Description of fast matrix multiplication algorithm: ⟨14×26×32:6776⟩

Algorithm type

X^{14} Y^{16} Z^{14} + X^{14} Y^{12} Z^{14} + 2 X^{12} Y^{14} Z^{14} + X^{12} Y^{12} Z^{14} + X^{10} Y^{10} Z^{14} + 2 X^{8} Y^{16} Z^{8} + X^{6} Y^{18} Z^{8} + X^{6} Y^{18} Z^{6} + X^{6} Y^{14} Z^{8} + X^{6} Y^{14} Z^{6} + X^{6} Y^{12} Z^{8} + 24 X^{8} Y^{8} Z^{8} + X^{4} Y^{12} Z^{8} + 8 X^{8} Y^{8} Z^{6} + 4 X^{8} Y^{6} Z^{8} + 6 X^{7} Y^{8} Z^{7} + X^{6} Y^{10} Z^{6} + 3 X^{6} Y^{8} Z^{8} + X^{4} Y^{10} Z^{8} + X^{8} Y^{4} Z^{8} + 6 X^{7} Y^{6} Z^{7} + 6 X^{6} Y^{8} Z^{6} + 12 X^{6} Y^{7} Z^{7} + 4 X^{6} Y^{6} Z^{8} + 15 X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{8} Z^{8} + 6 X^{6} Y^{6} Z^{7} + X^{8} Y^{4} Z^{6} + X^{6} Y^{6} Z^{6} + 2 X^{4} Y^{12} Z^{2} + 9 X^{4} Y^{10} Z^{4} + X^{2} Y^{12} Z^{4} + 6 X^{5} Y^{5} Z^{7} + 34 X^{4} Y^{8} Z^{4} + 6 X^{3} Y^{9} Z^{4} + X^{2} Y^{10} Z^{4} + 6 X^{3} Y^{9} Z^{3} + 2 X^{4} Y^{8} Z^{2} + 26 X^{4} Y^{6} Z^{4} + 6 X^{3} Y^{7} Z^{4} + 2 X^{2} Y^{8} Z^{4} + 6 X^{3} Y^{7} Z^{3} + 6 X^{3} Y^{6} Z^{4} + 395 X^{4} Y^{4} Z^{4} + 10 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{6} Z^{4} + 48 X^{4} Y^{4} Z^{3} + 24 X^{4} Y^{3} Z^{4} + 6 X^{3} Y^{5} Z^{3} + 18 X^{3} Y^{4} Z^{4} + 6 X^{2} Y^{5} Z^{4} + 7 X^{4} Y^{4} Z^{2} + 36 X^{4} Y^{2} Z^{4} + 36 X^{3} Y^{4} Z^{3} + 24 X^{3} Y^{3} Z^{4} + 204 X^{2} Y^{6} Z^{2} + 21 X^{2} Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{3} + 6 X^{3} Y^{3} Z^{3} + 12 X^{2} Y^{6} Z + 54 X^{2} Y^{5} Z^{2} + 6 X Y^{6} Z^{2} + 36 X^{4} Y^{2} Z^{2} + 241 X^{2} Y^{4} Z^{2} + 6 X Y^{5} Z^{2} + 12 X^{2} Y^{4} Z + 156 X^{2} Y^{3} Z^{2} + 12 X Y^{4} Z^{2} + 1756 X^{2} Y^{2} Z^{2} + 60 X Y^{4} Z + 12 X Y^{3} Z^{2} + 42 X^{2} Y^{2} Z + 180 X^{2} Y Z^{2} + 684 X Y^{3} Z + 54 X Y^{2} Z^{2} + 216 X^{2} Y Z + 654 X Y^{2} Z + 1500 X Y Z

Algorithm definition

The algorithm ⟨14×26×32:6776⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×13×16:968⟩.

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.

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