Description of fast matrix multiplication algorithm: ⟨18×26×28:7168⟩

Algorithm type

5 X^{12} Y^{12} Z^{8} + 11 X^{10} Y^{12} Z^{8} + 11 X^{12} Y^{8} Z^{8} + 8 X^{8} Y^{12} Z^{8} + 25 X^{10} Y^{8} Z^{8} + 6 X^{6} Y^{16} Z^{4} + 2 X^{12} Y^{4} Z^{8} + 22 X^{8} Y^{8} Z^{8} + 2 X^{4} Y^{16} Z^{4} + 16 X^{12} Y^{6} Z^{4} + 6 X^{10} Y^{4} Z^{8} + 34 X^{6} Y^{12} Z^{4} + 2 X^{6} Y^{8} Z^{8} + 43 X^{12} Y^{4} Z^{4} + 21 X^{10} Y^{6} Z^{4} + 12 X^{8} Y^{4} Z^{8} + 14 X^{4} Y^{12} Z^{4} + X^{12} Y^{4} Z^{2} + 6 X^{12} Y^{2} Z^{4} + 54 X^{10} Y^{4} Z^{4} + 22 X^{8} Y^{6} Z^{4} + 44 X^{6} Y^{8} Z^{4} + 4 X^{6} Y^{4} Z^{8} + 4 X^{12} Y^{2} Z^{2} + 8 X^{10} Y^{2} Z^{4} + 59 X^{8} Y^{4} Z^{4} + 4 X^{6} Y^{8} Z^{2} + 41 X^{6} Y^{6} Z^{4} + 4 X^{4} Y^{8} Z^{4} + 66 X^{5} Y^{6} Z^{4} + 24 X^{8} Y^{2} Z^{4} + 91 X^{6} Y^{6} Z^{2} + 130 X^{6} Y^{4} Z^{4} + 3 X^{6} Y^{2} Z^{6} + 11 X^{4} Y^{8} Z^{2} + 48 X^{4} Y^{6} Z^{4} + 150 X^{5} Y^{4} Z^{4} + 36 X^{3} Y^{8} Z^{2} + 107 X^{6} Y^{4} Z^{2} + 49 X^{6} Y^{2} Z^{4} + 36 X^{4} Y^{6} Z^{2} + 145 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 21 X^{2} Y^{8} Z^{2} + 96 X^{6} Y^{3} Z^{2} + 36 X^{5} Y^{2} Z^{4} + 204 X^{3} Y^{6} Z^{2} + 12 X^{3} Y^{4} Z^{4} + 329 X^{6} Y^{2} Z^{2} + 126 X^{5} Y^{3} Z^{2} + 37 X^{4} Y^{4} Z^{2} + 76 X^{4} Y^{2} Z^{4} + 94 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z + 36 X^{6} Y Z^{2} + 324 X^{5} Y^{2} Z^{2} + 132 X^{4} Y^{3} Z^{2} + 264 X^{3} Y^{4} Z^{2} + 24 X^{3} Y^{2} Z^{4} + 24 X^{6} Y Z + 48 X^{5} Y Z^{2} + 387 X^{4} Y^{2} Z^{2} + 24 X^{3} Y^{4} Z + 66 X^{3} Y^{3} Z^{2} + 25 X^{2} Y^{4} Z^{2} + 144 X^{4} Y Z^{2} + 546 X^{3} Y^{3} Z + 384 X^{3} Y^{2} Z^{2} + 18 X^{3} Y Z^{3} + 66 X^{2} Y^{4} Z + 642 X^{3} Y^{2} Z + 222 X^{3} Y Z^{2} + 216 X^{2} Y^{3} Z + 87 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 54 X Y^{4} Z + 426 X^{3} Y Z + 222 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 60 X Y^{3} Z + 12 X Y^{2} Z^{2} + 198 X^{2} Y Z + 6 X Y^{2} Z + 54 X Y Z

Algorithm definition

The algorithm ⟨18×26×28:7168⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×13×14:1024⟩.

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