Description of fast matrix multiplication algorithm: ⟨15×15×16:2160⟩

Algorithm type

168 X^{4} Y^{4} Z^{4} + 3 X^{6} Y^{2} Z^{2} + 6 X^{2} Y^{6} Z^{2} + 9 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 6 X^{6} Y Z + 375 X^{4} Y^{2} Z^{2} + 72 X^{2} Y^{4} Z^{2} + 66 X^{2} Y^{2} Z^{4} + 78 X^{4} Y Z + 12 X^{2} Y^{3} Z + 417 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 6 X^{3} Y Z + 144 X^{2} Y^{2} Z + 132 X^{2} Y Z^{2} + 12 X Y^{3} Z + 18 X Y^{2} Z^{2} + 12 X Y Z^{3} + 204 X^{2} Y Z + 144 X Y^{2} Z + 132 X Y Z^{2} + 126 X Y Z

Algorithm definition

The algorithm ⟨15×15×16:2160⟩ is the (Kronecker) tensor product of ⟨3×3×2:15⟩ with ⟨5×5×8:144⟩.

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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