Description of fast matrix multiplication algorithm: ⟨15×28×32:7426⟩

Algorithm type

252 X^{4} Y^{6} Z^{4} + 630 X^{4} Y^{4} Z^{4} + 84 X^{2} Y^{8} Z^{2} + 6 X^{6} Y^{3} Z^{2} + 6 X^{2} Y^{3} Z^{6} + 15 X^{6} Y^{2} Z^{2} + 256 X^{4} Y^{2} Z^{4} + 576 X^{2} Y^{6} Z^{2} + 64 X^{2} Y^{5} Z^{3} + 15 X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 6 X^{6} Y Z^{2} + 36 X^{4} Y^{3} Z^{2} + 11 X^{4} Y^{2} Z^{3} + 12 X^{3} Y^{2} Z^{4} + 114 X^{2} Y^{3} Z^{4} + 6 X^{2} Y Z^{6} + 80 X Y^{5} Z^{3} + X^{5} Y Z^{2} + 104 X^{4} Y^{2} Z^{2} + 2 X^{3} Y^{4} Z + 7 X^{3} Y^{2} Z^{3} + 688 X^{2} Y^{4} Z^{2} + 289 X^{2} Y^{2} Z^{4} + 144 X Y^{6} Z + 18 X Y^{4} Z^{3} + 2 X^{4} Y^{2} Z + 45 X^{4} Y Z^{2} + 12 X^{3} Y^{3} Z + 19 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{4} Z + 180 X^{2} Y^{3} Z^{2} + 3 X^{2} Y^{2} Z^{3} + 122 X^{2} Y Z^{4} + 38 X Y^{4} Z^{2} + 12 X Y^{3} Z^{3} + 8 X^{4} Y Z + 14 X^{3} Y^{2} Z + 7 X^{3} Y Z^{2} + 72 X^{2} Y^{3} Z + 974 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 206 X Y^{4} Z + 228 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 25 X^{3} Y Z + 79 X^{2} Y^{2} Z + 185 X^{2} Y Z^{2} + 348 X Y^{3} Z + 257 X Y^{2} Z^{2} + 11 X Y Z^{3} + 89 X^{2} Y Z + 491 X Y^{2} Z + 246 X Y Z^{2} + 280 X Y Z

Algorithm definition

The algorithm ⟨15×28×32:7426⟩ is serendipitous tensor product (⟨5×4×8:118⟩ - 24) ⊗ ⟨3×7×4:63⟩ +2⟨3×7×12:188⟩ +7⟨3×7×8:126⟩ +2⟨6×7×4:123⟩.

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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