Description of fast matrix multiplication algorithm: ⟨14×20×20:3276⟩

Algorithm type

6 X^{4} Y^{6} Z^{4} + X^{4} Y^{3} Z^{6} + 2 X^{2} Y^{9} Z^{2} + X^{5} Y^{3} Z^{4} + 282 X^{4} Y^{4} Z^{4} + X^{3} Y^{2} Z^{6} + X^{2} Y^{7} Z^{2} + 6 X Y^{9} Z + 19 X^{4} Y^{2} Z^{4} + X^{3} Y^{2} Z^{5} + 120 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + X^{2} Y^{2} Z^{6} + 2 X^{4} Y^{2} Z^{3} + 3 X^{3} Y^{2} Z^{4} + X^{2} Y^{2} Z^{5} + X Y^{7} Z + 2 X Y^{6} Z^{2} + 106 X^{4} Y^{2} Z^{2} + 2 X^{4} Y Z^{3} + 15 X^{3} Y^{2} Z^{3} + 432 X^{2} Y^{4} Z^{2} + 103 X^{2} Y^{2} Z^{4} + 43 X Y^{6} Z + X^{4} Y Z^{2} + X^{3} Y^{2} Z^{2} + 10 X^{2} Y^{3} Z^{2} + 9 X^{2} Y^{2} Z^{3} + 9 X Y^{4} Z^{2} + X Y Z^{5} + 34 X^{2} Y^{3} Z + 623 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 75 X Y^{4} Z + 36 X Y^{3} Z^{2} + 2 X^{3} Y Z + 136 X^{2} Y^{2} Z + 66 X^{2} Y Z^{2} + 68 X Y^{3} Z + 140 X Y^{2} Z^{2} + 9 X Y Z^{3} + 215 X^{2} Y Z + 242 X Y^{2} Z + 197 X Y Z^{2} + 239 X Y Z

Algorithm definition

The algorithm ⟨14×20×20:3276⟩ is serendipitous tensor product (⟨7×5×5:127⟩ - 15) ⊗ ⟨2×4×4:26⟩ +⟨2×4×8:51⟩ +⟨6×4×4:73⟩ +5⟨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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