Description of fast matrix multiplication algorithm: ⟨10×15×27:2411⟩

Algorithm type

X^{6} Y^{2} Z^{4} + 3 X^{5} Y^{2} Z^{5} + 192 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + X^{3} Y^{2} Z^{5} + X^{6} Y Z^{2} + X^{5} Y Z^{3} + X^{4} Y^{2} Z^{3} + X^{3} Y^{3} Z^{3} + X^{3} Y Z^{5} + X^{2} Y^{2} Z^{5} + X^{2} Y Z^{6} + 2 X^{5} Y Z^{2} + 27 X^{4} Y^{2} Z^{2} + 2 X^{4} Y Z^{3} + 4 X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 474 X^{2} Y^{4} Z^{2} + 76 X^{2} Y^{2} Z^{4} + 2 X^{2} Y Z^{5} + 3 X^{4} Y Z^{2} + 5 X^{3} Y Z^{3} + 4 X^{2} Y^{2} Z^{3} + 3 X^{2} Y Z^{4} + X Y Z^{5} + 6 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 470 X^{2} Y^{2} Z^{2} + 7 X^{2} Y Z^{3} + 180 X Y^{4} Z + 3 X Y Z^{4} + 3 X^{3} Y Z + 54 X^{2} Y^{2} Z + 5 X^{2} Y Z^{2} + 144 X Y^{2} Z^{2} + 9 X Y Z^{3} + 63 X^{2} Y Z + 336 X Y^{2} Z + 155 X Y Z^{2} + 163 X Y Z

Algorithm definition

The algorithm ⟨10×15×27:2411⟩ is serendipitous tensor product (⟨5×5×9:161⟩ - 8) ⊗ ⟨2×3×3:15⟩ +4⟨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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