Description of fast matrix multiplication algorithm: ⟨8×15×18:1347⟩

Algorithm type

90 X^{4} Y^{4} Z^{4} + X^{6} Y^{2} Z^{3} + 6 X^{4} Y^{4} Z^{2} + 5 X^{4} Y^{2} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 3 X^{6} Y Z^{2} + 3 X^{4} Y^{2} Z^{3} + X^{3} Y^{2} Z^{4} + 21 X^{4} Y^{2} Z^{2} + 2 X^{3} Y Z^{4} + 228 X^{2} Y^{4} Z^{2} + 40 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + 8 X^{4} Y Z^{2} + X^{3} Y^{3} Z + X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 12 X^{2} Y^{4} Z + X^{2} Y^{3} Z^{2} + 4 X^{2} Y^{2} Z^{3} + 7 X^{2} Y Z^{4} + 6 X Y^{4} Z^{2} + X^{4} Y Z + 4 X^{3} Y Z^{2} + 227 X^{2} Y^{2} Z^{2} + 96 X Y^{4} Z + 3 X Y Z^{4} + 2 X^{3} Y Z + 54 X^{2} Y^{2} Z + 13 X^{2} Y Z^{2} + 7 X Y^{3} Z + 78 X Y^{2} Z^{2} + 4 X Y Z^{3} + 43 X^{2} Y Z + 186 X Y^{2} Z + 83 X Y Z^{2} + 92 X Y Z

Algorithm definition

The algorithm ⟨8×15×18:1347⟩ is serendipitous tensor product (⟨4×5×6:90⟩ - 6) ⊗ ⟨2×3×3:15⟩ +3⟨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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