Description of fast matrix multiplication algorithm: ⟨10×20×30:3648⟩

Algorithm type

4 X Y^{20} Z + 4 X^{2} Y^{16} Z^{2} + X^{4} Y^{8} Z^{6} + 24 X Y^{16} Z + 23 X^{4} Y^{8} Z^{4} + 5 X^{4} Y^{6} Z^{6} + 20 X^{2} Y^{12} Z^{2} + X^{2} Y^{10} Z^{3} + 4 X^{8} Y^{4} Z^{2} + 115 X^{4} Y^{6} Z^{4} + 6 X^{4} Y^{4} Z^{6} + 23 X^{2} Y^{10} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 32 X Y^{12} Z + 20 X^{8} Y^{3} Z^{2} + 6 X^{2} Y^{8} Z^{3} + 8 X Y^{10} Z^{2} + 24 X^{8} Y^{2} Z^{2} + 138 X^{4} Y^{4} Z^{4} + 166 X^{2} Y^{8} Z^{2} + 40 X^{2} Y^{6} Z^{4} + 13 X^{2} Y^{4} Z^{6} + 4 X Y^{10} Z + 8 X^{2} Y^{6} Z^{3} + 65 X^{2} Y^{3} Z^{6} + 48 X Y^{8} Z^{2} + 4 X^{4} Y^{5} Z + 204 X^{2} Y^{6} Z^{2} + 52 X^{2} Y^{4} Z^{4} + 78 X^{2} Y^{2} Z^{6} + 56 X Y^{8} Z + 24 X^{4} Y^{4} Z + 8 X^{2} Y^{4} Z^{3} + 20 X^{2} Y^{3} Z^{4} + 64 X Y^{6} Z^{2} + 13 X Y^{5} Z^{3} + 32 X^{4} Y^{3} Z + 223 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{2} Z^{4} + 32 X Y^{6} Z + 4 X Y^{5} Z^{2} + 78 X Y^{4} Z^{3} + 32 X^{4} Y^{2} Z + 75 X^{2} Y^{3} Z^{2} + 13 X^{2} Y^{2} Z^{3} + 15 X Y^{5} Z + 88 X Y^{4} Z^{2} + 104 X Y^{3} Z^{3} + 52 X^{4} Y Z + 389 X^{2} Y^{2} Z^{2} + 174 X Y^{4} Z + 32 X Y^{3} Z^{2} + 104 X Y^{2} Z^{3} + 120 X Y^{3} Z + 136 X Y^{2} Z^{2} + 169 X Y Z^{3} + 172 X Y^{2} Z + 52 X Y Z^{2} + 195 X Y Z

Algorithm definition

The algorithm ⟨10×20×30:3648⟩ is the (Kronecker) tensor product of ⟨2×5×6:48⟩ with ⟨5×4×5:76⟩.

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