Description of fast matrix multiplication algorithm: ⟨6×24×25:2168⟩

Algorithm type

X^{4} Y^{13} Z^{4} + X^{6} Y^{12} Z^{2} + 16 X^{4} Y^{12} Z^{4} + 16 X^{2} Y^{16} Z^{2} + X^{4} Y^{10} Z^{4} + X^{2} Y^{14} Z^{2} + 16 X Y^{16} Z + X^{6} Y^{9} Z^{2} + 3 X^{4} Y^{9} Z^{4} + 7 X^{2} Y^{13} Z^{2} + 16 X^{6} Y^{8} Z^{2} + 128 X^{4} Y^{8} Z^{4} + 6 X^{3} Y^{12} Z + 49 X^{2} Y^{12} Z^{2} + 6 X Y^{14} Z + X^{3} Y^{11} Z + X^{2} Y^{11} Z^{2} + X^{2} Y^{9} Z^{4} + 7 X Y^{13} Z + 2 X^{6} Y^{6} Z^{2} + 16 X^{6} Y^{4} Z^{4} + X^{4} Y^{6} Z^{4} + 16 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{10} Z^{2} + 25 X^{2} Y^{8} Z^{4} + 38 X Y^{12} Z + 3 X^{6} Y^{5} Z^{2} + 5 X^{4} Y^{5} Z^{4} + 11 X^{2} Y^{9} Z^{2} + X^{2} Y^{7} Z^{4} + 5 X Y^{11} Z + 34 X^{6} Y^{4} Z^{2} + X^{4} Y^{6} Z^{2} + 6 X^{4} Y^{4} Z^{4} + 18 X^{3} Y^{8} Z + 171 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 48 X^{2} Y^{4} Z^{6} + 9 X Y^{10} Z + 7 X Y^{9} Z^{2} + 3 X^{3} Y^{7} Z + 6 X^{2} Y^{7} Z^{2} + 6 X^{2} Y^{5} Z^{4} + 6 X Y^{9} Z + 30 X Y^{8} Z^{2} + 3 X^{4} Y^{4} Z^{2} + 11 X^{2} Y^{6} Z^{2} + 46 X^{2} Y^{4} Z^{4} + 48 X Y^{8} Z + 2 X Y^{7} Z^{2} + 2 X^{4} Y^{3} Z^{2} + 6 X^{3} Y^{5} Z + 16 X^{3} Y^{4} Z^{2} + 16 X^{2} Y^{5} Z^{2} + 16 X^{2} Y^{4} Z^{3} + 10 X^{2} Y^{3} Z^{4} + 18 X Y^{7} Z + 6 X Y^{6} Z^{2} + X^{4} Y^{2} Z^{2} + 35 X^{3} Y^{4} Z + 20 X^{2} Y^{4} Z^{2} + 8 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + 5 X Y^{5} Z^{2} + 48 X Y^{4} Z^{3} + 9 X^{3} Y^{3} Z + 42 X^{2} Y^{3} Z^{2} + 24 X Y^{5} Z + 55 X Y^{4} Z^{2} + 38 X^{3} Y^{2} Z + 32 X^{3} Y Z^{2} + 274 X^{2} Y^{2} Z^{2} + 32 X^{2} Y Z^{3} + 44 X Y^{4} Z + 14 X Y^{3} Z^{2} + 68 X^{3} Y Z + 88 X Y^{3} Z + 69 X Y^{2} Z^{2} + 96 X Y Z^{3} + 96 X Y^{2} Z + 96 X Y Z^{2} + 19 X Y Z

Algorithm definition

The algorithm ⟨6×24×25:2168⟩ is serendipitous tensor product (⟨3×6×5:68⟩ - 16) ⊗ ⟨2×4×5:32⟩ +8⟨2×8×5:63⟩.

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