Description of fast matrix multiplication algorithm: ⟨14×15×18:2244⟩

Algorithm type

3 X^{4} Y^{6} Z^{4} + 177 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{4} Z^{2} + 12 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{3} + 49 X^{4} Y^{2} Z^{2} + 9 X^{3} Y^{2} Z^{3} + 402 X^{2} Y^{4} Z^{2} + 78 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + 10 X^{4} Y Z^{2} + 3 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 4 X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 12 X Y^{4} Z^{2} + 2 X^{4} Y Z + 6 X^{3} Y Z^{2} + 5 X^{2} Y^{3} Z + 421 X^{2} Y^{2} Z^{2} + 8 X^{2} Y Z^{3} + 96 X Y^{4} Z + 3 X Y Z^{4} + 10 X^{3} Y Z + 102 X^{2} Y^{2} Z + 16 X^{2} Y Z^{2} + 13 X Y^{3} Z + 156 X Y^{2} Z^{2} + 7 X Y Z^{3} + 110 X^{2} Y Z + 198 X Y^{2} Z + 176 X Y Z^{2} + 114 X Y Z

Algorithm definition

The algorithm ⟨14×15×18:2244⟩ is serendipitous tensor product (⟨7×5×6:150⟩ - 12) ⊗ ⟨2×3×3:15⟩ +6⟨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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