Description of fast matrix multiplication algorithm: ⟨12×16×18:2043⟩

Algorithm type

9 X^{6} Y^{4} Z^{4} + 180 X^{4} Y^{4} Z^{4} + 42 X^{6} Y^{2} Z^{2} + 36 X^{4} Y^{4} Z^{2} + 48 X^{4} Y^{2} Z^{4} + 54 X^{2} Y^{6} Z^{2} + 54 X^{2} Y^{2} Z^{6} + 18 X^{3} Y^{2} Z^{4} + 132 X^{4} Y^{2} Z^{2} + 198 X^{2} Y^{4} Z^{2} + 198 X^{2} Y^{2} Z^{4} + 54 X Y^{6} Z + 54 X Y Z^{6} + 18 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{4} Z + 60 X^{2} Y Z^{4} + 36 X^{3} Y^{2} Z + 48 X^{3} Y Z^{2} + 120 X^{2} Y^{2} Z^{2} + 18 X Y^{4} Z + 54 X Y^{3} Z^{2} + 54 X Y^{2} Z^{3} + 18 X Y Z^{4} + 12 X^{3} Y Z + 108 X^{2} Y^{2} Z + 180 X^{2} Y Z^{2} + 36 X Y^{2} Z^{2} + 48 X^{2} Y Z + 36 X Y^{2} Z + 60 X Y Z^{2} + 24 X Y Z

Algorithm definition

The algorithm ⟨12×16×18:2043⟩ is serendipitous tensor product (⟨4×4×3:38⟩ - 6) ⊗ ⟨3×4×6:54⟩ +3⟨6×4×6:105⟩.

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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