Description of fast matrix multiplication algorithm: ⟨6×6×8:203⟩

Algorithm type

7 X^{4} Y^{4} Z^{4} + X^{6} Y^{2} Z^{2} + 2 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{2} Z^{6} + 4 X^{2} Y^{4} Z^{2} + 4 X^{2} Y^{2} Z^{4} + 49 X^{2} Y^{2} Z^{2} + 6 X^{3} Y Z + 12 X Y^{3} Z + 12 X Y^{2} Z^{2} + 12 X Y Z^{3} + 24 X Y^{2} Z + 24 X Y Z^{2} + 42 X Y Z

Algorithm definition

The algorithm ⟨6×6×8:203⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨3×3×4:29⟩.

Algorithm description

Algorithm symmetries

The following group of 12 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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