Description of fast matrix multiplication algorithm: ⟨20×20×30:6652⟩

Algorithm type

24 X^{6} Y^{8} Z^{4} + 32 X^{4} Y^{8} Z^{2} + 24 X^{3} Y^{8} Z^{2} + 90 X^{8} Y^{2} Z^{2} + 16 X^{6} Y^{4} Z^{2} + 45 X^{4} Y^{6} Z^{2} + 765 X^{4} Y^{4} Z^{4} + 45 X^{4} Y^{2} Z^{6} + 32 X^{2} Y^{8} Z + 45 X^{6} Y^{2} Z^{2} + 170 X^{4} Y^{4} Z^{2} + 90 X^{4} Y^{2} Z^{4} + 225 X^{2} Y^{6} Z^{2} + 225 X^{2} Y^{2} Z^{6} + 30 X^{2} Y^{6} Z + 30 X^{2} Y Z^{6} + 360 X^{4} Y^{2} Z^{2} + 16 X^{3} Y^{4} Z + 571 X^{2} Y^{4} Z^{2} + 555 X^{2} Y^{2} Z^{4} + 150 X Y^{6} Z + 150 X Y Z^{6} + 60 X^{4} Y^{2} Z + 60 X^{4} Y Z^{2} + 48 X^{3} Y^{2} Z^{2} + 140 X^{2} Y^{4} Z + 30 X^{2} Y^{3} Z^{2} + 30 X^{2} Y^{2} Z^{3} + 60 X^{2} Y Z^{4} + 20 X^{4} Y Z + 30 X^{3} Y^{2} Z + 30 X^{3} Y Z^{2} + 10 X^{2} Y^{3} Z + 560 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 46 X Y^{4} Z + 150 X Y^{3} Z^{2} + 150 X Y^{2} Z^{3} + 30 X Y Z^{4} + 42 X^{3} Y Z + 324 X^{2} Y^{2} Z + 260 X^{2} Y Z^{2} + 50 X Y^{3} Z + 60 X Y^{2} Z^{2} + 50 X Y Z^{3} + 240 X^{2} Y Z + 190 X Y^{2} Z + 190 X Y Z^{2} + 92 X Y Z

Algorithm definition

The algorithm ⟨20×20×30:6652⟩ is serendipitous tensor product (⟨5×3×5:58⟩ - 6) ⊗ ⟨4×10×4:115⟩ +3⟨4×10×8:224⟩.

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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