Description of fast matrix multiplication algorithm: ⟨14×18×25:3694⟩

Algorithm type

4 X^{4} Y^{8} Z^{6} + 5 X^{8} Y^{4} Z^{4} + 48 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 2 X^{8} Y^{3} Z^{3} + 22 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{4} Z^{8} + 8 X Y^{12} Z + 8 X^{2} Y^{8} Z^{3} + 8 X^{6} Y^{4} Z^{2} + 3 X^{6} Y^{2} Z^{4} + 277 X^{4} Y^{4} Z^{4} + 100 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + 22 X^{2} Y^{2} Z^{8} + 3 X^{6} Y^{2} Z^{3} + 16 X^{2} Y^{6} Z^{3} + 16 X Y^{9} Z + 50 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{4} Z^{2} + 66 X^{4} Y^{2} Z^{4} + 214 X^{2} Y^{6} Z^{2} + 28 X^{2} Y^{4} Z^{4} + 44 X^{2} Y^{2} Z^{6} + 8 X Y^{8} Z + 10 X^{4} Y^{2} Z^{3} + 8 X^{2} Y^{4} Z^{3} + 8 X Y^{4} Z^{4} + 162 X^{4} Y^{2} Z^{2} + 16 X^{3} Y^{4} Z + 146 X^{2} Y^{4} Z^{2} + 154 X^{2} Y^{2} Z^{4} + 24 X Y^{6} Z + 16 X Y^{4} Z^{3} + 16 X Y^{3} Z^{4} + 2 X^{4} Y^{2} Z + 2 X^{4} Y Z^{2} + 32 X^{3} Y^{3} Z + 14 X^{3} Y Z^{3} + 48 X^{2} Y^{4} Z + 48 X^{2} Y^{3} Z^{2} + 39 X^{2} Y^{2} Z^{3} + 56 X Y^{4} Z^{2} + 32 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + 26 X^{4} Y Z + 16 X^{3} Y^{2} Z + 32 X^{3} Y Z^{2} + 96 X^{2} Y^{3} Z + 485 X^{2} Y^{2} Z^{2} + 16 X Y^{4} Z + 112 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 36 X Y Z^{4} + 110 X^{3} Y Z + 48 X^{2} Y^{2} Z + 108 X^{2} Y Z^{2} + 52 X Y^{3} Z + 56 X Y^{2} Z^{2} + 76 X Y Z^{3} + 216 X^{2} Y Z + 44 X Y^{2} Z + 262 X Y Z^{2} + 54 X Y Z

Algorithm definition

The algorithm ⟨14×18×25:3694⟩ is serendipitous tensor product (⟨7×3×5:79⟩ - 5) ⊗ ⟨2×6×5:47⟩ +⟨10×6×5:216⟩.

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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