Description of fast matrix multiplication algorithm: ⟨14×16×30:3899⟩

Algorithm type

16 X^{8} Y^{16} Z^{8} + 16 X^{8} Y^{16} Z^{6} + 4 X^{4} Y^{16} Z^{6} + 28 X^{4} Y^{16} Z^{4} + 16 X^{4} Y^{8} Z^{10} + 16 X^{4} Y^{8} Z^{8} + 16 X^{4} Y^{8} Z^{6} + 120 X^{4} Y^{8} Z^{4} + 13 X^{4} Y^{4} Z^{8} + 16 X^{2} Y^{8} Z^{6} + 96 X^{4} Y^{8} Z^{3} + 29 X^{4} Y^{4} Z^{6} + 28 X^{2} Y^{8} Z^{4} + X^{2} Y^{6} Z^{6} + 2 X^{2} Y^{4} Z^{8} + 4 X^{2} Y^{2} Z^{10} + 24 X^{2} Y^{8} Z^{3} + 4 X^{6} Y^{2} Z^{4} + 53 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 196 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{6} Z^{4} + 5 X^{2} Y^{4} Z^{6} + 10 X^{2} Y^{2} Z^{8} + 96 X^{2} Y^{4} Z^{5} + 3 X^{6} Y^{2} Z^{2} + 9 X^{4} Y^{4} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 108 X^{2} Y^{4} Z^{4} + 62 X^{2} Y^{2} Z^{6} + 96 X^{2} Y^{4} Z^{3} + 2 X^{4} Y^{2} Z^{2} + 155 X^{2} Y^{4} Z^{2} + 150 X^{2} Y^{2} Z^{4} + 96 X Y^{4} Z^{3} + 174 X^{2} Y^{2} Z^{3} + 168 X Y^{4} Z^{2} + 6 X Y^{3} Z^{3} + 12 X Y^{2} Z^{4} + 24 X Y Z^{5} + 24 X^{3} Y Z^{2} + 365 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 168 X Y^{4} Z + 12 X Y^{3} Z^{2} + 30 X Y^{2} Z^{3} + 60 X Y Z^{4} + 18 X^{3} Y Z + 54 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 18 X Y^{3} Z + 72 X Y^{2} Z^{2} + 372 X Y Z^{3} + 12 X^{2} Y Z + 66 X Y^{2} Z + 432 X Y Z^{2} + 282 X Y Z

Algorithm definition

The algorithm ⟨14×16×30:3899⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×8×15:557⟩.

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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