Description of fast matrix multiplication algorithm: ⟨6×8×16:511⟩

Algorithm type

2 X^{4} Y^{8} Z^{4} + 2 X^{2} Y^{8} Z^{6} + 4 X^{4} Y^{6} Z^{4} + 7 X^{4} Y^{4} Z^{6} + 10 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{6} Z^{4} + 5 X^{2} Y^{4} Z^{6} + X^{4} Y^{4} Z^{2} + 14 X^{2} Y^{2} Z^{6} + 14 X^{2} Y^{4} Z^{2} + 7 X^{2} Y^{2} Z^{4} + 12 X Y^{4} Z^{3} + 24 X^{2} Y^{3} Z^{2} + 42 X^{2} Y^{2} Z^{3} + 72 X^{2} Y^{2} Z^{2} + 18 X Y^{4} Z + 24 X Y^{3} Z^{2} + 30 X Y^{2} Z^{3} + 6 X^{2} Y^{2} Z + 84 X Y Z^{3} + 12 X Y^{2} Z + 42 X Y Z^{2} + 72 X Y Z

Algorithm definition

The algorithm ⟨6×8×16:511⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨3×4×8:73⟩.

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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