Description of fast matrix multiplication algorithm: ⟨8×8×10:427⟩

Algorithm type

6 X^{6} Y^{4} Z^{4} + X^{4} Y^{4} Z^{6} + X^{2} Y^{4} Z^{8} + 2 X^{6} Y^{4} Z^{2} + 9 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + X^{2} Y^{4} Z^{6} + 8 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 2 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 10 X^{4} Y^{2} Z^{2} + 2 X^{2} Y^{4} Z^{2} + 36 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 6 X Y^{2} Z^{4} + 12 X^{3} Y^{2} Z + 63 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 6 X Y^{2} Z^{3} + 48 X^{3} Y Z + 24 X^{2} Y Z^{2} + 12 X Y^{3} Z + 24 X Y^{2} Z^{2} + 60 X^{2} Y Z + 12 X Y^{2} Z + 54 X Y Z

Algorithm definition

The algorithm ⟨8×8×10:427⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×4×5:61⟩.

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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