6} + 2 X^{8} Y^{6} Z^{8} + 6 X^{7} Y^{8} Z^{7} + X^{6} Y^{8} Z^{8} + 2 X^{8} Y^{6} Z^{6} + 2 X^{8} Y^{4} Z^{8} + 3 X^{6} Y^{8} Z^{6} + 3 X^{6} Y^{6} Z^{8} + 2 X^{4} Y^{8} Z^{8} + 12 X^{6} Y^{6} Z^{7} + X^{6} Y^{6} Z^{6} + 12 X^{4} Y^{8} Z^{4} + 32 X^{4} Y^{6} Z^{6} + 12 X^{4} Y^{7} Z^{4} + 4 X^{4} Y^{8} Z^{2} + 13 X^{4} Y^{6} Z^{4} + 6 X^{3} Y^{7} Z^{4} + 5 X^{2} Y^{8} Z^{4} + 48 X^{2} Y^{6} Z^{6} + 6 X^{3} Y^{7} Z^{3} + 4 X^{8} Y^{2} Z^{2} + 3 X^{6} Y^{4} Z^{2} + 4 X^{6} Y^{2} Z^{4} + 2 X^{4} Y^{6} Z^{2} + 166 X^{4} Y^{4} Z^{4} + 4 X^{4} Y^{2} Z^{6} + 12 X^{3} Y^{6} Z^{3} + 5 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{6} Z^{4} + 3 X^{2} Y^{4} Z^{6} + 4 X^{2} Y^{2} Z^{8} + 24 X^{4} Y^{4} Z^{3} + 12 X^{4} Y^{3} Z^{4} + 6 X^{3} Y^{4} Z^{4} + 11 X^{6} Y^{2} Z^{2} + 10 X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{3} Z^{3} + 24 X^{4} Y^{2} Z^{4} + 18 X^{3} Y^{4} Z^{3} + 18 X^{3} Y^{3} Z^{4} + 25 X^{2} Y^{6} Z^{2} + 30 X^{2} Y^{4} Z^{4} + 11 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{3} Z^{3} + 29 X^{4} Y^{2} Z^{2} + 125 X^{2} Y^{4} Z^{2} + 192 X^{2} Y^{3} Z^{3} + 33 X^{2} Y^{2} Z^{4} + 24 X^{2} Y^{4} Z + 78 X^{2} Y^{3} Z^{2} + 30 X Y^{4} Z^{2} + 288 X Y^{3} Z^{3} + 24 X^{4} Y Z + 18 X^{3} Y^{2} Z + 24 X^{3} Y Z^{2} + 12 X^{2} Y^{3} Z + 907 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 30 X Y^{4} Z + 12 X Y^{3} Z^{2} + 18 X Y^{2} Z^{3} + 24 X Y Z^{4} + 66 X^{3} Y Z + 60 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 150 X Y^{3} Z + 108 X Y^{2} Z^{2} + 66 X Y Z^{3} + 174 X^{2} Y Z + 318 X Y^{2} Z + 198 X Y Z^{2} + 330 X Y Z

Algorithm definition

The algorithm ⟨14×22×22:4039⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×11×11:577⟩.

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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