Description of fast matrix multiplication algorithm: ⟨8×27×30:3825⟩

Algorithm type

21 X^{8} Y^{8} Z^{8} + 12 X^{8} Y^{6} Z^{6} + 6 X^{4} Y^{12} Z^{4} + 12 X^{4} Y^{10} Z^{4} + 6 X^{4} Y^{10} Z^{2} + 108 X^{4} Y^{8} Z^{4} + 18 X^{2} Y^{12} Z^{2} + 12 X^{4} Y^{6} Z^{4} + 42 X^{2} Y^{10} Z^{2} + 12 X Y^{12} Z + 24 X^{4} Y^{6} Z^{3} + 12 X^{2} Y^{10} Z + 174 X^{4} Y^{4} Z^{4} + 204 X^{2} Y^{8} Z^{2} + 36 X Y^{10} Z + 24 X^{4} Y^{3} Z^{3} + 12 X^{4} Y^{2} Z^{4} + 60 X^{2} Y^{6} Z^{2} + 144 X Y^{8} Z + 24 X^{2} Y^{5} Z^{2} + 6 X^{4} Y^{2} Z^{2} + 12 X^{2} Y^{5} Z + 594 X^{2} Y^{4} Z^{2} + 60 X Y^{6} Z + 24 X^{2} Y^{3} Z^{2} + 36 X Y^{5} Z + 450 X^{2} Y^{2} Z^{2} + 540 X Y^{4} Z + 12 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 48 X Y^{3} Z + 12 X^{2} Y Z + 720 X Y^{2} Z + 324 X Y Z

Algorithm definition

The algorithm ⟨8×27×30:3825⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨4×9×10:255⟩.

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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