Description of fast matrix multiplication algorithm: ⟨14×16×18:2429⟩

Algorithm type

8 X^{8} Y^{8} Z^{8} + 8 X^{8} Y^{8} Z^{6} + 16 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{4} Z^{10} + 16 X^{4} Y^{4} Z^{8} + X^{6} Y^{2} Z^{6} + 28 X^{4} Y^{4} Z^{6} + 9 X^{2} Y^{6} Z^{6} + X^{2} Y^{2} Z^{10} + 3 X^{6} Y^{2} Z^{4} + 93 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 10 X^{2} Y^{6} Z^{4} + 6 X^{2} Y^{4} Z^{6} + X^{2} Y^{2} Z^{8} + 48 X^{4} Y^{4} Z^{3} + 2 X^{6} Y^{2} Z^{2} + 14 X^{4} Y^{4} Z^{2} + 5 X^{4} Y^{2} Z^{4} + 119 X^{2} Y^{6} Z^{2} + 5 X^{2} Y^{4} Z^{4} + 41 X^{2} Y^{2} Z^{6} + 48 X^{2} Y^{2} Z^{5} + 7 X^{4} Y^{2} Z^{2} + 2 X^{2} Y^{4} Z^{2} + 145 X^{2} Y^{2} Z^{4} + 6 X^{3} Y Z^{3} + 168 X^{2} Y^{2} Z^{3} + 54 X Y^{3} Z^{3} + 6 X Y Z^{5} + 18 X^{3} Y Z^{2} + 308 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 60 X Y^{3} Z^{2} + 36 X Y^{2} Z^{3} + 6 X Y Z^{4} + 12 X^{3} Y Z + 84 X^{2} Y^{2} Z + 30 X^{2} Y Z^{2} + 138 X Y^{3} Z + 30 X Y^{2} Z^{2} + 246 X Y Z^{3} + 42 X^{2} Y Z + 12 X Y^{2} Z + 294 X Y Z^{2} + 228 X Y Z

Algorithm definition

The algorithm ⟨14×16×18:2429⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×8×9:347⟩.

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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