Description of fast matrix multiplication algorithm: ⟨14×25×25:5049⟩

Algorithm type

10 X^{4} Y^{6} Z^{4} + 4 X^{2} Y^{9} Z^{2} + 470 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{5} + 12 X Y^{9} Z + 2 X^{3} Y^{2} Z^{5} + 228 X^{2} Y^{6} Z^{2} + 10 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{2} Z^{6} + X^{5} Y Z^{3} + 3 X^{4} Y^{2} Z^{3} + 12 X^{3} Y^{2} Z^{4} + X^{3} Y Z^{5} + 4 X Y^{6} Z^{2} + 178 X^{4} Y^{2} Z^{2} + 3 X^{4} Y Z^{3} + 23 X^{3} Y^{2} Z^{3} + 570 X^{2} Y^{4} Z^{2} + 179 X^{2} Y^{2} Z^{4} + 4 X^{2} Y Z^{5} + 66 X Y^{6} Z + X Y Z^{6} + 7 X^{4} Y Z^{2} + 4 X^{3} Y^{2} Z^{2} + 5 X^{3} Y Z^{3} + 31 X^{2} Y^{3} Z^{2} + 21 X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 11 X Y^{4} Z^{2} + 3 X Y^{2} Z^{4} + 15 X^{4} Y Z + X^{3} Y Z^{2} + 90 X^{2} Y^{3} Z + 1012 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 105 X Y^{4} Z + 81 X Y^{3} Z^{2} + 11 X Y^{2} Z^{3} + 21 X Y Z^{4} + 3 X^{3} Y Z + 176 X^{2} Y^{2} Z + 21 X^{2} Y Z^{2} + 144 X Y^{3} Z + 204 X Y^{2} Z^{2} + 7 X Y Z^{3} + 296 X^{2} Y Z + 345 X Y^{2} Z + 292 X Y Z^{2} + 342 X Y Z

Algorithm definition

The algorithm ⟨14×25×25:5049⟩ is serendipitous tensor product (⟨7×5×5:127⟩ - 15) ⊗ ⟨2×5×5:40⟩ +⟨2×5×10:79⟩ +⟨6×5×5:110⟩ +5⟨4×5×5:76⟩.

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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