Description of fast matrix multiplication algorithm: ⟨8×27×30:3744⟩

Algorithm type

18 X^{8} Y^{8} Z^{8} + 18 X^{8} Y^{6} Z^{8} + 27 X^{4} Y^{10} Z^{4} + 3 X^{2} Y^{14} Z^{2} + 103 X^{4} Y^{8} Z^{4} + 9 X^{2} Y^{12} Z^{2} + 6 X Y^{14} Z + 2 X^{2} Y^{12} Z + X^{2} Y^{8} Z^{5} + 105 X^{4} Y^{6} Z^{4} + 90 X^{2} Y^{10} Z^{2} + 18 X Y^{12} Z + 6 X^{2} Y^{8} Z^{3} + 108 X^{4} Y^{4} Z^{4} + X^{2} Y^{9} Z + 182 X^{2} Y^{8} Z^{2} + 72 X Y^{10} Z + 36 X^{4} Y^{3} Z^{4} + X^{4} Y^{2} Z^{5} + X^{4} Y^{4} Z^{2} + 21 X^{4} Y^{2} Z^{4} + 272 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 90 X Y^{8} Z + 2 X^{2} Y^{6} Z + 54 X^{2} Y^{5} Z^{2} + 7 X^{2} Y^{4} Z^{3} + 6 X Y^{7} Z + X Y^{6} Z^{2} + 2 X^{4} Y Z^{3} + 2 X^{3} Y^{4} Z + X^{3} Y^{3} Z^{2} + 3 X^{3} Y^{2} Z^{3} + 430 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + X^{2} Y Z^{5} + 277 X Y^{6} Z + 2 X Y^{4} Z^{3} + 6 X^{2} Y^{4} Z + 139 X^{2} Y^{3} Z^{2} + X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 72 X Y^{5} Z + 7 X Y^{4} Z^{2} + X^{4} Y Z + 4 X^{3} Y^{2} Z + X^{3} Y Z^{2} + 5 X^{2} Y^{3} Z + 260 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 363 X Y^{4} Z + 10 X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 2 X^{3} Y Z + 7 X^{2} Y^{2} Z + 45 X^{2} Y Z^{2} + 263 X Y^{3} Z + 15 X Y^{2} Z^{2} + 4 X Y Z^{3} + 409 X Y^{2} Z + X Y Z^{2} + 134 X Y Z

Algorithm definition

The algorithm ⟨8×27×30:3744⟩ is serendipitous tensor product (⟨4×9×10:250⟩ - 12) ⊗ ⟨2×3×3:15⟩ +6⟨4×3×3:29⟩.

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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