Description of fast matrix multiplication algorithm: ⟨8×21×21:2156⟩

Algorithm type

3 X^{4} Y^{10} Z^{2} + 6 X^{4} Y^{8} Z^{2} + 24 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z + 3 X^{4} Y^{6} Z^{2} + 132 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{6} Z^{4} + 12 X^{2} Y^{8} Z + 3 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 66 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{2} Z^{6} + 6 X Y^{8} Z + 6 X^{2} Y^{6} Z + 4 X^{2} Y^{2} Z^{5} + X^{2} Y Z^{6} + 6 X Y^{6} Z^{2} + 34 X^{4} Y^{2} Z^{2} + 6 X^{2} Y^{5} Z + 327 X^{2} Y^{4} Z^{2} + 36 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 2 X Y Z^{6} + 3 X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 18 X^{2} Y^{4} Z + 48 X^{2} Y^{3} Z^{2} + 3 X^{2} Y^{2} Z^{3} + 6 X Y^{4} Z^{2} + 3 X Y Z^{5} + X^{4} Y Z + 8 X^{2} Y^{3} Z + 360 X^{2} Y^{2} Z^{2} + 4 X^{2} Y Z^{3} + 132 X Y^{4} Z + 7 X Y^{3} Z^{2} + 7 X^{3} Y Z + 72 X^{2} Y^{2} Z + 18 X^{2} Y Z^{2} + 37 X Y^{3} Z + 78 X Y^{2} Z^{2} + 12 X Y Z^{3} + 80 X^{2} Y Z + 276 X Y^{2} Z + 86 X Y Z^{2} + 162 X Y Z

Algorithm definition

The algorithm ⟨8×21×21:2156⟩ is serendipitous tensor product (⟨4×7×7:144⟩ - 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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