Description of fast matrix multiplication algorithm: ⟨10×18×32:3394⟩

Algorithm type

280 X^{4} Y^{4} Z^{4} + 12 X Y^{9} Z + 292 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 3 X^{3} Y^{2} Z^{4} + 2 X^{2} Y Z^{6} + 8 X Y^{6} Z^{2} + 58 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 116 X^{2} Y^{4} Z^{2} + 97 X^{2} Y^{2} Z^{4} + 116 X Y^{6} Z + 2 X Y Z^{6} + 3 X^{3} Y Z^{3} + 4 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + X Y^{3} Z^{3} + 60 X^{2} Y^{3} Z + 947 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 96 X Y^{3} Z^{2} + 3 X Y Z^{4} + 6 X^{3} Y Z + 2 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 128 X Y^{3} Z + 28 X Y^{2} Z^{2} + 7 X Y Z^{3} + 173 X^{2} Y Z + 349 X Y^{2} Z + 312 X Y Z^{2} + 267 X Y Z

Algorithm definition

The algorithm ⟨10×18×32:3394⟩ is serendipitous tensor product (⟨5×6×8:170⟩ - 6) ⊗ ⟨2×3×4:20⟩ +3⟨4×3×4:38⟩.

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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