Description of fast matrix multiplication algorithm: ⟨10×21×25:3154⟩

Algorithm type

5 X^{4} Y^{4} Z^{6} + 235 X^{4} Y^{4} Z^{4} + 2 X^{6} Y^{3} Z^{2} + 2 X^{4} Y^{5} Z^{2} + 2 X^{2} Y^{6} Z^{3} + 2 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 5 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{5} Z^{2} + 94 X^{2} Y^{6} Z^{2} + 15 X^{2} Y^{2} Z^{6} + 8 X^{4} Y^{3} Z^{2} + 5 X^{3} Y^{4} Z^{2} + X^{2} Y^{5} Z^{2} + 6 X^{2} Y^{4} Z^{3} + 88 X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{4} Z + 9 X^{3} Y^{3} Z^{2} + 18 X^{2} Y^{5} Z + 373 X^{2} Y^{4} Z^{2} + 45 X^{2} Y^{2} Z^{4} + 35 X Y^{6} Z + 8 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{4} Z + 10 X^{2} Y^{3} Z^{2} + 14 X^{2} Y^{2} Z^{3} + 6 X Y^{5} Z + 6 X Y^{3} Z^{3} + 5 X^{3} Y^{2} Z + 47 X^{2} Y^{3} Z + 689 X^{2} Y^{2} Z^{2} + 120 X Y^{4} Z + 18 X Y^{3} Z^{2} + 18 X Y^{2} Z^{3} + 11 X^{3} Y Z + 119 X^{2} Y^{2} Z + 13 X^{2} Y Z^{2} + 54 X Y^{3} Z + 56 X Y^{2} Z^{2} + 40 X Y Z^{3} + 231 X^{2} Y Z + 346 X Y^{2} Z + 114 X Y Z^{2} + 250 X Y Z

Algorithm definition

The algorithm ⟨10×21×25:3154⟩ is serendipitous tensor product (⟨5×7×5:127⟩ - 15) ⊗ ⟨2×3×5:25⟩ +⟨4×3×5:47⟩ +⟨2×9×5:72⟩ +5⟨2×6×5:47⟩.

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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