Description of fast matrix multiplication algorithm: ⟨8×22×32:3360⟩

Algorithm type

X^{8} Y^{10} Z^{8} + 18 X^{8} Y^{8} Z^{8} + X^{6} Y^{10} Z^{8} + X^{8} Y^{6} Z^{8} + 3 X^{4} Y^{14} Z^{4} + 4 X^{2} Y^{18} Z^{2} + X^{6} Y^{6} Z^{8} + 24 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{10} Z^{4} + 12 X^{2} Y^{14} Z^{2} + 19 X^{4} Y^{8} Z^{4} + 6 X^{2} Y^{12} Z^{2} + X^{2} Y^{10} Z^{4} + 5 X^{4} Y^{6} Z^{4} + 9 X^{2} Y^{10} Z^{2} + 6 X^{4} Y^{5} Z^{4} + 211 X^{4} Y^{4} Z^{4} + 6 X^{3} Y^{5} Z^{4} + 24 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 6 X^{4} Y^{3} Z^{4} + 18 X^{2} Y^{7} Z^{2} + 24 X Y^{9} Z + 2 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{3} Z^{4} + 221 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{5} Z^{2} + 72 X Y^{7} Z + 132 X^{2} Y^{4} Z^{2} + 36 X Y^{6} Z + 6 X Y^{5} Z^{2} + 30 X^{2} Y^{3} Z^{2} + 54 X Y^{5} Z + 760 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 6 X Y^{3} Z^{2} + 12 X^{2} Y Z^{2} + 462 X Y^{3} Z + 108 X Y^{2} Z + 852 X Y Z

Algorithm definition

The algorithm ⟨8×22×32:3360⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×11×16:480⟩.

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