Description of fast matrix multiplication algorithm: ⟨12×22×32:4788⟩

Algorithm type

4 X^{8} Y^{12} Z^{8} + 9 X^{8} Y^{10} Z^{8} + 4 X^{6} Y^{16} Z^{4} + 24 X^{8} Y^{8} Z^{8} + 10 X^{4} Y^{16} Z^{4} + X^{8} Y^{6} Z^{8} + X^{6} Y^{8} Z^{8} + 6 X^{4} Y^{14} Z^{4} + 8 X^{12} Y^{4} Z^{4} + X^{6} Y^{6} Z^{8} + 28 X^{4} Y^{12} Z^{4} + 13 X^{4} Y^{8} Z^{8} + 10 X^{4} Y^{4} Z^{12} + 15 X^{2} Y^{16} Z^{2} + 2 X^{10} Y^{4} Z^{4} + 20 X^{4} Y^{10} Z^{4} + 22 X^{4} Y^{6} Z^{8} + 2 X^{2} Y^{14} Z^{2} + 3 X^{2} Y^{12} Z^{4} + 2 X^{8} Y^{4} Z^{4} + 19 X^{4} Y^{8} Z^{4} + X^{4} Y^{4} Z^{8} + 25 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{10} Z^{4} + 11 X^{6} Y^{6} Z^{2} + 50 X^{4} Y^{6} Z^{4} + 13 X^{2} Y^{10} Z^{2} + 20 X^{2} Y^{8} Z^{4} + 8 X^{2} Y^{6} Z^{6} + 54 X^{4} Y^{5} Z^{4} + 24 X^{3} Y^{8} Z^{2} + 4 X^{4} Y^{6} Z^{2} + 229 X^{4} Y^{4} Z^{4} + 66 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{4} Z^{6} + 6 X^{4} Y^{3} Z^{4} + 6 X^{3} Y^{4} Z^{4} + 36 X^{2} Y^{7} Z^{2} + 79 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{3} Z^{4} + 214 X^{2} Y^{6} Z^{2} + 135 X^{2} Y^{4} Z^{4} + 94 X^{2} Y^{2} Z^{6} + 90 X Y^{8} Z + 12 X^{5} Y^{2} Z^{2} + 120 X^{2} Y^{5} Z^{2} + 132 X^{2} Y^{3} Z^{4} + 12 X Y^{7} Z + 18 X Y^{6} Z^{2} + 20 X^{4} Y^{2} Z^{2} + 160 X^{2} Y^{4} Z^{2} + 16 X^{2} Y^{2} Z^{4} + 150 X Y^{6} Z + 48 X Y^{5} Z^{2} + 66 X^{3} Y^{3} Z + 156 X^{2} Y^{3} Z^{2} + 78 X Y^{5} Z + 120 X Y^{4} Z^{2} + 48 X Y^{3} Z^{3} + 24 X^{2} Y^{3} Z + 523 X^{2} Y^{2} Z^{2} + 36 X Y^{4} Z + 144 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 186 X^{3} Y Z + 12 X^{2} Y Z^{2} + 276 X Y^{3} Z + 342 X Y^{2} Z^{2} + 204 X Y Z^{3} + 48 X^{2} Y Z + 276 X Y^{2} Z + 60 X Y Z^{2} + 78 X Y Z

Algorithm definition

The algorithm ⟨12×22×32:4788⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×11×16:684⟩.

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