Description of fast matrix multiplication algorithm: ⟨20×21×28:6528⟩

Algorithm type

216 X^{4} Y^{4} Z^{6} + 3 X^{6} Y^{4} Z^{2} + 540 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{2} Z^{8} + 3 X^{6} Y^{3} Z^{2} + 3 X^{5} Y^{4} Z^{2} + 3 X^{6} Y^{2} Z^{2} + 11 X^{5} Y^{3} Z^{2} + 248 X^{4} Y^{4} Z^{2} + 480 X^{2} Y^{2} Z^{6} + 16 X Y Z^{8} + X^{7} Y Z + 3 X^{6} Y^{2} Z + 2 X^{6} Y Z^{2} + 5 X^{5} Y^{2} Z^{2} + 41 X^{4} Y^{3} Z^{2} + 90 X^{4} Y^{2} Z^{3} + 24 X^{3} Y^{4} Z^{2} + X^{2} Y^{6} Z + 78 X^{2} Y^{4} Z^{3} + 2 X^{6} Y Z + 7 X^{5} Y^{2} Z + 254 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 52 X^{3} Y^{3} Z^{2} + 2 X^{2} Y^{5} Z + 234 X^{2} Y^{4} Z^{2} + 552 X^{2} Y^{2} Z^{4} + 96 X Y Z^{6} + X^{5} Y Z + 110 X^{4} Y^{2} Z + 8 X^{4} Y Z^{2} + 9 X^{3} Y^{3} Z + 49 X^{3} Y^{2} Z^{2} + 111 X^{2} Y^{4} Z + 36 X^{2} Y^{3} Z^{2} + 96 X^{2} Y^{2} Z^{3} + 30 X^{2} Y Z^{4} + X Y^{5} Z + 4 X Y^{4} Z^{2} + 26 X Y^{2} Z^{4} + 5 X^{4} Y Z + 38 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 53 X^{2} Y^{3} Z + 720 X^{2} Y^{2} Z^{2} + 180 X^{2} Y Z^{3} + 18 X Y^{4} Z + 4 X Y^{3} Z^{2} + 156 X Y^{2} Z^{3} + 128 X Y Z^{4} + 13 X^{3} Y Z + 209 X^{2} Y^{2} Z + 206 X^{2} Y Z^{2} + 22 X Y^{3} Z + 186 X Y^{2} Z^{2} + 192 X Y Z^{3} + 197 X^{2} Y Z + 197 X Y^{2} Z + 286 X Y Z^{2} + 188 X Y Z

Algorithm definition

The algorithm ⟨20×21×28:6528⟩ is serendipitous tensor product (⟨5×7×4:104⟩ - 17) ⊗ ⟨4×3×7:63⟩ +⟨4×9×7:186⟩ +7⟨4×6×7:123⟩.

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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