Description of fast matrix multiplication algorithm: ⟨10×15×18:1646⟩

Algorithm type

120 X^{4} Y^{4} Z^{4} + 5 X^{6} Y^{2} Z^{2} + X^{4} Y^{2} Z^{4} + 3 X^{3} Y^{2} Z^{5} + 9 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 7 X^{2} Y^{2} Z^{6} + 2 X^{7} Y Z + X^{6} Y Z^{2} + X^{2} Y^{2} Z^{5} + X Y Z^{7} + 3 X^{6} Y Z + 37 X^{4} Y^{2} Z^{2} + 282 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 40 X^{2} Y^{2} Z^{4} + X^{2} Y Z^{5} + 18 X Y^{6} Z + X Y Z^{6} + 3 X^{4} Y Z^{2} + X^{3} Y^{3} Z + 3 X^{3} Y Z^{3} + 4 X^{2} Y Z^{4} + 6 X Y^{4} Z^{2} + X Y Z^{5} + 6 X^{4} Y Z + 6 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 306 X^{2} Y^{2} Z^{2} + 7 X^{2} Y Z^{3} + 84 X Y^{4} Z + 12 X Y^{2} Z^{3} + 9 X^{3} Y Z + 60 X^{2} Y^{2} Z + 9 X^{2} Y Z^{2} + 19 X Y^{3} Z + 84 X Y^{2} Z^{2} + 16 X Y Z^{3} + 72 X^{2} Y Z + 198 X Y^{2} Z + 82 X Y Z^{2} + 121 X Y Z

Algorithm definition

The algorithm ⟨10×15×18:1646⟩ is serendipitous tensor product (⟨5×5×6:110⟩ - 8) ⊗ ⟨2×3×3:15⟩ +4⟨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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