Description of fast matrix multiplication algorithm: ⟨9×10×18:1020⟩

Algorithm type

6 X^{4} Y^{6} Z^{4} + 6 X^{6} Y^{2} Z^{4} + 54 X^{4} Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{6} + 6 X^{2} Y^{8} Z^{2} + 9 X^{2} Y^{4} Z^{6} + 18 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 15 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{2} Z^{6} + 12 X^{2} Y^{3} Z^{4} + 12 X^{2} Y Z^{6} + 18 X Y^{2} Z^{6} + 24 X^{4} Y^{2} Z^{2} + 12 X^{3} Y Z^{4} + 24 X^{2} Y^{4} Z^{2} + 108 X^{2} Y^{2} Z^{4} + 24 X Y Z^{6} + 12 X^{2} Y^{3} Z^{2} + 12 X Y^{4} Z^{2} + 48 X^{3} Y Z^{2} + 144 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 12 X Y^{4} Z + 30 X Y^{3} Z^{2} + 18 X Y^{2} Z^{3} + 36 X^{3} Y Z + 24 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 30 X Y^{3} Z + 48 X Y^{2} Z^{2} + 24 X Y Z^{3} + 48 X^{2} Y Z + 48 X Y^{2} Z + 24 X Y Z^{2} + 24 X Y Z

Algorithm definition

The algorithm ⟨9×10×18:1020⟩ is the (Kronecker) tensor product of ⟨3×2×3:15⟩ with ⟨3×5×6:68⟩.

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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