Description of fast matrix multiplication algorithm: ⟨10×15×15:1389⟩

Algorithm type

16 X^{5} Y^{2} Z^{6} + 3 X^{6} Y^{4} Z^{2} + 8 X^{5} Y Z^{6} + 96 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{6} Z^{4} + 8 X^{5} Y Z^{5} + 8 X^{4} Y Z^{6} + 3 X^{4} Y^{4} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 6 X Y^{6} Z^{2} + 33 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{4} Z + 225 X^{2} Y^{4} Z^{2} + 30 X^{2} Y^{2} Z^{4} + 6 X^{2} Y^{4} Z + 2 X^{2} Y^{2} Z^{3} + 6 X Y^{4} Z^{2} + 6 X^{3} Y^{2} Z + X^{2} Y^{3} Z + 257 X^{2} Y^{2} Z^{2} + 66 X Y^{4} Z + 6 X Y^{3} Z^{2} + 2 X^{3} Y Z + 72 X^{2} Y^{2} Z + 4 X^{2} Y Z^{2} + 66 X Y^{2} Z^{2} + 2 X Y Z^{3} + 69 X^{2} Y Z + 186 X Y^{2} Z + 67 X Y Z^{2} + 123 X Y Z

Algorithm definition

The algorithm ⟨10×15×15:1389⟩ is serendipitous tensor product (⟨5×5×5:93⟩ - 5) ⊗ ⟨2×3×3:15⟩+⟨4×3×3:29⟩+⟨6×3×3:40⟩.

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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