Description of fast matrix multiplication algorithm: ⟨8×12×15:915⟩

Algorithm type

18 X^{6} Y^{4} Z^{4} + 3 X^{4} Y^{4} Z^{6} + 3 X^{2} Y^{4} Z^{8} + 6 X^{6} Y^{4} Z^{2} + 27 X^{4} Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{6} + 3 X^{2} Y^{4} Z^{6} + 24 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 6 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 36 X^{3} Y^{4} Z^{2} + 6 X^{2} Y^{4} Z^{3} + 6 X Y^{4} Z^{4} + 30 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{4} Z + 60 X^{2} Y^{4} Z^{2} + 12 X Y^{6} Z + 6 X Y^{4} Z^{3} + 36 X^{3} Y^{2} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 24 X Y^{4} Z^{2} + 6 X Y^{2} Z^{4} + 60 X^{3} Y^{2} Z + 105 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 12 X Y^{4} Z + 6 X Y^{2} Z^{3} + 48 X^{3} Y Z + 60 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 12 X Y^{3} Z + 24 X Y^{2} Z^{2} + 60 X^{2} Y Z + 66 X Y^{2} Z + 54 X Y Z

Algorithm definition

The algorithm ⟨8×12×15:915⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨4×4×5:61⟩.

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