Description of fast matrix multiplication algorithm: ⟨15×20×25:4408⟩

Algorithm type

8 X Y^{16} Z + 4 X^{12} Y^{2} Z + X^{2} Y^{4} Z^{9} + 20 X^{12} Y Z + 17 X^{4} Y^{4} Z^{6} + 4 X Y^{12} Z + X^{6} Y^{4} Z^{3} + 2 X^{2} Y^{8} Z^{3} + 5 X^{2} Y^{2} Z^{9} + 68 X^{8} Y^{2} Z^{2} + 23 X^{6} Y^{4} Z^{2} + 391 X^{4} Y^{4} Z^{4} + 4 X^{3} Y^{8} Z + 114 X^{2} Y^{8} Z^{2} + 25 X^{2} Y^{4} Z^{6} + 4 X Y^{8} Z^{3} + 13 X Y^{2} Z^{9} + 8 X^{8} Y^{2} Z + 5 X^{6} Y^{2} Z^{3} + 2 X^{4} Y^{4} Z^{3} + 8 X^{2} Y^{8} Z + X^{2} Y^{6} Z^{3} + 24 X Y^{8} Z^{2} + 8 X Y^{4} Z^{6} + 65 X Y Z^{9} + 4 X^{8} Y Z + 115 X^{6} Y^{2} Z^{2} + 46 X^{4} Y^{4} Z^{2} + 23 X^{2} Y^{6} Z^{2} + 182 X^{2} Y^{4} Z^{4} + 337 X^{2} Y^{2} Z^{6} + 60 X Y^{8} Z + 8 X^{4} Y^{4} Z + 5 X^{4} Y^{2} Z^{3} + 8 X^{3} Y^{4} Z^{2} + 13 X^{2} Y^{4} Z^{3} + 8 X Y^{6} Z^{2} + 16 X Y^{4} Z^{4} + 70 X Y^{2} Z^{6} + 4 X^{4} Y^{3} Z + 31 X^{4} Y^{2} Z^{2} + 20 X^{4} Y Z^{3} + 24 X^{3} Y^{4} Z + 13 X^{3} Y^{2} Z^{3} + 383 X^{2} Y^{4} Z^{2} + 91 X^{2} Y^{2} Z^{4} + 4 X Y^{6} Z + 50 X Y^{4} Z^{3} + 33 X Y Z^{6} + 52 X^{4} Y^{2} Z + 4 X^{4} Y Z^{2} + 44 X^{3} Y^{2} Z^{2} + 65 X^{3} Y Z^{3} + 12 X^{2} Y^{4} Z + 33 X^{2} Y^{2} Z^{3} + 124 X Y^{4} Z^{2} + 13 X Y^{3} Z^{3} + 16 X Y^{2} Z^{4} + 28 X^{4} Y Z + 35 X^{3} Y^{2} Z + 20 X^{3} Y Z^{2} + 432 X^{2} Y^{2} Z^{2} + 13 X^{2} Y Z^{3} + 110 X Y^{4} Z + 4 X Y^{3} Z^{2} + 204 X Y^{2} Z^{3} + 4 X Y Z^{4} + 75 X^{3} Y Z + 34 X^{2} Y^{2} Z + 4 X^{2} Y Z^{2} + 15 X Y^{3} Z + 142 X Y^{2} Z^{2} + 166 X Y Z^{3} + 15 X^{2} Y Z + 223 X Y^{2} Z + 43 X Y Z^{2} + 105 X Y Z

Algorithm definition

The algorithm ⟨15×20×25:4408⟩ is the (Kronecker) tensor product of ⟨3×5×5:58⟩ with ⟨5×4×5:76⟩.

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