Description of fast matrix multiplication algorithm: ⟨8×12×20:1222⟩

Algorithm type

78 X^{4} Y^{4} Z^{4} + 8 X Y^{9} Z + 18 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 50 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 4 X Y^{6} Z^{2} + 18 X^{4} Y^{2} Z^{2} + 140 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 44 X Y^{6} Z + 6 X^{3} Y^{3} Z + 2 X^{2} Y^{3} Z^{2} + 16 X Y^{4} Z^{2} + 4 X Y^{3} Z^{3} + 24 X^{3} Y^{2} Z + 6 X^{2} Y^{3} Z + 168 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 16 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 30 X^{3} Y Z + 24 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 50 X Y^{3} Z + 84 X Y^{2} Z^{2} + 20 X Y Z^{3} + 30 X^{2} Y Z + 100 X Y^{2} Z + 80 X Y Z^{2} + 50 X Y Z

Algorithm definition

The algorithm ⟨8×12×20:1222⟩ is the (Kronecker) tensor product of ⟨2×4×4:26⟩ with ⟨4×3×5:47⟩.

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