Description of fast matrix multiplication algorithm: ⟨4×4×4:49⟩

Algorithm type

X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨4×4×4:49⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨2×2×2:7⟩.

Algorithm description

maple tensor representation (compressed by bzip2);
maple evaluation scheme (compressed by bzip2).

Algorithm symmetries

The following group of 432 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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