Description of fast matrix multiplication algorithm: ⟨12×16×30:3291⟩

Algorithm type

108 X^{6} Y^{4} Z^{4} + 18 X^{4} Y^{4} Z^{6} + 18 X^{2} Y^{4} Z^{8} + 36 X^{6} Y^{4} Z^{2} + 165 X^{4} Y^{4} Z^{4} + 36 X^{4} Y^{2} Z^{6} + 18 X^{2} Y^{4} Z^{6} + 18 X Y^{2} Z^{8} + 144 X^{6} Y^{2} Z^{2} + 72 X^{4} Y^{2} Z^{4} + 36 X^{2} Y^{6} Z^{2} + 72 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 108 X^{3} Y^{4} Z^{2} + 108 X^{3} Y^{2} Z^{4} + 18 X^{2} Y^{4} Z^{3} + 36 X^{2} Y Z^{6} + 18 X Y^{4} Z^{4} + 18 X Y^{2} Z^{6} + 174 X^{4} Y^{2} Z^{2} + 36 X^{3} Y^{4} Z + 198 X^{2} Y^{4} Z^{2} + 168 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 18 X Y^{4} Z^{3} + 36 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 72 X^{2} Y Z^{4} + 72 X Y^{4} Z^{2} + 72 X Y^{2} Z^{4} + 144 X^{3} Y^{2} Z + 144 X^{3} Y Z^{2} + 228 X^{2} Y^{2} Z^{2} + 36 X Y^{4} Z + 36 X Y^{3} Z^{2} + 162 X^{2} Y^{2} Z + 186 X^{2} Y Z^{2} + 36 X Y^{2} Z^{2} + 24 X^{2} Y Z + 144 X Y^{2} Z + 156 X Y Z^{2} + 12 X Y Z

Algorithm definition

The algorithm ⟨12×16×30:3291⟩ is serendipitous tensor product (⟨4×4×5:61⟩ - 2) ⊗ ⟨3×4×6:54⟩ +⟨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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