Description of fast matrix multiplication algorithm: ⟨16×24×30:6510⟩

Algorithm type

3 X^{16} Y^{16} Z^{16} + 6 X^{8} Y^{16} Z^{8} + 3 X^{8} Y^{12} Z^{8} + 66 X^{8} Y^{8} Z^{8} + 3 X^{8} Y^{8} Z^{4} + 6 X^{8} Y^{4} Z^{8} + 12 X^{4} Y^{12} Z^{4} + 3 X^{4} Y^{4} Z^{12} + 9 X^{8} Y^{4} Z^{4} + 144 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{4} Z^{8} + 12 X^{2} Y^{12} Z^{2} + 6 X^{4} Y^{8} Z^{2} + 24 X^{4} Y^{6} Z^{4} + 465 X^{4} Y^{4} Z^{4} + 48 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{4} Z^{6} + 42 X^{4} Y^{4} Z^{2} + 48 X^{4} Y^{2} Z^{4} + 84 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 24 X^{2} Y^{2} Z^{6} + 72 X^{4} Y^{2} Z^{2} + 858 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 36 X^{2} Y^{4} Z + 36 X^{2} Y^{3} Z^{2} + 1224 X^{2} Y^{2} Z^{2} + 288 X Y^{4} Z + 36 X Y^{2} Z^{3} + 144 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 72 X Y^{3} Z + 72 X Y^{2} Z^{2} + 36 X Y Z^{3} + 108 X^{2} Y Z + 1260 X Y^{2} Z + 72 X Y Z^{2} + 972 X Y Z

Algorithm definition

The algorithm ⟨16×24×30:6510⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×12×15:930⟩.

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