Description of fast matrix multiplication algorithm: ⟨20×20×25:5632⟩

Algorithm type

16 X^{16} Y Z + 4 X^{2} Y^{2} Z^{12} + 34 X^{4} Y^{6} Z^{4} + 12 X^{4} Y^{4} Z^{6} + 52 X Y Z^{12} + 4 X^{8} Y^{2} Z^{3} + 163 X^{4} Y^{5} Z^{4} + 140 X^{8} Y^{2} Z^{2} + 2 X^{4} Y^{6} Z^{2} + 415 X^{4} Y^{4} Z^{4} + 50 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + 92 X^{2} Y^{2} Z^{8} + 6 X^{6} Y^{3} Z^{2} + 16 X^{4} Y^{5} Z^{2} + 10 X^{2} Y^{7} Z^{2} + X^{2} Y^{3} Z^{6} + 2 X Y^{9} Z + 32 X Y^{8} Z^{2} + 32 X Y^{2} Z^{8} + 6 X^{6} Y^{2} Z^{2} + 314 X^{2} Y^{6} Z^{2} + 280 X^{2} Y^{4} Z^{4} + 165 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + 16 X Y Z^{8} + 16 X^{4} Y^{4} Z + 87 X^{4} Y^{3} Z^{2} + 16 X^{4} Y Z^{4} + 21 X^{2} Y^{6} Z + 105 X^{2} Y^{5} Z^{2} + 4 X^{2} Y^{4} Z^{3} + 17 X^{2} Y^{3} Z^{4} + 22 X Y^{7} Z + 80 X Y^{4} Z^{4} + 104 X Y^{2} Z^{6} + 109 X^{4} Y^{2} Z^{2} + 52 X^{4} Y Z^{3} + 458 X^{2} Y^{4} Z^{2} + 201 X^{2} Y^{2} Z^{4} + 141 X Y^{6} Z + 52 X Y Z^{6} + 32 X^{4} Y^{2} Z + 32 X^{4} Y Z^{2} + 17 X^{3} Y^{3} Z + 15 X^{2} Y^{4} Z + 47 X^{2} Y^{3} Z^{2} + 4 X^{2} Y^{2} Z^{3} + 80 X Y^{4} Z^{2} + 8 X Y^{3} Z^{3} + 80 X Y^{2} Z^{4} + 76 X^{4} Y Z + 217 X^{2} Y^{3} Z + 430 X^{2} Y^{2} Z^{2} + 165 X Y^{4} Z + 94 X Y^{3} Z^{2} + 52 X Y^{2} Z^{3} + 76 X Y Z^{4} + 7 X^{3} Y Z + 169 X Y^{3} Z + 184 X Y^{2} Z^{2} + 56 X Y Z^{3} + 47 X^{2} Y Z + 90 X Y^{2} Z + 138 X Y Z^{2} + 143 X Y Z

Algorithm definition

The algorithm ⟨20×20×25:5632⟩ is serendipitous tensor product (⟨4×5×5:76⟩ - 36) ⊗ ⟨5×4×5:76⟩ +18⟨5×8×5:144⟩.

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