Description of fast matrix multiplication algorithm: ⟨8×18×28:2457⟩

Algorithm type

6 X^{4} Y^{8} Z^{6} + 15 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{6} Z^{6} + 6 X^{4} Y^{8} Z^{2} + 60 X^{4} Y^{6} Z^{4} + 24 X^{4} Y^{4} Z^{6} + 2 X^{2} Y^{4} Z^{8} + 24 X^{2} Y^{8} Z^{3} + 8 X^{2} Y^{3} Z^{8} + 24 X^{4} Y^{6} Z^{2} + 60 X^{4} Y^{4} Z^{4} + 60 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{4} Z^{6} + 8 X^{2} Y^{2} Z^{8} + 24 X^{2} Y^{8} Z + 48 X^{2} Y^{6} Z^{3} + 48 X^{2} Y^{3} Z^{6} + 24 X^{4} Y^{4} Z^{2} + 120 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 48 X^{2} Y^{6} Z + 36 X^{2} Y^{4} Z^{3} + 48 X^{2} Y^{3} Z^{4} + 8 X Y^{4} Z^{4} + 100 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 48 X Y^{4} Z^{3} + 16 X Y^{3} Z^{4} + 36 X^{2} Y^{4} Z + 40 X^{2} Y^{3} Z^{2} + 72 X^{2} Y^{2} Z^{3} + 48 X Y^{4} Z^{2} + 96 X Y^{3} Z^{3} + 12 X Y^{2} Z^{4} + 220 X^{2} Y^{2} Z^{2} + 40 X Y^{4} Z + 96 X Y^{3} Z^{2} + 72 X Y^{2} Z^{3} + 24 X Y Z^{4} + 72 X^{2} Y^{2} Z + 80 X Y^{3} Z + 72 X Y^{2} Z^{2} + 144 X Y Z^{3} + 60 X Y^{2} Z + 144 X Y Z^{2} + 120 X Y Z

Algorithm definition

The algorithm ⟨8×18×28:2457⟩ is the (Kronecker) tensor product of ⟨2×6×4:39⟩ with ⟨4×3×7:63⟩.

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