Description of fast matrix multiplication algorithm: ⟨20×27×28:8196⟩

Algorithm type

8 X^{6} Y^{8} Z^{9} + 96 X^{6} Y^{8} Z^{6} + 2 X^{4} Y^{12} Z^{4} + 8 X^{3} Y^{4} Z^{12} + 2 X Y^{17} Z + 4 X^{4} Y^{10} Z^{4} + 16 X^{3} Y^{12} Z^{3} + 6 X^{2} Y^{14} Z^{2} + 4 X Y^{16} Z + 24 X^{3} Y^{8} Z^{6} + 2 X^{2} Y^{13} Z^{2} + 2 X Y^{15} Z + 8 X^{9} Y^{4} Z^{3} + 8 X^{4} Y^{8} Z^{4} + 16 X^{3} Y^{4} Z^{9} + 11 X^{2} Y^{12} Z^{2} + 4 X Y^{14} Z + 2 X^{4} Y^{7} Z^{4} + 6 X^{2} Y^{11} Z^{2} + 3 X Y^{13} Z + 2 X^{4} Y^{6} Z^{4} + 64 X^{4} Y^{4} Z^{6} + 48 X^{3} Y^{8} Z^{3} + 6 X^{2} Y^{10} Z^{2} + 19 X Y^{12} Z + 8 X^{6} Y^{4} Z^{3} + X^{4} Y^{5} Z^{4} + 56 X^{3} Y^{4} Z^{6} + 2 X^{2} Y^{9} Z^{2} + 8 X^{2} Y^{8} Z^{3} + 9 X Y^{11} Z + 769 X^{4} Y^{4} Z^{4} + 107 X^{2} Y^{8} Z^{2} + 64 X^{2} Y^{2} Z^{8} + 3 X Y^{10} Z + 4 X^{2} Y^{7} Z^{2} + 16 X Y^{9} Z + 24 X Y^{8} Z^{2} + 64 X^{6} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z^{3} + 170 X^{2} Y^{6} Z^{2} + 192 X^{2} Y^{4} Z^{4} + 128 X^{2} Y^{2} Z^{6} + 48 X Y^{8} Z + X^{2} Y^{5} Z^{2} + 35 X Y^{7} Z + 8 X Y^{4} Z^{4} + 64 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 428 X^{2} Y^{4} Z^{2} + 448 X^{2} Y^{2} Z^{4} + 24 X Y^{6} Z + 16 X Y^{4} Z^{3} + 8 X^{2} Y^{4} Z + 3 X^{2} Y^{3} Z^{2} + 128 X^{2} Y^{2} Z^{3} + 20 X Y^{5} Z + 56 X Y^{4} Z^{2} + 1622 X^{2} Y^{2} Z^{2} + 32 X Y^{4} Z + 128 X Y Z^{4} + 128 X^{3} Y Z + 352 X Y^{3} Z + 384 X Y^{2} Z^{2} + 256 X Y Z^{3} + 128 X^{2} Y Z + 786 X Y^{2} Z + 896 X Y Z^{2} + 185 X Y Z

Algorithm definition

The algorithm ⟨20×27×28:8196⟩ is serendipitous tensor product (⟨5×3×7:79⟩ - 5) ⊗ ⟨4×9×4:104⟩ +⟨4×9×20:500⟩.

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