Description of fast matrix multiplication algorithm: ⟨12×14×22:2226⟩

Algorithm type

9 X^{8} Y^{8} Z^{8} + X^{8} Y^{8} Z^{6} + 3 X^{6} Y^{8} Z^{8} + 3 X^{8} Y^{6} Z^{6} + X^{6} Y^{6} Z^{8} + X^{6} Y^{6} Z^{6} + 11 X^{4} Y^{8} Z^{4} + 32 X^{4} Y^{6} Z^{6} + 12 X^{4} Y^{4} Z^{8} + X^{4} Y^{8} Z^{2} + 3 X^{4} Y^{6} Z^{4} + 3 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{8} Z^{4} + 48 X^{2} Y^{6} Z^{6} + X^{2} Y^{4} Z^{8} + X^{4} Y^{6} Z^{2} + 107 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + X^{2} Y^{2} Z^{8} + 6 X^{4} Y^{4} Z^{3} + 18 X^{3} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{3} Z^{3} + 6 X^{3} Y^{3} Z^{4} + 4 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 10 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{3} Z^{3} + 6 X^{4} Y^{2} Z^{2} + 106 X^{2} Y^{4} Z^{2} + 192 X^{2} Y^{3} Z^{3} + 108 X^{2} Y^{2} Z^{4} + 6 X^{2} Y^{4} Z + 18 X^{2} Y^{3} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 12 X Y^{4} Z^{2} + 288 X Y^{3} Z^{3} + 6 X Y^{2} Z^{4} + 6 X^{2} Y^{3} Z + 341 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 6 X Y Z^{4} + 36 X^{3} Y Z + 12 X^{2} Y^{2} Z + 24 X Y^{3} Z + 24 X Y^{2} Z^{2} + 60 X Y Z^{3} + 36 X^{2} Y Z + 240 X Y^{2} Z + 216 X Y Z^{2} + 138 X Y Z

Algorithm definition

The algorithm ⟨12×14×22:2226⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×7×11:318⟩.

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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