Description of fast matrix multiplication algorithm: ⟨9×30×32:4851⟩

Algorithm type

6 X^{6} Y^{4} Z^{6} + 18 X^{6} Y^{2} Z^{6} + 54 X^{4} Y^{6} Z^{4} + 489 X^{4} Y^{4} Z^{4} + 18 X^{2} Y^{4} Z^{6} + 12 X^{6} Y^{2} Z^{3} + 6 X^{6} Y^{2} Z^{2} + 36 X^{6} Y Z^{3} + 6 X^{4} Y^{2} Z^{4} + 144 X^{2} Y^{6} Z^{2} + 126 X^{2} Y^{4} Z^{4} + 156 X^{2} Y^{2} Z^{6} + 54 X^{4} Y^{3} Z^{2} + 12 X^{6} Y Z + 498 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{2} Z^{3} + 774 X^{2} Y^{4} Z^{2} + 240 X^{2} Y^{2} Z^{4} + 90 X Y^{6} Z + 18 X Y^{4} Z^{3} + 12 X^{4} Y Z^{2} + 36 X^{3} Y Z^{3} + 18 X^{2} Y^{2} Z^{3} + 126 X Y^{4} Z^{2} + 12 X^{4} Y Z + 90 X^{2} Y^{3} Z + 204 X^{2} Y^{2} Z^{2} + 168 X^{2} Y Z^{3} + 288 X Y^{4} Z + 144 X Y^{2} Z^{3} + 12 X^{3} Y Z + 288 X^{2} Y^{2} Z + 258 X^{2} Y Z^{2} + 234 X Y^{2} Z^{2} + 24 X Y Z^{3} + 84 X^{2} Y Z + 72 X Y^{2} Z + 12 X Y Z^{2}

Algorithm definition

The algorithm ⟨9×30×32:4851⟩ is serendipitous tensor product (⟨3×5×8:90⟩ - 6) ⊗ ⟨3×6×4:54⟩ +3⟨6×6×4:105⟩.

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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