Description of fast matrix multiplication algorithm: ⟨8×18×20:1785⟩

Algorithm type

7 X^{8} Y^{8} Z^{8} + 4 X^{8} Y^{6} Z^{6} + 2 X^{4} Y^{12} Z^{4} + 4 X^{4} Y^{10} Z^{4} + 2 X^{4} Y^{10} Z^{2} + 22 X^{4} Y^{8} Z^{4} + 2 X^{2} Y^{12} Z^{2} + 4 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z^{2} + 86 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 24 X^{4} Y^{3} Z^{3} + 4 X^{4} Y^{2} Z^{4} + 20 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{5} Z^{2} + 2 X^{4} Y^{2} Z^{2} + 12 X^{2} Y^{5} Z + 198 X^{2} Y^{4} Z^{2} + 12 X Y^{6} Z + 24 X^{2} Y^{3} Z^{2} + 36 X Y^{5} Z + 318 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 24 X^{2} Y Z^{2} + 48 X Y^{3} Z + 12 X^{2} Y Z + 396 X Y^{2} Z + 324 X Y Z

Algorithm definition

The algorithm ⟨8×18×20:1785⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ 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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