Description of fast matrix multiplication algorithm: ⟨10×16×25:2378⟩

Algorithm type

32 X^{2} Y^{16} Z^{2} + 32 X Y^{16} Z + X^{6} Y^{4} Z^{6} + 96 X^{4} Y^{8} Z^{4} + 2 X^{6} Y^{4} Z^{5} + 6 X^{4} Y^{4} Z^{7} + 32 X^{8} Y^{4} Z^{2} + 33 X^{6} Y^{4} Z^{4} + 2 X^{4} Y^{4} Z^{6} + 64 X^{2} Y^{8} Z^{4} + 6 X^{2} Y^{4} Z^{8} + X^{6} Y^{4} Z^{3} + 12 X^{4} Y^{4} Z^{5} + X^{4} Y^{2} Z^{7} + 11 X^{6} Y^{4} Z^{2} + 40 X^{4} Y^{4} Z^{4} + 18 X^{4} Y^{2} Z^{6} + 128 X^{2} Y^{8} Z^{2} + 19 X^{2} Y^{4} Z^{6} + 4 X^{6} Y^{2} Z^{3} + 6 X^{4} Y^{2} Z^{5} + 15 X^{3} Y^{2} Z^{6} + X^{2} Y^{6} Z^{3} + 11 X^{2} Y^{4} Z^{5} + 12 X^{2} Y^{2} Z^{7} + 64 X Y^{8} Z^{2} + 12 X Y^{2} Z^{8} + 44 X^{6} Y^{2} Z^{2} + 11 X^{4} Y^{2} Z^{4} + 11 X^{2} Y^{6} Z^{2} + 32 X^{2} Y^{4} Z^{4} + 27 X^{2} Y^{2} Z^{6} + 13 X^{2} Y Z^{7} + 32 X Y^{8} Z + 5 X Y^{2} Z^{7} + 32 X^{4} Y^{4} Z + 55 X^{4} Y^{2} Z^{3} + 46 X^{3} Y^{2} Z^{4} + 12 X^{2} Y^{4} Z^{3} + 28 X^{2} Y Z^{6} + 35 X Y^{2} Z^{6} + 5 X^{4} Y^{2} Z^{2} + 13 X^{3} Y^{2} Z^{3} + 32 X^{2} Y^{4} Z^{2} + 70 X^{2} Y^{2} Z^{4} + 11 X^{2} Y Z^{5} + 7 X Y^{2} Z^{5} + 11 X^{3} Y^{2} Z^{2} + 52 X^{3} Y Z^{3} + 10 X^{2} Y^{2} Z^{3} + 8 X^{2} Y Z^{4} + 32 X Y^{4} Z^{2} + 13 X Y^{3} Z^{3} + 11 X Y^{2} Z^{4} + 64 X^{4} Y Z + 11 X^{3} Y^{2} Z + 247 X^{2} Y^{2} Z^{2} + 109 X^{2} Y Z^{3} + 96 X Y^{4} Z + 22 X Y^{2} Z^{3} + 44 X^{3} Y Z + 12 X^{2} Y Z^{2} + 11 X Y^{3} Z + 130 X Y^{2} Z^{2} + 63 X Y Z^{3} + 11 X^{2} Y Z + 66 X Y^{2} Z + 64 X Y Z^{2} + 109 X Y Z

Algorithm definition

The algorithm ⟨10×16×25:2378⟩ is serendipitous tensor product (⟨5×4×5:76⟩ - 36) ⊗ ⟨2×4×5:32⟩ +18⟨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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