Description of fast matrix multiplication algorithm: ⟨10×30×30:5154⟩

Algorithm type

80 X^{4} Y^{8} Z^{4} + 6 X^{2} Y^{12} Z^{2} + 2 X^{4} Y^{8} Z^{2} + 12 X Y^{12} Z + 4 X^{6} Y^{4} Z^{2} + 440 X^{4} Y^{4} Z^{4} + 188 X^{2} Y^{8} Z^{2} + 5 X^{6} Y^{2} Z^{3} + 8 X^{5} Y^{2} Z^{4} + 4 X^{2} Y^{8} Z + 24 X Y^{9} Z + X^{7} Y Z^{2} + 25 X^{6} Y^{2} Z^{2} + 4 X^{5} Y^{2} Z^{3} + 2 X^{5} Y Z^{4} + 37 X^{4} Y^{4} Z^{2} + 353 X^{2} Y^{6} Z^{2} + 20 X^{2} Y^{4} Z^{4} + 21 X^{2} Y^{2} Z^{6} + 56 X Y^{8} Z + X^{6} Y Z^{2} + 3 X^{5} Y^{2} Z^{2} + X^{4} Y^{2} Z^{3} + 8 X^{2} Y^{6} Z + 2 X^{2} Y Z^{6} + X Y^{2} Z^{6} + X^{6} Y Z + 3 X^{5} Y Z^{2} + 151 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + X^{3} Y^{2} Z^{3} + 3 X^{3} Y Z^{4} + 352 X^{2} Y^{4} Z^{2} + 140 X^{2} Y^{2} Z^{4} + 124 X Y^{6} Z + 11 X Y Z^{6} + X^{5} Y Z + 17 X^{3} Y^{3} Z + 7 X^{3} Y^{2} Z^{2} + 5 X^{3} Y Z^{3} + 56 X^{2} Y^{4} Z + 2 X^{2} Y^{2} Z^{3} + 3 X^{2} Y Z^{4} + 40 X Y^{4} Z^{2} + X Y^{3} Z^{3} + X Y^{2} Z^{4} + X^{4} Y Z + 11 X^{3} Y^{2} Z + 13 X^{3} Y Z^{2} + 104 X^{2} Y^{3} Z + 976 X^{2} Y^{2} Z^{2} + 8 X^{2} Y Z^{3} + 132 X Y^{4} Z + 81 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 14 X Y Z^{4} + 40 X^{3} Y Z + 72 X^{2} Y^{2} Z + 15 X^{2} Y Z^{2} + 207 X Y^{3} Z + 57 X Y^{2} Z^{2} + 16 X Y Z^{3} + 241 X^{2} Y Z + 344 X Y^{2} Z + 213 X Y Z^{2} + 358 X Y Z

Algorithm definition

The algorithm ⟨10×30×30:5154⟩ is serendipitous tensor product (⟨5×6×5:110⟩ - 8) ⊗ ⟨2×5×6:47⟩ +4⟨4×5×6:90⟩.

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.

Back to main table