Description of fast matrix multiplication algorithm: ⟨14×22×22:4067⟩

Algorithm type

X^{14} Y^{14} Z^{12} + X^{12} Y^{14} Z^{14} + X^{12} Y^{12} Z^{12} + X^{8} Y^{16} Z^{8} + X^{8} Y^{14} Z^{6} + X^{6} Y^{14} Z^{8} + 8 X^{8} Y^{8} Z^{8} + 3 X^{6} Y^{12} Z^{6} + X^{8} Y^{8} Z^{6} + 2 X^{8} Y^{6} Z^{8} + X^{6} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{4} + 3 X^{8} Y^{6} Z^{6} + X^{8} Y^{4} Z^{8} + 6 X^{7} Y^{7} Z^{6} + 3 X^{6} Y^{8} Z^{6} + 6 X^{6} Y^{7} Z^{7} + 3 X^{6} Y^{6} Z^{8} + 2 X^{4} Y^{8} Z^{8} + 6 X^{6} Y^{6} Z^{6} + 16 X^{6} Y^{6} Z^{4} + X^{6} Y^{4} Z^{6} + 24 X^{4} Y^{8} Z^{4} + 48 X^{4} Y^{6} Z^{6} + 24 X^{6} Y^{6} Z^{2} + 5 X^{4} Y^{8} Z^{2} + 6 X^{4} Y^{7} Z^{3} + 8 X^{4} Y^{6} Z^{4} + 6 X^{3} Y^{7} Z^{4} + 5 X^{2} Y^{8} Z^{4} + 72 X^{2} Y^{6} Z^{6} + 8 X^{8} Y^{2} Z^{2} + 2 X^{4} Y^{6} Z^{2} + 155 X^{4} Y^{4} Z^{4} + 18 X^{3} Y^{6} Z^{3} + X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{6} Z^{4} + 8 X^{2} Y^{2} Z^{8} + 6 X^{4} Y^{4} Z^{3} + 12 X^{4} Y^{3} Z^{4} + 6 X^{3} Y^{4} Z^{4} + 15 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{3} Z^{3} + 12 X^{4} Y^{2} Z^{4} + 18 X^{3} Y^{4} Z^{3} + 18 X^{3} Y^{3} Z^{4} + 26 X^{2} Y^{6} Z^{2} + 31 X^{2} Y^{4} Z^{4} + 12 X^{4} Y^{2} Z^{2} + 96 X^{3} Y^{3} Z^{2} + 6 X^{3} Y^{2} Z^{3} + 153 X^{2} Y^{4} Z^{2} + 288 X^{2} Y^{3} Z^{3} + 20 X^{2} Y^{2} Z^{4} + 144 X^{3} Y^{3} Z + 30 X^{2} Y^{4} Z + 48 X^{2} Y^{3} Z^{2} + 30 X Y^{4} Z^{2} + 432 X Y^{3} Z^{3} + 48 X^{4} Y Z + 12 X^{2} Y^{3} Z + 732 X^{2} Y^{2} Z^{2} + 6 X Y^{4} Z + 12 X Y^{3} Z^{2} + 48 X Y Z^{4} + 18 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 156 X Y^{3} Z + 114 X Y^{2} Z^{2} + 72 X^{2} Y Z + 270 X Y^{2} Z + 120 X Y Z^{2} + 540 X Y Z

Algorithm definition

The algorithm ⟨14×22×22:4067⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×11×11:581⟩.

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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