Description of fast matrix multiplication algorithm: ⟨9×10×27:1523⟩

Algorithm type

16 X^{5} Y^{7} Z^{2} + 9 X^{4} Y^{6} Z^{4} + 3 X^{4} Y^{4} Z^{6} + 12 X^{5} Y^{7} Z + 4 X^{5} Y^{6} Z + 4 X^{4} Y^{7} Z + 87 X^{4} Y^{4} Z^{4} + 4 X^{4} Y^{6} Z + 18 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 30 X^{2} Y^{2} Z^{6} + 18 X^{2} Y^{3} Z^{4} + X^{4} Y^{2} Z^{2} + 5 X^{3} Y^{3} Z^{2} + 53 X^{2} Y^{4} Z^{2} + 216 X^{2} Y^{2} Z^{4} + 48 X Y Z^{6} + X^{3} Y^{2} Z^{2} + 23 X^{2} Y^{3} Z^{2} + 7 X^{2} Y^{2} Z^{3} + 2 X Y^{5} Z + 36 X Y^{2} Z^{4} + X^{4} Y Z + X^{3} Y^{2} Z + 5 X^{2} Y^{3} Z + 207 X^{2} Y^{2} Z^{2} + 2 X Y^{4} Z + 36 X Y^{3} Z^{2} + X Y^{2} Z^{3} + 84 X Y Z^{4} + 4 X^{3} Y Z + 14 X^{2} Y^{2} Z + 39 X Y^{3} Z + 138 X Y^{2} Z^{2} + 48 X Y Z^{3} + 4 X^{2} Y Z + 107 X Y^{2} Z + 150 X Y Z^{2} + 67 X Y Z

Algorithm definition

The algorithm ⟨9×10×27:1523⟩ is serendipitous tensor product (⟨3×5×9:102⟩ - 7) ⊗ ⟨3×2×3:15⟩ +⟨3×6×3:40⟩ +2⟨3×4×3:29⟩.

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