Description of fast matrix multiplication algorithm: ⟨10×12×32:2340⟩

Algorithm type

6 X^{6} Y^{6} Z^{2} + 18 X^{4} Y^{4} Z^{6} + 2 X^{3} Y^{9} Z + 162 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{6} Z^{4} + 2 X Y^{9} Z^{2} + 6 X^{2} Y^{6} Z^{3} + 20 X Y^{9} Z + 6 X^{6} Y^{2} Z^{2} + 8 X^{3} Y^{6} Z + 114 X^{2} Y^{6} Z^{2} + 42 X^{2} Y^{4} Z^{4} + 30 X^{2} Y^{2} Z^{6} + 24 X^{2} Y^{4} Z^{3} + 22 X Y^{6} Z^{2} + 6 X^{4} Y^{2} Z^{2} + 300 X^{2} Y^{4} Z^{2} + 96 X^{2} Y^{2} Z^{4} + 108 X Y^{6} Z + 12 X^{3} Y^{3} Z + 30 X^{2} Y^{2} Z^{3} + 56 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 8 X^{3} Y^{2} Z + 2 X^{2} Y^{3} Z + 294 X^{2} Y^{2} Z^{2} + 112 X Y^{4} Z + 42 X Y^{3} Z^{2} + 40 X Y^{2} Z^{3} + 10 X^{3} Y Z + 8 X^{2} Y^{2} Z + 108 X Y^{3} Z + 198 X Y^{2} Z^{2} + 50 X Y Z^{3} + 10 X^{2} Y Z + 172 X Y^{2} Z + 160 X Y Z^{2} + 40 X Y Z

Algorithm definition

The algorithm ⟨10×12×32:2340⟩ is the (Kronecker) tensor product of ⟨2×4×4:26⟩ with ⟨5×3×8:90⟩.

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