Description of fast matrix multiplication algorithm: ⟨10×28×28:4560⟩

Algorithm type

6 X^{6} Y^{4} Z^{4} + 60 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{2} Z^{10} + 20 X^{2} Y^{9} Z^{2} + 348 X^{4} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{8} + 2 X^{3} Y^{6} Z^{2} + 16 X Y^{9} Z + 20 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 244 X^{2} Y^{6} Z^{2} + 42 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 4 X^{5} Y^{2} Z^{2} + X^{4} Y^{2} Z^{3} + 8 X^{3} Y^{4} Z^{2} + 2 X^{3} Y^{2} Z^{4} + 2 X^{2} Y^{6} Z + 14 X Y^{6} Z^{2} + 2 X Y^{3} Z^{5} + 121 X^{4} Y^{2} Z^{2} + 5 X^{3} Y^{2} Z^{3} + 614 X^{2} Y^{4} Z^{2} + 86 X^{2} Y^{2} Z^{4} + 114 X Y^{6} Z + 6 X Y^{3} Z^{4} + 8 X Y^{2} Z^{5} + 6 X^{3} Y^{3} Z + 23 X^{3} Y^{2} Z^{2} + 8 X^{2} Y^{4} Z + 100 X^{2} Y^{3} Z^{2} + 4 X^{2} Y^{2} Z^{3} + 56 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 24 X Y^{2} Z^{4} + 10 X Y Z^{5} + 24 X^{3} Y^{2} Z + 32 X^{2} Y^{3} Z + 706 X^{2} Y^{2} Z^{2} + 200 X Y^{4} Z + 28 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 30 X Y Z^{4} + 54 X^{3} Y Z + 138 X^{2} Y^{2} Z + 13 X^{2} Y Z^{2} + 120 X Y^{3} Z + 182 X Y^{2} Z^{2} + 10 X Y Z^{3} + 231 X^{2} Y Z + 410 X Y^{2} Z + 151 X Y Z^{2} + 209 X Y Z

Algorithm definition

The algorithm ⟨10×28×28:4560⟩ is serendipitous tensor product (⟨5×7×7:176⟩ - 8) ⊗ ⟨2×4×4:26⟩ +⟨8×4×4:96⟩ +2⟨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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