Description of fast matrix multiplication algorithm: ⟨15×16×30:4050⟩

Algorithm type

18 X^{8} Y^{8} Z^{8} + 72 X^{4} Y^{4} Z^{8} + 42 X^{4} Y^{4} Z^{6} + 72 X^{8} Y^{2} Z^{2} + 318 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{8} Z^{2} + 72 X^{2} Y^{2} Z^{8} + 144 X^{2} Y^{4} Z^{4} + 228 X^{2} Y^{2} Z^{6} + 72 X Y^{8} Z + 288 X^{2} Y^{4} Z^{2} + 492 X^{2} Y^{2} Z^{4} + 288 X Y Z^{6} + 72 X^{4} Y^{2} Z + 72 X^{4} Y Z^{2} + 84 X^{2} Y^{2} Z^{3} + 216 X Y^{4} Z^{2} + 144 X Y^{2} Z^{4} + 276 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 72 X Y Z^{4} + 144 X Y^{2} Z^{2} + 288 X Y Z^{3} + 72 X Y^{2} Z + 216 X Y Z^{2} + 144 X Y Z

Algorithm definition

The algorithm ⟨15×16×30:4050⟩ is serendipitous tensor product (⟨5×4×5:76⟩ - 36) ⊗ ⟨3×4×6:54⟩ +18⟨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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