Description of fast matrix multiplication algorithm: ⟨4×28×30:2109⟩

Algorithm type

24 X^{2} Y^{24} Z^{2} + 24 X Y^{24} Z + 40 X^{4} Y^{16} Z^{4} + 32 X^{2} Y^{20} Z^{2} + 32 X Y^{20} Z + 112 X^{2} Y^{16} Z^{2} + 72 X Y^{16} Z + 104 X^{4} Y^{8} Z^{4} + 56 X^{2} Y^{12} Z^{2} + 56 X Y^{12} Z + 16 X^{4} Y^{4} Z^{4} + 152 X^{2} Y^{8} Z^{2} + 48 X Y^{8} Z + 216 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 6 X^{3} Y^{2} Z^{2} + 2 X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 64 X Y^{5} Z + 3 X Y^{2} Z^{4} + 2 X^{3} Y^{2} Z + 215 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 264 X Y^{4} Z + 3 X Y^{2} Z^{3} + 8 X^{3} Y Z + 43 X^{2} Y Z^{2} + 114 X Y^{3} Z + 2 X Y^{2} Z^{2} + X^{2} Y Z + 96 X Y^{2} Z + X Y Z^{2} + 248 X Y Z

Algorithm definition

The algorithm ⟨4×28×30:2109⟩ is serendipitous tensor product (⟨2×7×6:66⟩ - 2) ⊗ ⟨2×4×5:32⟩ +⟨4×4×5:61⟩.

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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