Description of fast matrix multiplication algorithm: ⟨16×28×30:7588⟩

Algorithm type

2 X^{8} Y^{16} Z^{8} + X^{8} Y^{12} Z^{8} + 6 X^{16} Y^{4} Z^{4} + 55 X^{8} Y^{8} Z^{8} + 2 X^{6} Y^{10} Z^{8} + 10 X^{4} Y^{4} Z^{16} + 6 X^{14} Y^{4} Z^{4} + 2 X^{8} Y^{6} Z^{8} + 2 X^{6} Y^{8} Z^{8} + 2 X^{4} Y^{2} Z^{16} + 12 X^{6} Y^{6} Z^{8} + 33 X^{4} Y^{12} Z^{4} + 16 X^{4} Y^{8} Z^{8} + 6 X^{4} Y^{10} Z^{4} + 4 X^{4} Y^{6} Z^{8} + 128 X^{4} Y^{8} Z^{4} + 10 X^{4} Y^{4} Z^{8} + 46 X^{2} Y^{12} Z^{2} + 6 X^{2} Y^{10} Z^{4} + 4 X^{2} Y^{6} Z^{8} + 16 X^{8} Y^{4} Z^{2} + 2 X^{4} Y^{8} Z^{2} + 28 X^{4} Y^{6} Z^{4} + 10 X^{2} Y^{10} Z^{2} + 24 X^{2} Y^{8} Z^{4} + 14 X^{2} Y^{4} Z^{8} + 52 X^{8} Y^{2} Z^{2} + 495 X^{4} Y^{4} Z^{4} + 12 X^{3} Y^{5} Z^{4} + 30 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{4} Z^{6} + 80 X^{2} Y^{2} Z^{8} + 36 X^{7} Y^{2} Z^{2} + 12 X^{4} Y^{3} Z^{4} + 12 X^{3} Y^{4} Z^{4} + 12 X^{2} Y Z^{8} + 8 X^{4} Y^{4} Z^{2} + 8 X^{4} Y^{2} Z^{4} + 72 X^{3} Y^{3} Z^{4} + 256 X^{2} Y^{6} Z^{2} + 146 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{2} Z^{6} + 36 X^{2} Y^{5} Z^{2} + 24 X^{2} Y^{3} Z^{4} + 6 X^{4} Y^{2} Z^{2} + 838 X^{2} Y^{4} Z^{2} + 82 X^{2} Y^{2} Z^{4} + 276 X Y^{6} Z + 36 X Y^{5} Z^{2} + 24 X Y^{3} Z^{4} + 96 X^{4} Y^{2} Z + 12 X^{2} Y^{4} Z + 132 X^{2} Y^{3} Z^{2} + 60 X Y^{5} Z + 144 X Y^{4} Z^{2} + 84 X Y^{2} Z^{4} + 96 X^{4} Y Z + 1108 X^{2} Y^{2} Z^{2} + 180 X Y^{4} Z + 48 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 120 X Y Z^{4} + 48 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 348 X Y^{3} Z + 300 X Y^{2} Z^{2} + 12 X Y Z^{3} + 36 X^{2} Y Z + 852 X Y^{2} Z + 132 X Y Z^{2} + 708 X Y Z

Algorithm definition

The algorithm ⟨16×28×30:7588⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×14×15:1084⟩.

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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