Description of fast matrix multiplication algorithm: ⟨4×18×28:1316⟩

Algorithm type

12 X Y^{18} Z + 16 X Y^{15} Z + 20 X^{4} Y^{8} Z^{4} + 32 X^{2} Y^{12} Z^{2} + 16 X^{2} Y^{10} Z^{2} + 36 X Y^{12} Z + 52 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{7} Z^{2} + 28 X Y^{9} Z + 8 X^{4} Y^{2} Z^{4} + 96 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{5} Z^{2} + 24 X Y^{7} Z + 60 X^{2} Y^{4} Z^{2} + 76 X Y^{6} Z + 4 X^{2} Y^{4} Z + 48 X^{2} Y^{3} Z^{2} + 40 X Y^{5} Z + 180 X^{2} Y^{2} Z^{2} + 84 X Y^{4} Z + 8 X^{2} Y Z^{2} + 148 X Y^{3} Z + 4 X Y^{2} Z^{2} + 96 X Y^{2} Z + 4 X Y Z^{2} + 172 X Y Z

Algorithm definition

The algorithm ⟨4×18×28:1316⟩ is serendipitous tensor product (⟨2×3×4:20⟩ - 8) ⊗ ⟨2×6×7:66⟩ +4⟨2×6×14:131⟩.

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