Description of fast matrix multiplication algorithm: ⟨8×20×30:2860⟩

Algorithm type

12 X^{6} Y^{8} Z^{4} + 2 X^{4} Y^{8} Z^{6} + 2 X^{2} Y^{8} Z^{8} + 4 X^{6} Y^{8} Z^{2} + 18 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{8} Z^{6} + 66 X^{6} Y^{4} Z^{4} + 15 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{9} Z^{3} + 8 X^{2} Y^{8} Z^{4} + 11 X^{2} Y^{4} Z^{8} + 4 X Y^{12} Z + 12 X^{3} Y^{8} Z^{2} + 8 X^{2} Y^{9} Z^{2} + 10 X^{2} Y^{8} Z^{3} + 2 X Y^{8} Z^{4} + 38 X^{6} Y^{4} Z^{2} + 107 X^{4} Y^{4} Z^{4} + 22 X^{4} Y^{2} Z^{6} + 4 X^{3} Y^{8} Z + 47 X^{2} Y^{8} Z^{2} + 11 X^{2} Y^{4} Z^{6} + X Y^{10} Z + 5 X Y^{9} Z^{2} + 2 X Y^{8} Z^{3} + 48 X^{3} Y^{6} Z^{2} + 8 X^{2} Y^{6} Z^{3} + 24 X Y^{9} Z + 11 X Y^{8} Z^{2} + 8 X Y^{6} Z^{4} + 88 X^{6} Y^{2} Z^{2} + 20 X^{4} Y^{4} Z^{2} + 44 X^{4} Y^{2} Z^{4} + 16 X^{3} Y^{6} Z + 96 X^{2} Y^{6} Z^{2} + 44 X^{2} Y^{4} Z^{4} + 16 X Y^{8} Z + 8 X Y^{6} Z^{3} + 24 X^{3} Y^{4} Z^{2} + 8 X^{2} Y^{4} Z^{3} + 32 X Y^{6} Z^{2} + 5 X Y^{5} Z^{3} + 5 X Y^{4} Z^{4} + 110 X^{4} Y^{2} Z^{2} + 24 X^{3} Y^{4} Z + 84 X^{2} Y^{4} Z^{2} + 16 X^{2} Y^{3} Z^{3} + 25 X Y^{6} Z + 3 X Y^{5} Z^{2} + 12 X Y^{4} Z^{3} + 64 X^{3} Y^{3} Z + 108 X^{3} Y^{2} Z^{2} + 20 X^{2} Y^{4} Z + 32 X^{2} Y^{3} Z^{2} + 26 X^{2} Y^{2} Z^{3} + 3 X Y^{5} Z + 32 X Y^{4} Z^{2} + 18 X Y^{2} Z^{4} + 68 X^{3} Y^{2} Z + 80 X^{2} Y^{3} Z + 277 X^{2} Y^{2} Z^{2} + 36 X^{2} Y Z^{3} + 30 X Y^{4} Z + 18 X Y^{2} Z^{3} + 144 X^{3} Y Z + 40 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 108 X Y^{3} Z + 72 X Y^{2} Z^{2} + 180 X^{2} Y Z + 72 X Y^{2} Z + 162 X Y Z

Algorithm definition

The algorithm ⟨8×20×30:2860⟩ is serendipitous tensor product (⟨2×5×6:47⟩ - 2) ⊗ ⟨4×4×5:61⟩ +⟨4×4×10:115⟩.

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