Description of fast matrix multiplication algorithm: ⟨8×24×28:3164⟩

Algorithm type

2 X^{8} Y^{12} Z^{8} + 14 X^{8} Y^{10} Z^{8} + 8 X^{4} Y^{18} Z^{4} + 6 X^{8} Y^{8} Z^{8} + 12 X^{4} Y^{16} Z^{4} + 23 X^{4} Y^{14} Z^{4} + 23 X^{4} Y^{12} Z^{4} + 9 X^{2} Y^{16} Z^{2} + 32 X^{4} Y^{10} Z^{4} + 33 X^{2} Y^{14} Z^{2} + 18 X^{4} Y^{8} Z^{4} + 22 X^{2} Y^{12} Z^{2} + 38 X^{4} Y^{6} Z^{4} + 19 X^{2} Y^{10} Z^{2} + 84 X^{4} Y^{5} Z^{4} + 48 X^{2} Y^{9} Z^{2} + 56 X^{4} Y^{4} Z^{4} + 81 X^{2} Y^{8} Z^{2} + 138 X^{2} Y^{7} Z^{2} + 259 X^{2} Y^{6} Z^{2} + 54 X Y^{8} Z + 192 X^{2} Y^{5} Z^{2} + 198 X Y^{7} Z + 130 X^{2} Y^{4} Z^{2} + 132 X Y^{6} Z + 156 X^{2} Y^{3} Z^{2} + 114 X Y^{5} Z + 153 X^{2} Y^{2} Z^{2} + 54 X Y^{4} Z + 726 X Y^{3} Z + 132 X Y^{2} Z + 198 X Y Z

Algorithm definition

The algorithm ⟨8×24×28:3164⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×12×14:452⟩.

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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