Description of fast matrix multiplication algorithm: ⟨16×22×26:5250⟩

Algorithm type

4 X^{12} Y^{8} Z^{8} + 2 X^{10} Y^{8} Z^{8} + 6 X^{10} Y^{6} Z^{8} + 22 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{6} Z^{10} + 2 X^{8} Y^{4} Z^{12} + 2 X^{8} Y^{8} Z^{6} + 2 X^{8} Y^{6} Z^{8} + 2 X^{6} Y^{4} Z^{12} + 2 X^{4} Y^{6} Z^{12} + 2 X^{4} Y^{4} Z^{14} + 4 X^{12} Y^{4} Z^{4} + 2 X^{10} Y^{8} Z^{2} + 2 X^{8} Y^{6} Z^{6} + 4 X^{8} Y^{4} Z^{8} + 2 X^{4} Y^{12} Z^{4} + 6 X^{4} Y^{8} Z^{8} + 2 X^{10} Y^{6} Z^{2} + 8 X^{10} Y^{4} Z^{4} + 2 X^{8} Y^{2} Z^{8} + 4 X^{6} Y^{6} Z^{6} + 2 X^{4} Y^{10} Z^{4} + 2 X^{4} Y^{6} Z^{8} + 4 X^{10} Y^{2} Z^{4} + 10 X^{8} Y^{4} Z^{4} + 2 X^{8} Y^{2} Z^{6} + 2 X^{6} Y^{4} Z^{6} + 72 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 2 X^{8} Y^{2} Z^{4} + 40 X^{6} Y^{4} Z^{4} + 18 X^{4} Y^{6} Z^{4} + 2 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{10} Z^{2} + 2 X^{2} Y^{8} Z^{4} + 2 X^{2} Y^{4} Z^{8} + 12 X^{5} Y^{4} Z^{4} + 2 X^{8} Y^{2} Z^{2} + 10 X^{6} Y^{4} Z^{2} + 36 X^{5} Y^{3} Z^{4} + 2 X^{4} Y^{6} Z^{2} + 250 X^{4} Y^{4} Z^{4} + 12 X^{4} Y^{3} Z^{5} + 16 X^{4} Y^{2} Z^{6} + 4 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{6} Z^{4} + 6 X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{4} Z^{3} + 12 X^{4} Y^{3} Z^{4} + 12 X^{3} Y^{2} Z^{6} + 12 X^{2} Y^{3} Z^{6} + 12 X^{2} Y^{2} Z^{7} + 48 X^{6} Y^{2} Z^{2} + 12 X^{5} Y^{4} Z + 4 X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{3} Z^{3} + 40 X^{4} Y^{2} Z^{4} + 30 X^{2} Y^{6} Z^{2} + 62 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 12 X^{5} Y^{3} Z + 48 X^{5} Y^{2} Z^{2} + 12 X^{4} Y Z^{4} + 24 X^{3} Y^{3} Z^{3} + 12 X^{2} Y^{5} Z^{2} + 12 X^{2} Y^{3} Z^{4} + 24 X^{5} Y Z^{2} + 84 X^{4} Y^{2} Z^{2} + 12 X^{4} Y Z^{3} + 12 X^{3} Y^{2} Z^{3} + 576 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{2} Z^{4} + 24 X Y^{6} Z + 12 X^{4} Y Z^{2} + 96 X^{3} Y^{2} Z^{2} + 108 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 24 X Y^{5} Z + 12 X Y^{4} Z^{2} + 12 X Y^{2} Z^{4} + 12 X^{4} Y Z + 60 X^{3} Y^{2} Z + 12 X^{2} Y^{3} Z + 798 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 24 X Y^{4} Z + 12 X Y^{3} Z^{2} + 36 X Y^{2} Z^{3} + 144 X^{3} Y Z + 24 X^{2} Y^{2} Z + 96 X^{2} Y Z^{2} + 108 X Y^{3} Z + 156 X Y^{2} Z^{2} + 24 X Y Z^{3} + 144 X^{2} Y Z + 864 X Y^{2} Z + 144 X Y Z^{2} + 540 X Y Z

Algorithm definition

The algorithm ⟨16×22×26:5250⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×13:750⟩.

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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