Description of fast matrix multiplication algorithm: ⟨18×20×30:5919⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 738 X^{4} Y^{4} Z^{4} + 42 X^{6} Y^{2} Z^{2} + 9 X^{4} Y^{2} Z^{4} + 36 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 54 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{2} Z^{4} + 237 X^{4} Y^{2} Z^{2} + 936 X^{2} Y^{4} Z^{2} + 975 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 54 X Y Z^{6} + 6 X^{3} Y^{2} Z^{2} + 18 X^{2} Y Z^{4} + 18 X Y^{4} Z^{2} + 18 X Y^{2} Z^{4} + 36 X^{3} Y^{2} Z + 48 X^{3} Y Z^{2} + 339 X^{2} Y^{2} Z^{2} + 216 X Y^{4} Z + 36 X Y^{3} Z^{2} + 54 X Y^{2} Z^{3} + 258 X Y Z^{4} + 12 X^{3} Y Z + 198 X^{2} Y^{2} Z + 294 X^{2} Y Z^{2} + 396 X Y^{2} Z^{2} + 78 X^{2} Y Z + 270 X Y^{2} Z + 414 X Y Z^{2} + 66 X Y Z

Algorithm definition

The algorithm ⟨18×20×30:5919⟩ is serendipitous tensor product (⟨6×5×5:110⟩ - 14) ⊗ ⟨3×4×6:54⟩ +7⟨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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