Description of fast matrix multiplication algorithm: ⟨6×10×10:406⟩

Algorithm type

X^{6} Y^{4} Z^{2} + 17 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + X^{2} Y^{4} Z^{6} + 5 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 5 X^{2} Y^{2} Z^{6} + X^{4} Y^{2} Z^{2} + 13 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + 6 X^{3} Y^{2} Z + 109 X^{2} Y^{2} Z^{2} + 12 X Y^{4} Z + 6 X Y^{2} Z^{3} + 30 X^{3} Y Z + 12 X^{2} Y^{2} Z + 6 X Y^{3} Z + 12 X Y^{2} Z^{2} + 30 X Y Z^{3} + 6 X^{2} Y Z + 78 X Y^{2} Z + 6 X Y Z^{2} + 42 X Y Z

Algorithm definition

The algorithm ⟨6×10×10:406⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨3×5×5:58⟩.

Algorithm description

Algorithm symmetries

The following group of 6 isotropies acts as a permutation group on algorithm tensor representation:

maple tensor representation (compressed by bzip2);

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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