Description of fast matrix multiplication algorithm: ⟨8×18×27:2400⟩

Algorithm type

9 X^{8} Y^{8} Z^{8} + 6 X^{8} Y^{6} Z^{6} + 3 X^{4} Y^{10} Z^{4} + 3 X^{4} Y^{10} Z^{2} + 33 X^{4} Y^{8} Z^{4} + 3 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z^{2} + 12 X^{4} Y^{6} Z^{3} + 6 X^{2} Y^{10} Z + 126 X^{4} Y^{4} Z^{4} + 30 X^{2} Y^{8} Z^{2} + 12 X^{4} Y^{3} Z^{3} + 6 X^{4} Y^{2} Z^{4} + 60 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{5} Z^{2} + 3 X^{4} Y^{2} Z^{2} + 6 X^{2} Y^{5} Z + 300 X^{2} Y^{4} Z^{2} + 108 X Y^{6} Z + 6 X^{2} Y^{3} Z^{2} + 444 X^{2} Y^{2} Z^{2} + 108 X Y^{4} Z + 6 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 108 X Y^{3} Z + 6 X^{2} Y Z + 540 X Y^{2} Z + 432 X Y Z

Algorithm definition

The algorithm ⟨8×18×27:2400⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨4×6×9:160⟩.

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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