Description of fast matrix multiplication algorithm: ⟨14×16×20:2723⟩

Algorithm type

X^{14} Y^{16} Z^{14} + X^{6} Y^{12} Z^{8} + 11 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{6} + 6 X^{7} Y^{8} Z^{7} + 3 X^{6} Y^{8} Z^{8} + X^{8} Y^{8} Z^{4} + X^{8} Y^{4} Z^{8} + X^{6} Y^{8} Z^{6} + 2 X^{4} Y^{12} Z^{4} + X^{6} Y^{4} Z^{8} + X^{4} Y^{4} Z^{10} + 2 X^{8} Y^{4} Z^{4} + 8 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{4} Z^{8} + X^{6} Y^{4} Z^{4} + 3 X^{4} Y^{6} Z^{4} + 6 X^{3} Y^{6} Z^{4} + 170 X^{4} Y^{4} Z^{4} + 12 X^{4} Y^{4} Z^{3} + 18 X^{3} Y^{4} Z^{4} + 9 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{4} Z^{3} + 24 X^{2} Y^{6} Z^{2} + 10 X^{2} Y^{4} Z^{4} + 15 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{2} Z^{4} + 6 X^{2} Y^{2} Z^{5} + 30 X^{4} Y^{2} Z^{2} + 96 X^{2} Y^{4} Z^{2} + 36 X^{2} Y^{2} Z^{4} + 6 X^{3} Y^{2} Z^{2} + 18 X^{2} Y^{3} Z^{2} + 720 X^{2} Y^{2} Z^{2} + 54 X^{3} Y Z + 36 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 72 X Y^{3} Z + 60 X Y^{2} Z^{2} + 90 X Y Z^{3} + 108 X^{2} Y Z + 288 X Y^{2} Z + 144 X Y Z^{2} + 576 X Y Z

Algorithm definition

The algorithm ⟨14×16×20:2723⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×8×10:389⟩.

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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