Description of fast matrix multiplication algorithm: ⟨10×18×27:2888⟩

Algorithm type

15 X^{4} Y^{6} Z^{4} + 216 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{6} Z^{4} + X^{4} Y^{2} Z^{5} + 3 X^{4} Y^{4} Z^{2} + 19 X^{3} Y^{2} Z^{5} + 42 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{2} Z^{6} + 22 X^{3} Y Z^{5} + 2 X^{2} Y Z^{6} + 6 X Y^{6} Z^{2} + 47 X^{4} Y^{2} Z^{2} + 3 X^{4} Y Z^{3} + 2 X^{3} Y Z^{4} + 528 X^{2} Y^{4} Z^{2} + 78 X^{2} Y^{2} Z^{4} + 2 X^{2} Y Z^{5} + 24 X Y^{6} Z + X Y Z^{6} + 2 X^{5} Y Z + X^{4} Y Z^{2} + X^{3} Y^{3} Z + 2 X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 6 X^{2} Y^{4} Z + 31 X^{2} Y^{3} Z^{2} + X^{2} Y^{2} Z^{3} + 12 X Y^{4} Z^{2} + X Y Z^{5} + 3 X^{4} Y Z + 2 X^{3} Y Z^{2} + 519 X^{2} Y^{2} Z^{2} + 4 X^{2} Y Z^{3} + 192 X Y^{4} Z + 6 X Y^{3} Z^{2} + X^{3} Y Z + 90 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 24 X Y^{3} Z + 168 X Y^{2} Z^{2} + 5 X Y Z^{3} + 91 X^{2} Y Z + 366 X Y^{2} Z + 156 X Y Z^{2} + 174 X Y Z

Algorithm definition

The algorithm ⟨10×18×27:2888⟩ is serendipitous tensor product (⟨5×6×9:193⟩ - 8) ⊗ ⟨2×3×3:15⟩ +⟨8×3×3:55⟩ +2⟨4×3×3:29⟩.

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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