Description of fast matrix multiplication algorithm: ⟨12×20×27:3742⟩

Algorithm type

36 X^{6} Y^{8} Z^{6} + 8 X^{9} Y^{4} Z^{3} + 8 X^{4} Y^{8} Z^{4} + 24 X^{3} Y^{8} Z^{3} + 24 X^{6} Y^{4} Z^{3} + 288 X^{4} Y^{4} Z^{4} + 52 X^{2} Y^{8} Z^{2} + 64 X^{6} Y^{2} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 44 X^{3} Y^{4} Z^{3} + 32 X Y^{8} Z + 198 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 206 X^{2} Y^{4} Z^{2} + 2 X Y^{6} Z + 32 X^{2} Y^{4} Z + 2 X^{2} Y^{3} Z + 946 X^{2} Y^{2} Z^{2} + 60 X Y^{4} Z + 128 X^{3} Y Z + 8 X^{2} Y^{2} Z + 4 X^{2} Y Z^{2} + 2 X Y^{3} Z + 410 X^{2} Y Z + 418 X Y^{2} Z + 730 X Y Z

Algorithm definition

The algorithm ⟨12×20×27:3742⟩ is serendipitous tensor product (⟨3×5×3:36⟩ - 2) ⊗ ⟨4×4×9:104⟩ +⟨4×8×9:206⟩.

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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