Description of fast matrix multiplication algorithm: ⟨12×16×16:1824⟩

Algorithm type

160 X^{4} Y^{4} Z^{4} + 48 X^{6} Y^{2} Z^{2} + 32 X^{4} Y^{4} Z^{2} + 32 X^{2} Y^{6} Z^{2} + 32 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 16 X^{4} Y^{2} Z^{2} + 176 X^{2} Y^{4} Z^{2} + 16 X^{2} Y^{2} Z^{4} + 368 X^{2} Y^{2} Z^{2} + 96 X^{3} Y Z + 64 X^{2} Y^{2} Z + 64 X Y^{3} Z + 64 X Y^{2} Z^{2} + 96 X Y Z^{3} + 32 X^{2} Y Z + 352 X Y^{2} Z + 32 X Y Z^{2} + 96 X Y Z

Algorithm definition

The algorithm ⟨12×16×16:1824⟩ is the (Kronecker) tensor product of ⟨3×4×4:38⟩ 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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