Description of fast matrix multiplication algorithm: ⟨9×16×25:2209⟩

Algorithm type

169 X^{4} Y^{4} Z^{4} + 9 X^{9} Y Z + 4 X Y^{9} Z + 16 X Y Z^{9} + 78 X^{6} Y^{2} Z^{2} + 26 X^{4} Y^{4} Z^{2} + 52 X^{2} Y^{6} Z^{2} + 52 X^{2} Y^{4} Z^{4} + 104 X^{2} Y^{2} Z^{6} + 6 X^{6} Y^{2} Z + X^{4} Y^{4} Z + 4 X^{2} Y^{6} Z + 8 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 16 X Y^{2} Z^{6} + 18 X^{6} Y Z + 78 X^{4} Y^{2} Z^{2} + 212 X^{2} Y^{4} Z^{2} + 156 X^{2} Y^{2} Z^{4} + 32 X Y^{6} Z + 48 X Y Z^{6} + 6 X^{4} Y^{2} Z + 12 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 24 X^{3} Y Z^{3} + 16 X^{2} Y^{4} Z + 8 X^{2} Y^{2} Z^{3} + 32 X Y^{4} Z^{2} + 16 X Y^{3} Z^{3} + 24 X Y^{2} Z^{4} + 9 X^{4} Y Z + 48 X^{3} Y^{2} Z + 36 X^{3} Y Z^{2} + 12 X^{2} Y^{3} Z + 154 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 64 X Y^{4} Z + 24 X Y^{3} Z^{2} + 64 X Y^{2} Z^{3} + 36 X Y Z^{4} + 30 X^{3} Y Z + 58 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 20 X Y^{3} Z + 116 X Y^{2} Z^{2} + 40 X Y Z^{3} + 30 X^{2} Y Z + 80 X Y^{2} Z + 60 X Y Z^{2} + 25 X Y Z

Algorithm definition

The algorithm ⟨9×16×25:2209⟩ is the (Kronecker) tensor product of ⟨3×4×5:47⟩ with ⟨3×4×5:47⟩.

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