Description of fast matrix multiplication algorithm: ⟨10×30×32:5426⟩

Algorithm type

X^{2} Y^{13} Z^{4} + 2 X^{2} Y^{12} Z^{4} + 2 X^{2} Y^{12} Z^{3} + X^{2} Y^{11} Z^{4} + 560 X^{4} Y^{8} Z^{4} + 6 X Y^{13} Z^{2} + X^{2} Y^{10} Z^{3} + 7 X Y^{12} Z^{2} + 14 X^{2} Y^{8} Z^{4} + X Y^{12} Z + 4 X Y^{11} Z^{2} + 6 X^{2} Y^{8} Z^{3} + 2 X^{2} Y^{7} Z^{4} + 748 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{7} Z^{3} + 2 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{4} Z^{6} + 2 X Y^{10} Z + 4 X Y^{9} Z^{2} + 3 X^{2} Y^{7} Z^{2} + 8 X^{2} Y^{6} Z^{3} + 10 X^{2} Y^{5} Z^{4} + X^{2} Y^{3} Z^{6} + 2 X Y^{9} Z + 45 X Y^{8} Z^{2} + 120 X^{4} Y^{4} Z^{2} + 4 X^{2} Y^{6} Z^{2} + 9 X^{2} Y^{5} Z^{3} + 155 X^{2} Y^{4} Z^{4} + 5 X^{2} Y^{2} Z^{6} + 196 X Y^{8} Z + 14 X Y^{7} Z^{2} + 3 X^{2} Y^{5} Z^{2} + 23 X^{2} Y^{4} Z^{3} + 15 X^{2} Y^{3} Z^{4} + 5 X Y^{7} Z + 15 X Y^{6} Z^{2} + 6 X Y^{5} Z^{3} + 154 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 16 X^{2} Y^{2} Z^{4} + 20 X Y^{6} Z + 34 X Y^{5} Z^{2} + 4 X Y^{4} Z^{3} + 120 X^{2} Y^{4} Z + 9 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 29 X Y^{5} Z + 187 X Y^{4} Z^{2} + 7 X Y^{3} Z^{3} + 1151 X^{2} Y^{2} Z^{2} + 160 X Y^{4} Z + 66 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 37 X Y^{3} Z + 75 X Y^{2} Z^{2} + 13 X Y Z^{3} + 240 X^{2} Y Z + 410 X Y^{2} Z + 351 X Y Z^{2} + 304 X Y Z

Algorithm definition

The algorithm ⟨10×30×32:5426⟩ is serendipitous tensor product (⟨5×6×8:170⟩ - 27) ⊗ ⟨2×5×4:32⟩ +⟨2×5×12:94⟩ +12⟨2×5×8:63⟩.

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