Description of fast matrix multiplication algorithm: ⟨4×16×32:1318⟩

Algorithm type

X^{2} Y^{16} Z^{2} + X^{4} Y^{11} Z^{4} + X^{2} Y^{15} Z^{2} + X Y^{16} Z^{2} + X Y^{16} Z + 3 X Y^{15} Z + 6 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + X Y^{14} Z + X^{2} Y^{11} Z^{2} + 2 X^{4} Y^{6} Z^{4} + X^{2} Y^{10} Z^{2} + 10 X Y^{12} Z + X Y^{11} Z^{2} + 2 X Y^{11} Z + 70 X^{4} Y^{4} Z^{4} + 31 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{7} Z^{3} + 5 X Y^{10} Z + 16 X^{2} Y^{7} Z^{2} + 14 X Y^{9} Z + 62 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 27 X Y^{8} Z + X Y^{7} Z^{2} + 5 X Y^{7} Z + 102 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + 42 X Y^{6} Z + 4 X Y^{5} Z^{2} + 10 X^{2} Y^{3} Z^{2} + X Y^{5} Z + 8 X Y^{4} Z^{2} + 257 X^{2} Y^{2} Z^{2} + 67 X Y^{4} Z + 10 X Y^{3} Z^{2} + 129 X Y^{3} Z + 148 X Y^{2} Z + 5 X Y Z^{2} + 261 X Y Z

Algorithm definition

The algorithm ⟨4×16×32:1318⟩ is serendipitous tensor product (⟨2×4×8:51⟩ - 17) ⊗ ⟨2×4×4:26⟩ +⟨2×4×12:77⟩ +7⟨2×4×8:51⟩.

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