Description of fast matrix multiplication algorithm: ⟨20×22×25:6181⟩

Algorithm type

8 X^{6} Y^{4} Z^{8} + 632 X^{4} Y^{4} Z^{8} + 8 X^{2} Y^{10} Z^{4} + 8 X^{4} Y^{2} Z^{8} + 16 X^{2} Y^{8} Z^{4} + 8 X^{3} Y^{2} Z^{8} + 3 X^{6} Y^{4} Z^{2} + 8 X^{6} Y^{2} Z^{4} + 8 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{6} Z^{4} + 656 X^{2} Y^{2} Z^{8} + 10 X^{6} Y^{3} Z^{2} + 5 X^{5} Y^{4} Z^{2} + 8 X^{2} Y Z^{8} + 12 X^{5} Y^{3} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{3} Z^{3} + 226 X^{4} Y^{2} Z^{4} + X^{3} Y^{4} Z^{3} + X^{3} Y^{2} Z^{5} + 2 X^{2} Y^{6} Z^{2} + 248 X^{2} Y^{4} Z^{4} + 8 X Y^{5} Z^{4} + 24 X Y Z^{8} + 3 X^{6} Y^{2} Z + 14 X^{5} Y^{2} Z^{2} + 24 X^{4} Y^{3} Z^{2} + 7 X^{3} Y^{4} Z^{2} + X^{3} Y^{2} Z^{4} + 2 X^{2} Y^{6} Z + 2 X^{2} Y^{5} Z^{2} + X^{2} Y^{4} Z^{3} + X^{2} Y^{3} Z^{4} + X Y^{6} Z^{2} + 16 X Y^{4} Z^{4} + 12 X^{5} Y^{2} Z + 5 X^{4} Y^{3} Z + 16 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 8 X^{3} Y^{4} Z + 32 X^{3} Y^{3} Z^{2} + 14 X^{3} Y^{2} Z^{3} + 8 X^{3} Y Z^{4} + 35 X^{2} Y^{4} Z^{2} + 10 X^{2} Y^{3} Z^{3} + 91 X^{2} Y^{2} Z^{4} + 6 X^{2} Y Z^{5} + X Y^{5} Z^{2} + 8 X Y^{3} Z^{4} + 9 X^{5} Y Z + 24 X^{4} Y^{2} Z + 2 X^{4} Y Z^{2} + 23 X^{3} Y^{3} Z + 132 X^{3} Y^{2} Z^{2} + X^{3} Y Z^{3} + 10 X^{2} Y^{4} Z + 16 X^{2} Y^{3} Z^{2} + 26 X^{2} Y^{2} Z^{3} + 227 X^{2} Y Z^{4} + 16 X Y^{5} Z + 16 X Y^{4} Z^{2} + 251 X Y^{2} Z^{4} + X Y Z^{5} + 31 X^{4} Y Z + 56 X^{3} Y^{2} Z + 28 X^{3} Y Z^{2} + 36 X^{2} Y^{3} Z + 1315 X^{2} Y^{2} Z^{2} + 8 X^{2} Y Z^{3} + 39 X Y^{4} Z + 3 X Y^{3} Z^{2} + 75 X Y Z^{4} + 124 X^{3} Y Z + 106 X^{2} Y^{2} Z + 31 X^{2} Y Z^{2} + 36 X Y^{3} Z + 6 X Y^{2} Z^{2} + 3 X Y Z^{3} + 489 X^{2} Y Z + 593 X Y^{2} Z + 50 X Y Z^{2} + 157 X Y Z

Algorithm definition

The algorithm ⟨20×22×25:6181⟩ is serendipitous tensor product (⟨5×11×5:195⟩ - 37) ⊗ ⟨4×2×5:32⟩ +⟨8×2×5:63⟩ +⟨4×8×5:118⟩ +⟨4×6×5:90⟩ +14⟨4×4×5:61⟩.

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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