Description of fast matrix multiplication algorithm: ⟨16×20×30:5345⟩

Algorithm type

585 X^{4} Y^{4} Z^{4} + 90 X^{6} Y^{2} Z^{2} + 90 X^{4} Y^{4} Z^{2} + 45 X^{4} Y^{2} Z^{4} + 180 X^{2} Y^{6} Z^{2} + 56 X^{2} Y^{4} Z^{4} + 135 X^{2} Y^{2} Z^{6} + 52 X^{2} Y^{4} Z^{3} + 58 X^{2} Y^{3} Z^{4} + 360 X^{4} Y^{2} Z^{2} + 563 X^{2} Y^{4} Z^{2} + 77 X^{2} Y^{3} Z^{3} + 460 X^{2} Y^{2} Z^{4} + 80 X Y^{6} Z + 60 X Y Z^{6} + 44 X^{2} Y^{4} Z + 23 X^{2} Y^{3} Z^{2} + 79 X^{2} Y^{2} Z^{3} + 20 X^{2} Y Z^{4} + 67 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 40 X Y^{2} Z^{4} + 46 X^{3} Y^{2} Z + 44 X^{3} Y Z^{2} + 14 X^{2} Y^{3} Z + 362 X^{2} Y^{2} Z^{2} + 145 X Y^{4} Z + 165 X Y^{3} Z^{2} + 151 X Y^{2} Z^{3} + 87 X Y Z^{4} + 5 X^{3} Y Z + 215 X^{2} Y^{2} Z + 170 X^{2} Y Z^{2} + 32 X Y^{3} Z + 340 X Y^{2} Z^{2} + 39 X Y Z^{3} + 12 X^{2} Y Z + 165 X Y^{2} Z + 163 X Y Z^{2} + 16 X Y Z

Algorithm definition

The algorithm ⟨16×20×30:5345⟩ is serendipitous tensor product (⟨4×4×10:115⟩ - 30) ⊗ ⟨4×5×3:47⟩ +15⟨4×5×6:90⟩.

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