Description of fast matrix multiplication algorithm: ⟨4×5×8:122⟩

Algorithm type

2 X^{4} Y^{2} Z + 2 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 2 X^{3} Y^{2} Z + 4 X^{3} Y Z^{2} + 18 X^{2} Y^{2} Z^{2} + 4 X Y^{2} Z^{3} + 8 X^{2} Y^{2} Z + 8 X^{2} Y Z^{2} + 4 X Y^{3} Z + 16 X Y Z^{3} + 4 X Y^{2} Z + 20 X Y Z^{2} + 18 X Y Z

Algorithm definition

The algorithm ⟨4×5×8:122⟩ is the (Kronecker) tensor product of ⟨4×5×4:61⟩ with ⟨1×1×2:2⟩.

Algorithm description

Algorithm symmetries

The following group of 2 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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