Description of fast matrix multiplication algorithm: ⟨10×20×27:3208⟩

Algorithm type

4 X^{6} Y^{2} Z^{4} + 256 X^{4} Y^{4} Z^{4} + 4 X^{4} Y^{2} Z^{6} + 258 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{5} Z^{3} + 4 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{5} Z^{2} + 6 X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{3} Z^{4} + 4 X Y^{6} Z^{2} + 40 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{3} Z^{2} + 118 X^{2} Y^{4} Z^{2} + 10 X^{2} Y^{3} Z^{3} + 94 X^{2} Y^{2} Z^{4} + 110 X Y^{6} Z + 2 X Y^{5} Z^{2} + 32 X^{2} Y^{3} Z^{2} + 7 X^{2} Y^{2} Z^{3} + 28 X Y^{5} Z + 18 X Y^{4} Z^{2} + 12 X^{3} Y Z^{2} + 40 X^{2} Y^{3} Z + 845 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 22 X Y^{4} Z + 107 X Y^{3} Z^{2} + 115 X Y^{3} Z + 30 X Y^{2} Z^{2} + 120 X^{2} Y Z + 360 X Y^{2} Z + 323 X Y Z^{2} + 217 X Y Z

Algorithm definition

The algorithm ⟨10×20×27:3208⟩ is serendipitous tensor product (⟨5×5×9:161⟩ - 24) ⊗ ⟨2×4×3:20⟩ +12⟨2×4×6:39⟩.

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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