Description of fast matrix multiplication algorithm: ⟨12×14×26:2604⟩

Algorithm type

4 X^{8} Y^{10} Z^{8} + 2 X^{8} Y^{10} Z^{6} + 8 X^{8} Y^{8} Z^{8} + 3 X^{8} Y^{6} Z^{8} + X^{6} Y^{8} Z^{8} + 2 X^{4} Y^{14} Z^{4} + 3 X^{8} Y^{6} Z^{6} + 3 X^{8} Y^{4} Z^{8} + 2 X^{4} Y^{12} Z^{4} + 2 X^{6} Y^{4} Z^{8} + 9 X^{4} Y^{10} Z^{4} + X^{8} Y^{2} Z^{6} + X^{4} Y^{10} Z^{2} + 6 X^{4} Y^{8} Z^{4} + 48 X^{4} Y^{6} Z^{6} + 11 X^{4} Y^{6} Z^{4} + 72 X^{2} Y^{6} Z^{6} + 24 X^{4} Y^{5} Z^{4} + X^{4} Y^{6} Z^{2} + 12 X^{4} Y^{5} Z^{3} + 108 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + 18 X^{4} Y^{3} Z^{4} + 6 X^{3} Y^{4} Z^{4} + 12 X^{2} Y^{7} Z^{2} + 18 X^{4} Y^{3} Z^{3} + 24 X^{4} Y^{2} Z^{4} + 24 X^{2} Y^{6} Z^{2} + 12 X^{3} Y^{2} Z^{4} + 54 X^{2} Y^{5} Z^{2} + X^{4} Y^{2} Z^{2} + 6 X^{4} Y Z^{3} + 6 X^{2} Y^{5} Z + 84 X^{2} Y^{4} Z^{2} + 288 X^{2} Y^{3} Z^{3} + 36 X^{2} Y^{2} Z^{4} + 66 X^{2} Y^{3} Z^{2} + 432 X Y^{3} Z^{3} + 6 X^{2} Y^{3} Z + 388 X^{2} Y^{2} Z^{2} + 12 X Y^{4} Z + 36 X^{2} Y Z^{2} + 72 X Y^{3} Z + 6 X^{2} Y Z + 288 X Y^{2} Z + 216 X Y Z^{2} + 168 X Y Z

Algorithm definition

The algorithm ⟨12×14×26:2604⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×7×13:372⟩.

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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