Description of fast matrix multiplication algorithm: ⟨8×18×21:1843⟩

Algorithm type

135 X^{4} Y^{4} Z^{4} + X^{6} Y^{2} Z^{2} + 5 X^{4} Y^{2} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 9 X^{2} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{3} + X^{6} Y Z + 30 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 2 X^{3} Y^{3} Z^{2} + X^{3} Y^{2} Z^{3} + 351 X^{2} Y^{4} Z^{2} + 35 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + 6 X^{4} Y Z^{2} + X^{3} Y^{2} Z^{2} + 4 X^{3} Y Z^{3} + 6 X^{2} Y Z^{4} + 18 X Y^{4} Z^{2} + 2 X^{4} Y Z + 4 X^{3} Y Z^{2} + 337 X^{2} Y^{2} Z^{2} + 5 X^{2} Y Z^{3} + 162 X Y^{4} Z + X Y Z^{4} + 2 X^{3} Y Z + 60 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 6 X Y^{3} Z + 84 X Y^{2} Z^{2} + 3 X Y Z^{3} + 60 X^{2} Y Z + 294 X Y^{2} Z + 67 X Y Z^{2} + 132 X Y Z

Algorithm definition

The algorithm ⟨8×18×21:1843⟩ is serendipitous tensor product (⟨4×6×7:123⟩ - 4) ⊗ ⟨2×3×3:15⟩ +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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