Description of fast matrix multiplication algorithm: ⟨10×24×25:3508⟩

Algorithm type

320 X^{4} Y^{8} Z^{4} + 24 X^{2} Y^{12} Z^{2} + 8 X^{4} Y^{8} Z^{2} + 24 X Y^{12} Z + X^{7} Y^{2} Z^{3} + 16 X^{6} Y^{4} Z^{2} + X^{6} Y^{2} Z^{4} + 432 X^{2} Y^{8} Z^{2} + 2 X^{7} Y^{2} Z^{2} + 2 X^{6} Y^{2} Z^{3} + X^{5} Y^{2} Z^{4} + 4 X^{3} Y^{2} Z^{6} + 8 X^{2} Y^{8} Z + X^{2} Y^{2} Z^{7} + X Y^{2} Z^{8} + X^{7} Y^{2} Z + 2 X^{7} Y Z^{2} + 3 X^{6} Y^{2} Z^{2} + X^{5} Y^{2} Z^{3} + X^{5} Y Z^{4} + 104 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 80 X^{2} Y^{4} Z^{4} + 5 X^{2} Y^{2} Z^{6} + 2 X^{2} Y Z^{7} + 112 X Y^{8} Z + X Y^{2} Z^{7} + 2 X^{7} Y Z + 6 X^{6} Y Z^{2} + X^{5} Y Z^{3} + 2 X^{4} Y Z^{4} + 7 X^{3} Y^{2} Z^{4} + 4 X^{2} Y Z^{6} + 4 X Y^{2} Z^{6} + 2 X^{6} Y Z + 4 X^{5} Y Z^{2} + 4 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 16 X^{3} Y^{4} Z + 4 X^{3} Y^{2} Z^{3} + 152 X^{2} Y^{4} Z^{2} + 13 X^{2} Y^{2} Z^{4} + 3 X^{4} Y Z^{2} + X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 8 X^{3} Y Z^{3} + 104 X^{2} Y^{4} Z + X^{2} Y^{3} Z^{2} + X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 80 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 7 X Y^{2} Z^{4} + 2 X^{3} Y^{2} Z + 8 X^{3} Y Z^{2} + 653 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 152 X Y^{4} Z + 2 X Y^{3} Z^{2} + 3 X Y^{2} Z^{3} + 44 X^{3} Y Z + 16 X^{2} Y^{2} Z + 19 X^{2} Y Z^{2} + 50 X Y^{3} Z + 6 X Y^{2} Z^{2} + 9 X Y Z^{3} + 218 X^{2} Y Z + 226 X Y^{2} Z + 169 X Y Z^{2} + 313 X Y Z

Algorithm definition

The algorithm ⟨10×24×25:3508⟩ is serendipitous tensor product (⟨5×6×5:110⟩ - 8) ⊗ ⟨2×4×5:32⟩ +4⟨4×4×5:61⟩.

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