Description of fast matrix multiplication algorithm: ⟨12×20×32:4320⟩

Algorithm type

16 X^{6} Y^{2} Z^{6} + 48 X^{4} Y^{6} Z^{4} + 432 X^{4} Y^{4} Z^{4} + 16 X^{2} Y^{4} Z^{6} + 16 X^{6} Y^{2} Z^{2} + 80 X^{2} Y^{6} Z^{2} + 112 X^{2} Y^{4} Z^{4} + 160 X^{2} Y^{2} Z^{6} + 16 X^{4} Y^{2} Z^{2} + 256 X^{2} Y^{4} Z^{2} + 224 X^{2} Y^{2} Z^{4} + 32 X^{3} Y Z^{3} + 96 X^{2} Y^{3} Z^{2} + 928 X^{2} Y^{2} Z^{2} + 32 X Y^{2} Z^{3} + 32 X^{3} Y Z + 160 X Y^{3} Z + 224 X Y^{2} Z^{2} + 320 X Y Z^{3} + 32 X^{2} Y Z + 512 X Y^{2} Z + 448 X Y Z^{2} + 128 X Y Z

Algorithm definition

The algorithm ⟨12×20×32:4320⟩ is the (Kronecker) tensor product of ⟨3×5×8:90⟩ with ⟨4×4×4:48⟩.

Algorithm description

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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