Description of fast matrix multiplication algorithm: ⟨14×20×25:4043⟩

Algorithm type

8 X^{4} Y^{12} Z^{4} + 376 X^{4} Y^{8} Z^{4} + 32 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 24 X Y^{12} Z + 448 X^{2} Y^{8} Z^{2} + 8 X Y^{8} Z^{2} + 136 X^{4} Y^{4} Z^{2} + 128 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{2} Z^{6} + 72 X Y^{8} Z + 4 X^{4} Y^{2} Z^{3} + 15 X^{3} Y^{2} Z^{4} + 5 X^{2} Y^{2} Z^{5} + 8 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 9 X^{3} Y^{2} Z^{3} + 4 X^{3} Y Z^{4} + 160 X^{2} Y^{4} Z^{2} + 14 X^{2} Y^{2} Z^{4} + X^{2} Y Z^{5} + 2 X Y Z^{6} + 2 X^{4} Y^{2} Z + 12 X^{4} Y Z^{2} + 23 X^{3} Y^{2} Z^{2} + 4 X^{3} Y Z^{3} + 136 X^{2} Y^{4} Z + 16 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 13 X^{2} Y Z^{4} + 128 X Y^{4} Z^{2} + 15 X Y^{2} Z^{4} + 3 X Y Z^{5} + 5 X^{4} Y Z + 5 X^{3} Y^{2} Z + 15 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 781 X^{2} Y^{2} Z^{2} + 17 X^{2} Y Z^{3} + 160 X Y^{4} Z + 3 X Y^{3} Z^{2} + 10 X Y^{2} Z^{3} + X Y Z^{4} + 28 X^{3} Y Z + 2 X^{2} Y^{2} Z + 32 X^{2} Y Z^{2} + 53 X Y^{3} Z + 28 X Y^{2} Z^{2} + 8 X Y Z^{3} + 304 X^{2} Y Z + 148 X Y^{2} Z + 269 X Y Z^{2} + 342 X Y Z

Algorithm definition

The algorithm ⟨14×20×25:4043⟩ is serendipitous tensor product (⟨7×5×5:127⟩ - 13) ⊗ ⟨2×4×5:32⟩ +⟨6×4×5:90⟩ +5⟨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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