Description of fast matrix multiplication algorithm: ⟨9×16×21:1821⟩

Algorithm type

42 X^{4} Y^{6} Z^{4} + 4 X Y^{12} Z + 12 X^{2} Y^{9} Z^{2} + 12 X^{4} Y^{6} Z^{2} + 105 X^{4} Y^{4} Z^{4} + 14 X^{2} Y^{8} Z^{2} + 12 X^{6} Y^{3} Z^{2} + 4 X^{2} Y^{8} Z + 6 X^{2} Y^{3} Z^{6} + 24 X Y^{9} Z + 30 X^{6} Y^{2} Z^{2} + 30 X^{4} Y^{4} Z^{2} + 48 X^{4} Y^{2} Z^{4} + 138 X^{2} Y^{6} Z^{2} + 15 X^{2} Y^{2} Z^{6} + 8 X Y^{8} Z + 12 X^{6} Y Z^{2} + 24 X^{4} Y^{3} Z^{2} + 6 X^{4} Y^{2} Z^{3} + 6 X^{3} Y^{2} Z^{4} + 24 X^{2} Y^{6} Z + 6 X^{2} Y Z^{6} + 78 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 22 X^{3} Y^{2} Z^{3} + 144 X^{2} Y^{4} Z^{2} + 8 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 2 X Y^{4} Z^{3} + 4 X^{4} Y^{2} Z + 28 X^{4} Y Z^{2} + 24 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 32 X^{2} Y^{4} Z + 30 X^{2} Y^{3} Z^{2} + 10 X^{2} Y^{2} Z^{3} + 8 X^{2} Y Z^{4} + 12 X Y^{3} Z^{3} + 2 X^{4} Y Z + 24 X^{3} Y^{2} Z + 14 X^{3} Y Z^{2} + 48 X^{2} Y^{3} Z + 157 X^{2} Y^{2} Z^{2} + 18 X^{2} Y Z^{3} + 54 X Y^{4} Z + 16 X Y^{2} Z^{3} + 2 X Y Z^{4} + 22 X^{3} Y Z + 80 X^{2} Y^{2} Z + 38 X^{2} Y Z^{2} + 56 X Y^{3} Z + 10 X Y^{2} Z^{2} + 18 X Y Z^{3} + 52 X^{2} Y Z + 78 X Y^{2} Z + 24 X Y Z^{2} + 38 X Y Z

Algorithm definition

The algorithm ⟨9×16×21:1821⟩ is serendipitous tensor product (⟨3×4×3:29⟩ - 4) ⊗ ⟨3×4×7:63⟩ +2⟨6×4×7:123⟩.

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