Description of fast matrix multiplication algorithm: ⟨14×16×25:3301⟩

Algorithm type

288 X^{4} Y^{8} Z^{4} + 352 X^{2} Y^{8} Z^{2} + 96 X^{4} Y^{4} Z^{2} + 10 X^{4} Y^{2} Z^{4} + 120 X^{2} Y^{4} Z^{4} + X^{2} Y^{2} Z^{6} + 64 X Y^{8} Z + 4 X^{4} Y^{2} Z^{3} + 2 X^{4} Y Z^{4} + 9 X^{3} Y^{2} Z^{4} + 2 X^{2} Y^{2} Z^{5} + X^{2} Y Z^{6} + 3 X Y^{2} Z^{6} + 25 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 8 X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 128 X^{2} Y^{4} Z^{2} + 18 X^{2} Y^{2} Z^{4} + 3 X^{2} Y Z^{5} + 3 X Y^{2} Z^{5} + 2 X^{4} Y^{2} Z + 22 X^{4} Y Z^{2} + 34 X^{3} Y^{2} Z^{2} + 96 X^{2} Y^{4} Z + 2 X^{2} Y^{3} Z^{2} + 13 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + 120 X Y^{4} Z^{2} + 13 X Y^{2} Z^{4} + 23 X^{4} Y Z + 7 X^{3} Y^{2} Z + 23 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 615 X^{2} Y^{2} Z^{2} + 19 X^{2} Y Z^{3} + 128 X Y^{4} Z + 5 X Y^{3} Z^{2} + 10 X Y^{2} Z^{3} + 32 X^{3} Y Z + 9 X^{2} Y^{2} Z + 54 X^{2} Y Z^{2} + 5 X Y^{3} Z + 9 X Y^{2} Z^{2} + X Y Z^{3} + 226 X^{2} Y Z + 132 X Y^{2} Z + 266 X Y Z^{2} + 280 X Y Z

Algorithm definition

The algorithm ⟨14×16×25:3301⟩ is serendipitous tensor product (⟨7×4×5:104⟩ - 17) ⊗ ⟨2×4×5:32⟩ +⟨6×4×5:90⟩ +7⟨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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