Description of fast matrix multiplication algorithm: ⟨8×21×30:2958⟩

Algorithm type

3 X^{4} Y^{12} Z^{4} + 36 X^{4} Y^{10} Z^{4} + 3 X^{4} Y^{10} Z^{2} + 36 X^{4} Y^{8} Z^{4} + 6 X^{2} Y^{12} Z^{2} + 18 X^{4} Y^{6} Z^{4} + 135 X^{2} Y^{10} Z^{2} + 6 X^{2} Y^{10} Z + 189 X^{4} Y^{4} Z^{4} + 162 X^{2} Y^{8} Z^{2} + 108 X Y^{10} Z + 36 X^{2} Y^{5} Z^{4} + 18 X^{4} Y^{2} Z^{4} + 96 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 126 X Y^{8} Z + 18 X^{2} Y^{3} Z^{4} + 9 X^{4} Y^{2} Z^{2} + 6 X^{2} Y^{5} Z + 294 X^{2} Y^{4} Z^{2} + 180 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 90 X Y^{5} Z^{2} + 18 X^{2} Y Z^{4} + 18 X Y^{5} Z + 126 X Y^{4} Z^{2} + 261 X^{2} Y^{2} Z^{2} + 120 X Y^{4} Z + 72 X Y^{3} Z^{2} + 18 X^{2} Y^{2} Z + 72 X Y^{2} Z^{2} + 18 X^{2} Y Z + 300 X Y^{2} Z + 198 X Y Z^{2} + 54 X Y Z

Algorithm definition

The algorithm ⟨8×21×30:2958⟩ is serendipitous tensor product (⟨2×7×5:55⟩ - 8) ⊗ ⟨4×3×6:54⟩ +4⟨4×6×6:105⟩.

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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