Description of fast matrix multiplication algorithm: ⟨6×20×32:2329⟩

Algorithm type

X^{2} Y^{18} Z^{6} + 16 X^{4} Y^{16} Z^{4} + 4 X^{2} Y^{16} Z^{6} + 7 X Y^{18} Z^{3} + 32 X^{4} Y^{12} Z^{4} + 28 X^{2} Y^{16} Z^{2} + X^{2} Y^{13} Z^{5} + 3 X^{2} Y^{12} Z^{6} + 6 X Y^{16} Z^{3} + X^{2} Y^{12} Z^{5} + 56 X^{4} Y^{8} Z^{6} + 17 X^{2} Y^{12} Z^{4} + 21 X Y^{16} Z + X^{2} Y^{13} Z^{2} + 6 X Y^{13} Z^{3} + 80 X^{4} Y^{8} Z^{4} + 33 X^{2} Y^{12} Z^{2} + X^{2} Y^{9} Z^{5} + 24 X^{2} Y^{8} Z^{6} + X Y^{13} Z^{2} + 11 X Y^{12} Z^{3} + 19 X Y^{12} Z^{2} + 8 X^{4} Y^{8} Z^{2} + 4 X^{2} Y^{8} Z^{4} + X^{2} Y^{6} Z^{6} + 8 X Y^{12} Z + 56 X^{2} Y^{8} Z^{3} + 6 X^{2} Y^{6} Z^{5} + 5 X Y^{9} Z^{3} + 99 X^{2} Y^{8} Z^{2} + 5 X^{2} Y^{6} Z^{4} + X^{2} Y^{5} Z^{5} + 135 X^{2} Y^{4} Z^{6} + 3 X Y^{9} Z^{2} + 33 X Y^{8} Z^{3} + 8 X^{2} Y^{8} Z + X^{2} Y^{4} Z^{5} + 53 X^{2} Y^{4} Z^{4} + X^{2} Y^{3} Z^{5} + 16 X Y^{8} Z + 28 X Y^{6} Z^{3} + 6 X^{2} Y^{2} Z^{5} + 2 X Y^{6} Z^{2} + 6 X Y^{5} Z^{3} + 128 X^{2} Y^{4} Z^{2} + 5 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + X Y^{5} Z^{2} + 148 X Y^{4} Z^{3} + 64 X^{2} Y^{3} Z^{2} + 112 X^{2} Y^{2} Z^{3} + 43 X Y^{4} Z^{2} + 17 X Y^{3} Z^{3} + 160 X^{2} Y^{2} Z^{2} + 133 X Y^{4} Z + 40 X Y^{3} Z^{2} + 73 X Y^{2} Z^{3} + 16 X^{2} Y^{2} Z + 2 X Y^{2} Z^{2} + 236 X Y Z^{3} + 18 X Y^{2} Z + 84 X Y Z^{2} + 193 X Y Z

Algorithm definition

The algorithm ⟨6×20×32:2329⟩ is serendipitous tensor product (⟨3×4×8:73⟩ - 13) ⊗ ⟨2×5×4:32⟩ +⟨2×5×12:94⟩ +5⟨2×5×8:63⟩.

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