Description of fast matrix multiplication algorithm: ⟨16×21×28:5334⟩

Algorithm type

162 X^{4} Y^{4} Z^{6} + 405 X^{4} Y^{4} Z^{4} + 54 X^{2} Y^{2} Z^{8} + 180 X^{4} Y^{4} Z^{2} + 354 X^{2} Y^{2} Z^{6} + 10 X Y Z^{8} + 18 X^{4} Y^{3} Z^{2} + 66 X^{4} Y^{2} Z^{3} + 18 X^{3} Y^{4} Z^{2} + 66 X^{2} Y^{4} Z^{3} + 183 X^{4} Y^{2} Z^{2} + 66 X^{3} Y^{3} Z^{2} + 198 X^{2} Y^{4} Z^{2} + 399 X^{2} Y^{2} Z^{4} + 60 X Y Z^{6} + 78 X^{4} Y^{2} Z + 12 X^{4} Y Z^{2} + 30 X^{3} Y^{2} Z^{2} + 90 X^{2} Y^{4} Z + 49 X^{2} Y^{3} Z^{2} + 102 X^{2} Y^{2} Z^{3} + 22 X^{2} Y Z^{4} + X Y^{4} Z^{2} + 22 X Y^{2} Z^{4} + 6 X^{4} Y Z + 42 X^{3} Y^{2} Z + 54 X^{2} Y^{3} Z + 626 X^{2} Y^{2} Z^{2} + 132 X^{2} Y Z^{3} + 11 X Y^{4} Z + 14 X Y^{3} Z^{2} + 132 X Y^{2} Z^{3} + 94 X Y Z^{4} + 7 X^{3} Y Z + 171 X^{2} Y^{2} Z + 170 X^{2} Y Z^{2} + 37 X Y^{3} Z + 167 X Y^{2} Z^{2} + 204 X Y Z^{3} + 147 X^{2} Y Z + 204 X Y^{2} Z + 267 X Y Z^{2} + 204 X Y Z

Algorithm definition

The algorithm ⟨16×21×28:5334⟩ is serendipitous tensor product (⟨4×7×4:85⟩ - 14) ⊗ ⟨4×3×7:63⟩ +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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