Description of fast matrix multiplication algorithm: ⟨8×18×26:2275⟩

Algorithm type

3 X^{8} Y^{10} Z^{8} + 7 X^{8} Y^{8} Z^{8} + 3 X^{8} Y^{6} Z^{8} + 2 X^{4} Y^{14} Z^{4} + 2 X^{8} Y^{4} Z^{8} + 8 X^{4} Y^{12} Z^{4} + X^{2} Y^{16} Z^{2} + 8 X^{4} Y^{10} Z^{4} + 3 X^{2} Y^{14} Z^{2} + 17 X^{4} Y^{8} Z^{4} + 9 X^{2} Y^{12} Z^{2} + 35 X^{4} Y^{6} Z^{4} + 9 X^{2} Y^{10} Z^{2} + 18 X^{4} Y^{5} Z^{4} + 75 X^{4} Y^{4} Z^{4} + 15 X^{2} Y^{8} Z^{2} + 18 X^{4} Y^{3} Z^{4} + 12 X^{2} Y^{7} Z^{2} + 19 X^{4} Y^{2} Z^{4} + 100 X^{2} Y^{6} Z^{2} + 6 X Y^{8} Z + 48 X^{2} Y^{5} Z^{2} + 18 X Y^{7} Z + 158 X^{2} Y^{4} Z^{2} + 54 X Y^{6} Z + 210 X^{2} Y^{3} Z^{2} + 54 X Y^{5} Z + 253 X^{2} Y^{2} Z^{2} + 90 X Y^{4} Z + 42 X^{2} Y Z^{2} + 312 X Y^{3} Z + 336 X Y^{2} Z + 330 X Y Z

Algorithm definition

The algorithm ⟨8×18×26:2275⟩ is the (Kronecker) tensor product of ⟨4×9×13:325⟩ with ⟨2×2×2:7⟩.

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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