Description of fast matrix multiplication algorithm: ⟨20×27×32:9356⟩

Algorithm type

8 X^{12} Y^{16} Z^{4} + 8 X^{6} Y^{16} Z^{2} + 12 X^{6} Y^{8} Z^{9} + 4 X^{3} Y^{12} Z^{6} + 16 X^{6} Y^{12} Z^{2} + 108 X^{6} Y^{8} Z^{6} + 8 X^{4} Y^{8} Z^{8} + 40 X^{3} Y^{12} Z^{3} + 24 X^{3} Y^{8} Z^{6} + 16 X^{3} Y^{12} Z + 20 X^{3} Y^{4} Z^{9} + 4 X Y^{12} Z^{2} + 12 X^{6} Y^{6} Z^{2} + 96 X^{4} Y^{4} Z^{6} + 56 X^{3} Y^{8} Z^{3} + 24 X^{2} Y^{8} Z^{4} + 40 X Y^{12} Z + 4 X^{6} Y^{4} Z^{3} + 4 X^{3} Y^{9} Z + 60 X^{3} Y^{4} Z^{6} + 12 X^{2} Y^{8} Z^{3} + 20 X^{6} Y^{4} Z^{2} + 864 X^{4} Y^{4} Z^{4} + 108 X^{2} Y^{8} Z^{2} + 32 X^{2} Y^{6} Z^{4} + 4 X^{6} Y^{3} Z^{2} + 40 X Y^{8} Z^{2} + 6 X^{6} Y^{2} Z^{2} + 16 X^{3} Y^{6} Z + 16 X^{3} Y^{4} Z^{3} + 320 X^{2} Y^{6} Z^{2} + 212 X^{2} Y^{4} Z^{4} + 160 X^{2} Y^{2} Z^{6} + 56 X Y^{8} Z + 4 X Y^{6} Z^{2} + 32 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 448 X^{2} Y^{4} Z^{2} + 502 X^{2} Y^{2} Z^{4} + 20 X Y^{4} Z^{3} + 54 X^{3} Y^{3} Z + 4 X^{2} Y^{4} Z + 192 X^{2} Y^{2} Z^{3} + 84 X Y^{4} Z^{2} + 8 X^{3} Y^{2} Z + 1856 X^{2} Y^{2} Z^{2} + 16 X Y^{4} Z + 66 X Y^{3} Z^{2} + 26 X^{3} Y Z + 640 X Y^{3} Z + 444 X Y^{2} Z^{2} + 320 X Y Z^{3} + 64 X^{2} Y Z + 896 X Y^{2} Z + 986 X Y Z^{2} + 256 X Y Z

Algorithm definition

The algorithm ⟨20×27×32:9356⟩ is serendipitous tensor product (⟨5×3×8:90⟩ - 4) ⊗ ⟨4×9×4:104⟩ +2⟨4×9×8:206⟩.

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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