Description of fast matrix multiplication algorithm: ⟨14×25×30:5938⟩

Algorithm type

2 X^{4} Y^{12} Z^{4} + 94 X^{4} Y^{8} Z^{4} + 10 X^{2} Y^{12} Z^{2} + 11 X^{4} Y^{6} Z^{4} + 2 X^{2} Y^{8} Z^{4} + 12 X Y^{12} Z + 8 X^{2} Y^{9} Z^{2} + 517 X^{4} Y^{4} Z^{4} + 206 X^{2} Y^{8} Z^{2} + X^{3} Y^{2} Z^{6} + 24 X Y^{9} Z + 4 X Y^{8} Z^{2} + 34 X^{4} Y^{4} Z^{2} + 17 X^{4} Y^{2} Z^{4} + 5 X^{3} Y^{2} Z^{5} + 413 X^{2} Y^{6} Z^{2} + 43 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 36 X Y^{8} Z + 2 X^{5} Y Z^{3} + 9 X^{4} Y^{2} Z^{3} + 18 X^{3} Y^{2} Z^{4} + 8 X Y^{6} Z^{2} + 196 X^{4} Y^{2} Z^{2} + 2 X^{4} Y Z^{3} + 37 X^{3} Y^{2} Z^{3} + 327 X^{2} Y^{4} Z^{2} + 187 X^{2} Y^{2} Z^{4} + 3 X^{2} Y Z^{5} + 84 X Y^{6} Z + X Y Z^{6} + 14 X^{4} Y Z^{2} + 9 X^{3} Y^{2} Z^{2} + 13 X^{3} Y Z^{3} + 68 X^{2} Y^{4} Z + 20 X^{2} Y^{3} Z^{2} + 28 X^{2} Y^{2} Z^{3} + 20 X^{2} Y Z^{4} + 68 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 2 X Y Z^{5} + 3 X^{4} Y Z + 8 X^{3} Y Z^{2} + 137 X^{2} Y^{3} Z + 1158 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 116 X Y^{4} Z + 129 X Y^{3} Z^{2} + X Y^{2} Z^{3} + 4 X Y Z^{4} + 3 X^{3} Y Z + 85 X^{2} Y^{2} Z + 49 X^{2} Y Z^{2} + 215 X Y^{3} Z + 106 X Y^{2} Z^{2} + 20 X Y Z^{3} + 329 X^{2} Y Z + 274 X Y^{2} Z + 327 X Y Z^{2} + 390 X Y Z

Algorithm definition

The algorithm ⟨14×25×30:5938⟩ is serendipitous tensor product (⟨7×5×5:127⟩ - 13) ⊗ ⟨2×5×6:47⟩ +⟨6×5×6:130⟩ +5⟨4×5×6:90⟩.

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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