Description of fast matrix multiplication algorithm: ⟨10×18×30:3190⟩

Algorithm type

4 X^{4} Y^{12} Z^{2} + 4 X^{4} Y^{8} Z^{6} + 6 X^{2} Y^{12} Z^{4} + 4 X^{6} Y^{8} Z^{2} + 36 X^{4} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z^{2} + X^{4} Y^{9} Z^{2} + X^{3} Y^{10} Z^{2} + 5 X^{2} Y^{12} Z + 6 X Y^{12} Z^{2} + 22 X^{4} Y^{4} Z^{6} + 10 X^{3} Y^{9} Z^{2} + 4 X^{2} Y^{4} Z^{8} + 9 X Y^{12} Z + 2 X^{4} Y^{7} Z^{2} + 7 X^{3} Y^{8} Z^{2} + X^{2} Y^{10} Z + 3 X^{2} Y^{9} Z^{2} + 4 X^{2} Y^{8} Z^{3} + 34 X^{6} Y^{4} Z^{2} + 29 X^{4} Y^{6} Z^{2} + 206 X^{4} Y^{4} Z^{4} + 4 X^{3} Y^{8} Z + X^{3} Y^{7} Z^{2} + 19 X^{2} Y^{9} Z + 48 X^{2} Y^{8} Z^{2} + 33 X^{2} Y^{6} Z^{4} + 10 X^{2} Y^{4} Z^{6} + 22 X^{2} Y^{2} Z^{8} + 24 X Y^{9} Z^{2} + 3 X^{2} Y^{8} Z + 3 X^{2} Y^{7} Z^{2} + 16 X^{2} Y^{6} Z^{3} + 34 X Y^{9} Z + 66 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{5} Z + 16 X^{4} Y^{4} Z^{2} + 44 X^{4} Y^{2} Z^{4} + 16 X^{3} Y^{6} Z + 2 X^{2} Y^{7} Z + 192 X^{2} Y^{6} Z^{2} + 16 X^{2} Y^{4} Z^{4} + 55 X^{2} Y^{2} Z^{6} + 3 X Y^{8} Z + 7 X^{3} Y^{5} Z + X^{3} Y^{4} Z^{2} + 10 X^{2} Y^{6} Z + X^{2} Y^{5} Z^{2} + 9 X^{2} Y^{4} Z^{3} + X Y^{7} Z + 12 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 2 X^{4} Y^{3} Z + 88 X^{4} Y^{2} Z^{2} + 25 X^{3} Y^{4} Z + 6 X^{2} Y^{5} Z + 95 X^{2} Y^{4} Z^{2} + 88 X^{2} Y^{2} Z^{4} + 17 X Y^{6} Z + 4 X Y^{5} Z^{2} + 10 X Y^{4} Z^{3} + 16 X Y^{3} Z^{4} + 49 X^{3} Y^{3} Z + 22 X^{2} Y^{4} Z + 32 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 4 X Y^{5} Z + 18 X Y^{4} Z^{2} + 41 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + 60 X^{3} Y^{2} Z + 100 X^{2} Y^{3} Z + 384 X^{2} Y^{2} Z^{2} + 12 X Y^{4} Z + 120 X Y^{3} Z^{2} + 20 X Y^{2} Z^{3} + 36 X Y Z^{4} + 108 X^{3} Y Z + 32 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 106 X Y^{3} Z + 32 X Y^{2} Z^{2} + 90 X Y Z^{3} + 144 X^{2} Y Z + 16 X Y^{2} Z + 144 X Y Z^{2} + 72 X Y Z

Algorithm definition

The algorithm ⟨10×18×30:3190⟩ is serendipitous tensor product (⟨2×6×5:47⟩ - 2) ⊗ ⟨5×3×6:68⟩ +⟨5×6×6:130⟩.

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