Description of fast matrix multiplication algorithm: ⟨10×16×28:2685⟩

Algorithm type

X^{2} Y^{8} Z^{4} + 2 X^{2} Y^{7} Z^{4} + 216 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{7} Z^{2} + X Y^{8} Z^{2} + 8 X^{4} Y^{2} Z^{4} + 73 X^{2} Y^{6} Z^{2} + 10 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 3 X Y^{8} Z + 2 X Y^{7} Z^{2} + X^{2} Y^{4} Z^{3} + 3 X^{2} Y^{3} Z^{4} + 12 X Y^{7} Z + 7 X Y^{6} Z^{2} + 44 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{2} Z^{3} + 367 X^{2} Y^{4} Z^{2} + 8 X^{2} Y^{3} Z^{3} + 107 X^{2} Y^{2} Z^{4} + 28 X Y^{6} Z + 4 X Y^{5} Z^{2} + X Y^{4} Z^{3} + 8 X^{2} Y^{3} Z^{2} + 13 X^{2} Y^{2} Z^{3} + 5 X Y^{5} Z + 18 X Y^{4} Z^{2} + 4 X Y^{3} Z^{3} + 14 X^{2} Y^{3} Z + 479 X^{2} Y^{2} Z^{2} + 108 X Y^{4} Z + 41 X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 56 X^{2} Y^{2} Z + 26 X^{2} Y Z^{2} + 34 X Y^{3} Z + 166 X Y^{2} Z^{2} + 9 X Y Z^{3} + 100 X^{2} Y Z + 293 X Y^{2} Z + 207 X Y Z^{2} + 181 X Y Z

Algorithm definition

The algorithm ⟨10×16×28:2685⟩ is serendipitous tensor product (⟨5×4×7:104⟩ - 21) ⊗ ⟨2×4×4:26⟩ +⟨2×4×12:77⟩ +6⟨2×4×8:51⟩ +3⟨4×4×4:48⟩.

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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