Description of fast matrix multiplication algorithm: ⟨8×20×22:2184⟩

Algorithm type

X^{8} Y^{14} Z^{8} + X^{8} Y^{12} Z^{8} + 4 X^{8} Y^{10} Z^{8} + X^{4} Y^{18} Z^{4} + 3 X^{8} Y^{8} Z^{8} + X^{8} Y^{6} Z^{8} + 6 X^{4} Y^{14} Z^{4} + 2 X^{8} Y^{6} Z^{6} + 3 X^{4} Y^{12} Z^{4} + 5 X^{4} Y^{10} Z^{4} + 6 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{7} Z^{4} + X^{4} Y^{8} Z^{2} + 25 X^{4} Y^{6} Z^{4} + 3 X^{2} Y^{10} Z^{2} + 24 X^{4} Y^{5} Z^{4} + 6 X^{2} Y^{9} Z^{2} + 75 X^{4} Y^{4} Z^{4} + 18 X^{2} Y^{8} Z^{2} + 6 X^{4} Y^{3} Z^{4} + 36 X^{2} Y^{7} Z^{2} + 12 X^{4} Y^{3} Z^{3} + 3 X^{4} Y^{2} Z^{4} + 54 X^{2} Y^{6} Z^{2} + 30 X^{2} Y^{5} Z^{2} + X^{4} Y^{2} Z^{2} + 90 X^{2} Y^{4} Z^{2} + 6 X^{2} Y^{4} Z + 114 X^{2} Y^{3} Z^{2} + 18 X Y^{5} Z + 429 X^{2} Y^{2} Z^{2} + 108 X Y^{4} Z + 18 X^{2} Y Z^{2} + 216 X Y^{3} Z + 6 X^{2} Y Z + 324 X Y^{2} Z + 522 X Y Z

Algorithm definition

The algorithm ⟨8×20×22:2184⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×10×11:312⟩.

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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