Description of fast matrix multiplication algorithm: ⟨4×21×25:1363⟩

Algorithm type

2 X^{2} Y^{16} Z + 4 X^{2} Y^{15} Z^{2} + X^{4} Y^{12} Z^{2} + 10 X^{4} Y^{10} Z^{4} + X^{3} Y^{12} Z^{2} + 10 X Y^{15} Z + 10 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{12} Z + 5 X^{4} Y^{6} Z^{4} + 2 X^{2} Y^{11} Z + 40 X^{2} Y^{10} Z^{2} + 14 X Y^{12} Z + 2 X^{2} Y^{9} Z^{2} + 3 X Y^{11} Z + 2 X^{4} Y^{6} Z^{2} + 50 X^{4} Y^{4} Z^{4} + 47 X^{2} Y^{8} Z^{2} + 30 X Y^{10} Z + X^{4} Y^{5} Z^{2} + 4 X^{3} Y^{6} Z^{2} + 8 X Y^{9} Z + 5 X^{4} Y^{2} Z^{4} + X^{3} Y^{5} Z^{2} + 3 X^{2} Y^{7} Z + 46 X^{2} Y^{6} Z^{2} + 42 X Y^{8} Z + 3 X^{4} Y^{3} Z^{2} + X^{3} Y^{4} Z^{2} + 3 X^{2} Y^{6} Z + 26 X^{2} Y^{5} Z^{2} + 3 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{3} Z^{2} + 14 X^{2} Y^{5} Z + 109 X^{2} Y^{4} Z^{2} + 32 X Y^{6} Z + 2 X^{2} Y^{4} Z + 25 X^{2} Y^{3} Z^{2} + 80 X Y^{5} Z + 191 X^{2} Y^{2} Z^{2} + 122 X Y^{4} Z + 10 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 78 X Y^{3} Z + 12 X^{2} Y Z + 137 X Y^{2} Z + 150 X Y Z

Algorithm definition

The algorithm ⟨4×21×25:1363⟩ is serendipitous tensor product (⟨2×7×5:55⟩ - 8) ⊗ ⟨2×3×5:25⟩ +4⟨2×6×5:47⟩.

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