Description of fast matrix multiplication algorithm: ⟨4×24×28:1709⟩

Algorithm type

X^{2} Y^{24} Z^{2} + X Y^{24} Z + 3 X Y^{19} Z + 4 X Y^{18} Z + 8 X Y^{15} Z + 30 X^{4} Y^{8} Z^{4} + 23 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{11} Z^{2} + 6 X Y^{13} Z + 24 X^{2} Y^{10} Z^{2} + 26 X Y^{12} Z + X Y^{11} Z + 78 X^{4} Y^{4} Z^{4} + 94 X^{2} Y^{8} Z^{2} + 32 X Y^{10} Z + 5 X^{2} Y^{7} Z^{2} + 13 X Y^{9} Z + 12 X^{4} Y^{2} Z^{4} + 65 X^{2} Y^{6} Z^{2} + 75 X Y^{8} Z + 4 X^{2} Y^{5} Z^{2} + 2 X Y^{7} Z + 8 X^{4} Y^{2} Z^{2} + 182 X^{2} Y^{4} Z^{2} + 97 X Y^{6} Z + 13 X^{2} Y^{3} Z^{2} + 45 X Y^{5} Z + 242 X^{2} Y^{2} Z^{2} + 129 X Y^{4} Z + 20 X^{2} Y Z^{2} + 106 X Y^{3} Z + 32 X^{2} Y Z + 176 X Y^{2} Z + 150 X Y Z

Algorithm definition

The algorithm ⟨4×24×28:1709⟩ is serendipitous tensor product (⟨2×6×7:66⟩ - 8) ⊗ ⟨2×4×4:26⟩ +3⟨2×4×8:51⟩ +⟨4×4×4:48⟩.

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