Description of fast matrix multiplication algorithm: ⟨8×9×9:430⟩

Algorithm type

21 X^{4} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{2} Z^{6} + 12 X^{4} Y^{2} Z^{2} + 16 X^{3} Y^{2} Z^{3} + 42 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + 24 X^{3} Y Z^{3} + 12 X^{3} Y^{2} Z + 66 X^{2} Y^{2} Z^{2} + 12 X Y^{2} Z^{3} + 12 X^{3} Y Z + 24 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 6 X Y^{3} Z + 24 X Y^{2} Z^{2} + 12 X Y Z^{3} + 24 X^{2} Y Z + 24 X Y^{2} Z + 24 X Y Z^{2} + 24 X Y Z

Algorithm definition

The algorithm ⟨8×9×9:430⟩ is serendipitous tensor product (⟨4×3×3:29⟩ - 3) ⊗ ⟨2×3×3:15⟩ +⟨6×3×3:40⟩.

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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