Description of fast matrix multiplication algorithm: ⟨16×28×30:7200⟩

Algorithm type

270 X^{6} Y^{4} Z^{4} + 90 X^{8} Y^{2} Z^{2} + 675 X^{4} Y^{4} Z^{4} + 540 X^{6} Y^{2} Z^{2} + 313 X^{2} Y^{4} Z^{4} + 120 X^{3} Y^{4} Z^{2} + 120 X^{3} Y^{2} Z^{4} + 73 X^{2} Y^{4} Z^{3} + 107 X^{2} Y^{3} Z^{4} + 540 X^{4} Y^{2} Z^{2} + 374 X^{2} Y^{4} Z^{2} + 183 X^{2} Y^{3} Z^{3} + 337 X^{2} Y^{2} Z^{4} + 10 X Y^{5} Z^{2} + 4 X Y Z^{6} + 40 X^{4} Y^{2} Z + 40 X^{4} Y Z^{2} + 4 X^{2} Y^{4} Z + 41 X^{2} Y^{3} Z^{2} + 75 X^{2} Y^{2} Z^{3} + 22 X^{2} Y Z^{4} + 186 X Y^{4} Z^{2} + 178 X Y^{2} Z^{4} + 2 X Y Z^{5} + 240 X^{3} Y^{2} Z + 240 X^{3} Y Z^{2} + 12 X^{2} Y^{3} Z + 567 X^{2} Y^{2} Z^{2} + 31 X Y^{4} Z + 153 X Y^{3} Z^{2} + 81 X Y^{2} Z^{3} + 5 X Y Z^{4} + 305 X^{2} Y^{2} Z + 304 X^{2} Y Z^{2} + 44 X Y^{3} Z + 200 X Y^{2} Z^{2} + 7 X Y Z^{3} + 13 X^{2} Y Z + 330 X Y^{2} Z + 292 X Y Z^{2} + 32 X Y Z

Algorithm definition

The algorithm ⟨16×28×30:7200⟩ is serendipitous tensor product (⟨4×4×10:115⟩ - 30) ⊗ ⟨4×7×3:63⟩ +15⟨4×7×6:123⟩.

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