Description of fast matrix multiplication algorithm: ⟨10×16×30:2871⟩

Algorithm type

240 X^{4} Y^{8} Z^{4} + 16 X^{4} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 352 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + 2 X^{6} Y^{2} Z^{3} + 16 X^{2} Y^{8} Z + 8 X Y^{8} Z^{2} + 3 X^{6} Y^{2} Z^{2} + 48 X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 112 X^{2} Y^{4} Z^{4} + 112 X Y^{8} Z + X^{6} Y^{2} Z + 4 X^{6} Y Z^{2} + 4 X^{4} Y^{2} Z^{3} + 2 X^{4} Y Z^{4} + 3 X^{3} Y^{2} Z^{4} + 4 X^{6} Y Z + 9 X^{4} Y^{2} Z^{2} + 2 X^{4} Y Z^{3} + 3 X^{3} Y^{2} Z^{3} + X^{3} Y Z^{4} + 128 X^{2} Y^{4} Z^{2} + 9 X^{2} Y^{2} Z^{4} + 8 X Y^{4} Z^{3} + X^{4} Y^{2} Z + 19 X^{4} Y Z^{2} + X^{3} Y^{3} Z + 7 X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 48 X^{2} Y^{4} Z + 2 X^{2} Y^{3} Z^{2} + X^{2} Y^{2} Z^{3} + 5 X^{2} Y Z^{4} + 112 X Y^{4} Z^{2} + 4 X Y^{2} Z^{4} + 17 X^{4} Y Z + 3 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 491 X^{2} Y^{2} Z^{2} + X^{2} Y Z^{3} + 128 X Y^{4} Z + 2 X Y^{3} Z^{2} + 11 X^{3} Y Z + 34 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 18 X Y^{2} Z^{2} + 16 X Y Z^{3} + 106 X^{2} Y Z + 228 X Y^{2} Z + 232 X Y Z^{2} + 256 X Y Z

Algorithm definition

The algorithm ⟨10×16×30:2871⟩ is serendipitous tensor product (⟨5×4×6:90⟩ - 6) ⊗ ⟨2×4×5:32⟩ +3⟨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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