Description of fast matrix multiplication algorithm: ⟨20×22×30:7350⟩

Algorithm type

X^{12} Y^{6} Z^{8} + 10 X^{8} Y^{10} Z^{8} + X^{12} Y^{4} Z^{8} + 50 X^{8} Y^{8} Z^{8} + 4 X^{4} Y^{12} Z^{8} + 4 X^{4} Y^{4} Z^{16} + 3 X^{12} Y^{6} Z^{4} + 2 X^{8} Y^{6} Z^{8} + 2 X^{4} Y^{10} Z^{8} + 2 X^{2} Y^{16} Z^{4} + 13 X^{12} Y^{4} Z^{4} + 2 X^{8} Y^{8} Z^{4} + 4 X^{8} Y^{4} Z^{8} + 49 X^{4} Y^{12} Z^{4} + 4 X^{4} Y^{8} Z^{8} + 9 X^{4} Y^{4} Z^{12} + 10 X^{2} Y^{16} Z^{2} + 3 X^{2} Y^{14} Z^{4} + 2 X^{8} Y^{6} Z^{4} + 24 X^{4} Y^{10} Z^{4} + 8 X^{4} Y^{6} Z^{8} + 9 X^{2} Y^{14} Z^{2} + 7 X^{2} Y^{12} Z^{4} + X^{8} Y^{4} Z^{4} + 3 X^{6} Y^{6} Z^{4} + X^{4} Y^{10} Z^{2} + 54 X^{4} Y^{8} Z^{4} + 42 X^{4} Y^{4} Z^{8} + 4 X^{2} Y^{6} Z^{8} + 19 X^{6} Y^{6} Z^{2} + 2 X^{4} Y^{8} Z^{2} + 88 X^{4} Y^{6} Z^{4} + 5 X^{2} Y^{10} Z^{2} + 5 X^{2} Y^{8} Z^{4} + 6 X^{2} Y^{6} Z^{6} + 3 X^{2} Y^{4} Z^{8} + 6 X^{6} Y^{3} Z^{4} + 60 X^{4} Y^{5} Z^{4} + 6 X^{6} Y^{4} Z^{2} + 8 X^{6} Y^{2} Z^{4} + 13 X^{4} Y^{6} Z^{2} + 407 X^{4} Y^{4} Z^{4} + 29 X^{2} Y^{8} Z^{2} + 83 X^{2} Y^{6} Z^{4} + 4 X^{2} Y^{4} Z^{6} + 27 X^{2} Y^{2} Z^{8} + 18 X^{6} Y^{3} Z^{2} + 12 X^{4} Y^{3} Z^{4} + 12 X^{2} Y^{5} Z^{4} + 12 X Y^{8} Z^{2} + 96 X^{6} Y^{2} Z^{2} + 42 X^{4} Y^{4} Z^{2} + 32 X^{4} Y^{2} Z^{4} + 362 X^{2} Y^{6} Z^{2} + 62 X^{2} Y^{4} Z^{4} + 58 X^{2} Y^{2} Z^{6} + 60 X Y^{8} Z + 18 X Y^{7} Z^{2} + 12 X^{4} Y^{3} Z^{2} + 144 X^{2} Y^{5} Z^{2} + 48 X^{2} Y^{3} Z^{4} + 54 X Y^{7} Z + 42 X Y^{6} Z^{2} + 23 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{3} Z^{2} + 6 X^{2} Y^{5} Z + 385 X^{2} Y^{4} Z^{2} + 322 X^{2} Y^{2} Z^{4} + 24 X Y^{3} Z^{4} + 114 X^{3} Y^{3} Z + 12 X^{2} Y^{4} Z + 528 X^{2} Y^{3} Z^{2} + 30 X Y^{5} Z + 30 X Y^{4} Z^{2} + 36 X Y^{3} Z^{3} + 18 X Y^{2} Z^{4} + 36 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 78 X^{2} Y^{3} Z + 699 X^{2} Y^{2} Z^{2} + 174 X Y^{4} Z + 354 X Y^{3} Z^{2} + 24 X Y^{2} Z^{3} + 18 X Y Z^{4} + 108 X^{3} Y Z + 180 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 408 X Y^{3} Z + 228 X Y^{2} Z^{2} + 24 X Y Z^{3} + 102 X^{2} Y Z + 366 X Y^{2} Z + 420 X Y Z^{2} + 342 X Y Z

Algorithm definition

The algorithm ⟨20×22×30:7350⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×11×15:1050⟩.

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