Description of fast matrix multiplication algorithm: ⟨20×30×32:10200⟩

Algorithm type

45 X^{6} Y^{6} Z^{2} + 135 X^{4} Y^{4} Z^{6} + 1215 X^{4} Y^{4} Z^{4} + 45 X^{2} Y^{6} Z^{4} + 20 X^{6} Y^{3} Z + 45 X^{6} Y^{2} Z^{2} + 92 X^{4} Y^{4} Z^{2} + 20 X^{3} Y^{6} Z + 450 X^{2} Y^{6} Z^{2} + 315 X^{2} Y^{4} Z^{4} + 225 X^{2} Y^{2} Z^{6} + 98 X^{4} Y^{3} Z^{2} + 60 X^{4} Y^{2} Z^{3} + 100 X^{3} Y^{4} Z^{2} + 60 X^{2} Y^{4} Z^{3} + 20 X Y^{6} Z^{2} + 20 X^{6} Y Z + 697 X^{4} Y^{2} Z^{2} + 270 X^{3} Y^{3} Z^{2} + 1288 X^{2} Y^{4} Z^{2} + 720 X^{2} Y^{2} Z^{4} + 206 X Y^{6} Z + 30 X^{4} Y^{2} Z + 90 X^{3} Y^{2} Z^{2} + 75 X^{2} Y^{4} Z + 122 X^{2} Y^{3} Z^{2} + 146 X Y^{4} Z^{2} + 50 X^{4} Y Z + 109 X^{3} Y^{2} Z + 352 X^{2} Y^{3} Z + 453 X^{2} Y^{2} Z^{2} + 104 X^{2} Y Z^{3} + 367 X Y^{4} Z + 106 X Y^{2} Z^{3} + 18 X^{3} Y Z + 476 X^{2} Y^{2} Z + 438 X^{2} Y Z^{2} + 40 X Y^{3} Z + 441 X Y^{2} Z^{2} + 5 X Y Z^{3} + 225 X^{2} Y Z + 247 X Y^{2} Z + 80 X Y Z^{2} + 80 X Y Z

Algorithm definition

The algorithm ⟨20×30×32:10200⟩ is serendipitous tensor product (⟨4×10×4:115⟩ - 30) ⊗ ⟨5×3×8:90⟩ +15⟨5×6×8:170⟩.

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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